Atoms<\/title>\n <meta name=\"viewport\" content=\"width=device-width, initial-scale=1\">\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.mathpix.com\/fonts\/cmu.css\"\/>\n <style>\n html,body {\n width: 100%;\n height: 100%;\n }\n *, *::before,*::after {\n box-sizing: border-box;\n }\n @-ms-viewport {\n width: device-width;\n }\n body {\n margin: 0;\n color: #1E2029;\n font-size: 14px;\n line-height: normal;\n }\n hr {\n box-sizing: content-box;\n height: 0;\n overflow: visible;\n }\n h1, h2, h3, h4, h5, h6 {\n margin-top: 0;\n margin-bottom: 0.5em;\n color: rgba(0, 0, 0, 0.85);\n font-weight: 500;\n }\n p {\n margin-top: 0;\n margin-bottom: 1em;\n }\n ol, ul, dl {\n margin-top: 0;\n margin-bottom: 1em;\n }\n ol ol, ul ul, ol ul, ul ol {\n margin-bottom: 0;\n }\n dt {\n font-weight: 500;\n }\n dd {\n margin-bottom: 0.5em;\n margin-left: 0;\n }\n blockquote {\n margin: 0 0 1em;\n }\n dfn {\n font-style: italic;\n }\n b, strong {\n font-weight: bolder;\n }\n small {\n font-size: 80%;\n 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id=\"atoms\" data_line_start=\"0\" data_line_end=\"2\" data_line=\"0,3\" count_line=\"3\">\nAtoms<\/h1>\n<div class=\"preview-paragraph-4 preview-line 4\" data_line_start=\"4\" data_line_end=\"4\" data_line=\"4,5\" count_line=\"1\">12.2 Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom<\/div>\n<div class=\"preview-paragraph-6 preview-line 6\" data_line_start=\"6\" data_line_end=\"6\" data_line=\"6,7\" count_line=\"1\">12.3 Atomic Spectra<\/div>\n<div class=\"preview-paragraph-8 preview-line 8\" data_line_start=\"8\" data_line_end=\"8\" data_line=\"8,9\" count_line=\"1\">12.4 Bohr Model of the Hydrogen Atom 12.5 The Line Spectra of the Hydrogen Atom<\/div>\n<div class=\"preview-paragraph-10 preview-line 10\" data_line_start=\"10\" data_line_end=\"10\" data_line=\"10,11\" count_line=\"1\">12.6 De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation<\/div>\n<div class=\"preview-paragraph-12 preview-line 12\" data_line_start=\"12\" data_line_end=\"12\" data_line=\"12,13\" count_line=\"1\">Topicwise Analysis of Last 10 Years’ CBSE Board Questions (2016-2007)<\/div>\n<div class=\"preview-paragraph-14 preview-line 14\" data_line_start=\"14\" data_line_end=\"14\" data_line=\"14,15\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-01.jpg?height=788&width=1448&top_left_y=1162&top_left_x=287\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-16 preview-line 16\" data_line_start=\"16\" data_line_end=\"16\" data_line=\"16,17\" count_line=\"1\">M Maximum weightage is of Bohr Model of Hydrogen <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad<\/asciimath><latex style=\"display: none\">\\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.262ex\" height=\"0\" role=\"img\" focusable=\"false\" viewBox=\"0 0 1000 0\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> No VBQ type questions were asked till now. Atom.<\/div>\n<ul class=\"preview-paragraph-18 preview-line 18 19\" data_line_start=\"18\" data_line_end=\"19\" data_line=\"18,20\" count_line=\"2\">\n<li>Maximum VSA, SAI, SAll and LA type questions were asked from Bohr Model of Hydrogen Atom.<\/li>\n<\/ul>\n<div class=\"preview-paragraph-20 preview-line 20\" data_line_start=\"20\" data_line_end=\"20\" data_line=\"20,21\" count_line=\"1\">QUICK RECAP<\/div>\n<div class=\"preview-paragraph-22 preview-line 22\" data_line_start=\"22\" data_line_end=\"22\" data_line=\"22,23\" count_line=\"1\">Thomson’s model of atom : It was proposed by J. J. Thomson in 1898. According to<\/div>\n<div class=\"preview-paragraph-24 preview-line 24\" data_line_start=\"24\" data_line_end=\"24\" data_line=\"24,25\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-01.jpg?height=189&width=343&top_left_y=2330&top_left_x=662\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-26 preview-line 26\" data_line_start=\"26\" data_line_end=\"26\" data_line=\"26,27\" count_line=\"1\">this model, the positive charge of the atom is uniformly distributed throughout the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon. (1) Rutherford’s <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-scattering experiment Rutherford and his two associates, Geiger and Marsden, studies the scattering of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles from a thin gold foil in order to investigate the structure of the atom.<\/div>\n<div class=\"preview-paragraph-28 preview-line 28\" data_line_start=\"28\" data_line_end=\"28\" data_line=\"28,29\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=465&width=737&top_left_y=687&top_left_x=288\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-30 preview-line 30\" data_line_start=\"30\" data_line_end=\"30\" data_line=\"30,31\" count_line=\"1\">Schematic arrangement of the Geiger-Marsden experiment<\/div>\n<div class=\"preview-paragraph-32 preview-line 32\" data_line_start=\"32\" data_line_end=\"32\" data_line=\"32,33\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=326&width=434&top_left_y=1202&top_left_x=454\" alt=\"\"><\/div>\n<ul class=\"preview-paragraph-34 preview-line 34 35 36 37 38 39 40 41\" data_line_start=\"34\" data_line_end=\"41\" data_line=\"34,42\" count_line=\"8\">\n<li>\n<div>Rutherford’s observations and results :<\/div>\n<\/li>\n<li>\n<div>Most of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles pass through the gold foil without any deflection. This shows that most of the space in an atom is empty.<\/div>\n<\/li>\n<li>\n<div>Few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles got scattered, deflecting at various angles from 0 to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">pi<\/asciimath><latex style=\"display: none\">\\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.29ex\" height=\"1ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -431 570 442\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. This shows that atom has a small positively charged core called ‘nucleus’ at centre of atom, which deflects the positively charged <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles at different angles depending on their distance from centre of nucleus.<\/div>\n<\/li>\n<li>\n<div>Very few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles (1 in 8000) suffers deflection of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>180<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>180<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">180^(@)<\/asciimath><latex style=\"display: none\">180^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.307ex\" height=\"1.649ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 1903.6 729\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1500, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>180<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. This shows that size of nucleus is very small, nearly <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/8000<\/asciimath><latex style=\"display: none\">1 \/ 8000<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.787ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3000 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1000, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>8000<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the size of atom.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-42 preview-line 42\" data_line_start=\"42\" data_line_end=\"42\" data_line=\"42,43\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=288&width=311&top_left_y=2169&top_left_x=564\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-44 preview-line 44\" data_line_start=\"44\" data_line_end=\"44\" data_line=\"44,45\" count_line=\"1\">This graph shows deflection of number of particles with angle of deflection <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. (A) Rutherford’s <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-scattering formulae Number of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particles scattered per unit area, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N(theta)<\/asciimath><latex style=\"display: none\">N(\\theta)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.83ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2135 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(888, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1277, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1746, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> at scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> varies inversely as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">sin^(4)(theta\/\/2)<\/asciimath><latex style=\"display: none\">\\sin ^{4}(\\theta \/ 2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.775ex\" height=\"2.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -874.8 3878.6 1124.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(394, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(672, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1228, 396.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2020.6, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2489.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2989.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3489.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>sin<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, i.e.,<\/div>\n<div class=\"preview-paragraph-46 preview-line 46 47 48\" data_line_start=\"46\" data_line_end=\"48\" data_line=\"46,49\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N(theta)prop(1)\/(sin^(4)(theta\/\/2))<\/asciimath><latex style=\"display: none\">N(\\theta) \\propto \\frac{1}{\\sin ^{4}(\\theta \/ 2)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.454ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.618ex\" height=\"5.49ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1342 7787.1 2426.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(888, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1277, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1746, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2412.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 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data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" 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442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2020.6, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2489.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2989.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3489.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><rect width=\"4078.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u221d<\/mo><mfrac><mn>1<\/mn><mrow><msup><mi>sin<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-50 preview-line 50 51 52 53\" data_line_start=\"50\" data_line_end=\"53\" data_line=\"50,54\" count_line=\"4\">\n<li>\n<div>Impact parameter : It is defined as the perpendicular distance of the initial velocity vector of the alpha particle from the centre of the nucleus, when the particle is far away from the nucleus of the atom.<\/div>\n<\/li>\n<li>\n<div>The scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particle and impact parameter <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b<\/asciimath><latex style=\"display: none\">b<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.971ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 429 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are related as<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-54 preview-line 54 55 56\" data_line_start=\"54\" data_line_end=\"56\" data_line=\"54,57\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b=(Ze^(2)cot(theta\/\/2))\/(4piepsi_(0)K)<\/asciimath><latex style=\"display: none\">b=\\frac{Z e^{2} \\cot (\\theta \/ 2)}{4 \\pi \\varepsilon_{0} K}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.063ex\" 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178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(444, 0)\"><\/path><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\" transform=\"translate(944, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3481.2, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3950.2, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(4450.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4950.2, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1475.3, -686)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><rect width=\"5539.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>b<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>cot<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>K<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-58 preview-line 58\" data_line_start=\"58\" data_line_end=\"58\" data_line=\"58,59\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K<\/asciimath><latex style=\"display: none\">K<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.011ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 889 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the kinetic energy of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z<\/asciimath><latex style=\"display: none\">Z<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.636ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 723 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the atomic number of the nucleus.<\/div>\n<ul class=\"preview-paragraph-60 preview-line 60 61\" data_line_start=\"60\" data_line_end=\"61\" data_line=\"60,62\" count_line=\"2\">\n<li>Smaller the impact parameter, larger the angle of scattering <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ul>\n<div class=\"preview-paragraph-62 preview-line 62\" data_line_start=\"62\" data_line_end=\"62\" data_line=\"62,63\" count_line=\"1\">Distance of closest approach : At the distance of closest approach whole kinetic energy of the alpha particles is converted into potential energy.<\/div>\n<ul class=\"preview-paragraph-64 preview-line 64 65\" data_line_start=\"64\" data_line_end=\"65\" data_line=\"64,66\" count_line=\"2\">\n<li>Distance of closest approach<\/li>\n<\/ul>\n<div class=\"preview-paragraph-66 preview-line 66 67 68\" data_line_start=\"66\" data_line_end=\"68\" data_line=\"66,69\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(0)=(2Ze^(2))\/(4piepsi_(0)K)<\/asciimath><latex style=\"display: none\">r_{0}=\\frac{2 Z e^{2}}{4 \\pi \\varepsilon_{0} K}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.345ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 5456.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2188.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(588, 676)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1223, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 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317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><rect width=\"3028.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>r<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>K<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-70 preview-line 70\" data_line_start=\"70\" data_line_end=\"70\" data_line=\"70,71\" count_line=\"1\">(A) Rutherford’s nuclear model of the atom :<\/div>\n<div class=\"preview-paragraph-72 preview-line 72\" data_line_start=\"72\" data_line_end=\"72\" data_line=\"72,73\" count_line=\"1\">According to this the entire positive charge and most of the mass of the atom is concentrated in a small volume known as the nucleus with electrons revolving around it just as planets revolve around the sun.<\/div>\n<div class=\"preview-paragraph-74 preview-line 74\" data_line_start=\"74\" data_line_end=\"74\" data_line=\"74,75\" count_line=\"1\">(A) Bohr’s model : Bohr combined classical and early quantum concepts and gave his theory of hydrogen and hydrogen-like atoms which have only one orbital electron. His postulates are<\/div>\n<ul class=\"preview-paragraph-76 preview-line 76 77 78 79\" data_line_start=\"76\" data_line_end=\"79\" data_line=\"76,80\" count_line=\"4\">\n<li>\n<div>An electron can revolve around the nucleus only in certain allowed circular orbits of definite energy and in these orbits it does not radiate. These orbits are known as stationary orbits.<\/div>\n<\/li>\n<li>\n<div>Angular momentum of the electron in a stationary orbit is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h\/\/2pi<\/asciimath><latex style=\"display: none\">h \/ 2 \\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.855ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2146 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">L=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.435ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3286.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>L<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: 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data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-80 preview-line 80\" data_line_start=\"80\" data_line_end=\"80\" data_line=\"80,81\" count_line=\"1\">This is known as Bohr’s quantisation condition. – The emission of radiation takes place when an electron makes a transition from a higher to a lower orbit. The frequency of the radiation is given by<\/div>\n<div class=\"preview-paragraph-82 preview-line 82\" data_line_start=\"82\" data_line_end=\"82\" data_line=\"82,83\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(E_(2)-E_(1))\/(h)<\/asciimath><latex style=\"display: none\">v=\\frac{E_{2}-E_{1}}{h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.007ex\" height=\"2.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -926.9 4423.1 1279.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 446.1) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1141.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1919.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1098.6, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"2364.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mrow><mi>h<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-84 preview-line 84\" data_line_start=\"84\" data_line_end=\"84\" data_line=\"84,85\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(2)<\/asciimath><latex style=\"display: none\">E_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.583ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1141.6 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)<\/asciimath><latex style=\"display: none\">E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.583ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1141.6 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies of the electron in the higher and lower orbits respectively.<\/div>\n<div class=\"preview-paragraph-86 preview-line 86\" data_line_start=\"86\" data_line_end=\"86\" data_line=\"86,87\" count_line=\"1\">(1) Bohr’s formulae<\/div>\n<div class=\"preview-paragraph-88 preview-line 88\" data_line_start=\"88\" data_line_end=\"88\" data_line=\"88,89\" count_line=\"1\">Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-90 preview-line 90\" data_line_start=\"90\" data_line_end=\"90\" data_line=\"90,91\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>0.53<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>Z<\/mi>\n <\/mfrac>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>0.53<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>Z<\/mi>\n <\/mfrac>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(4piepsi_(0)n^(2)h^(2))\/(4pi^(2)mZe^(2));r_(n)=(0.53n^(2))\/(Z)”\u212b”<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{4 \\pi \\varepsilon_{0} n^{2} h^{2}}{4 \\pi^{2} m Z e^{2}} ; r_{n}=\\frac{0.53 n^{2}}{Z} \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.335ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 11198.1 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>;<\/mo><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>0.53<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>Z<\/mi><\/mfrac><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-92 preview-line 92 93\" data_line_start=\"92\" data_line_end=\"93\" data_line=\"92,94\" count_line=\"2\">\n<li>Velocity of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 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style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>6<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mi mathvariant=\"normal\">Z<\/mi>\n <\/mrow>\n <\/mrow>\n <mi>n<\/mi>\n <\/mfrac>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>6<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mi mathvariant=\"normal\">Z<\/mi>\n <\/mrow>\n <\/mrow>\n <mi>n<\/mi>\n <\/mfrac>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v_(n)=(1)\/(4piepsi_(0))(2pi 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mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ul>\n<div class=\"preview-paragraph-94 preview-line 94\" data_line_start=\"94\" data_line_end=\"94\" data_line=\"94,95\" count_line=\"1\">The kinetic energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-96 preview-line 96 97 98 99 100 101\" data_line_start=\"96\" data_line_end=\"101\" data_line=\"96,102\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[K_(n)=(1)\/(4piepsi_(0))(Ze^(2))\/(2r_(n))=((1)\/(4piepsi_(0)))^(2)(2pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=(13.6Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nK_{n} &=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r_{n}}=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{2 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.6ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 17503.2 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 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data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mn>13.6<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-103 preview-line 103\" data_line_start=\"103\" data_line_end=\"103\" data_line=\"103,104\" count_line=\"1\">The potential energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-105 preview-line 105 106 107 108 109 110\" data_line_start=\"105\" data_line_end=\"110\" data_line=\"105,111\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>27.2<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>27.2<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[U_(n)=-(1)\/(4piepsi_(0))(Ze^(2))\/(r_(n))=-((1)\/(4piepsi_(0)))^(2)(4pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=(-27.2Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nU_{n} &=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r_{n}}=-\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{4 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=\\frac{-27.2 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"42.745ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 18893.2 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 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rowspacing=\"3pt\"><mtr><mtd><msub><mi>U<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>27.2<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-112 preview-line 112 113\" data_line_start=\"112\" data_line_end=\"113\" data_line=\"112,114\" count_line=\"2\">\n<li>Total energy of electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 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orbit<\/li>\n<\/ul>\n<div class=\"preview-paragraph-114 preview-line 114 115 116 117 118 119\" data_line_start=\"114\" data_line_end=\"119\" data_line=\"114,120\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E_(n)=U_(n)+K_(n)=-((1)\/(4piepsi_(0)))^(2)(2pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=-(13.6Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nE_{n} &=U_{n}+K_{n}=-\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{2 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=-\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.505ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 17461.1 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>K<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>,<\/mo><msub><mi>U<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>2<\/mn><msub><mi>K<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-123 preview-line 123 124\" data_line_start=\"123\" data_line_end=\"124\" data_line=\"123,125\" count_line=\"2\">\n<li>Frequency of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 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<mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v_(n)=((1)\/(4piepsi_(0)))^(2)(4pi^(2)Z^(2)e^(4)m)\/(n^(3)h^(3))=(6.62 xx10^(15)Z^(2))\/(n^(3))<\/asciimath><latex style=\"display: none\">v_{n}=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{4 \\pi^{2} Z^{2} e^{4} m}{n^{3} h^{3}}=\\frac{6.62 \\times 10^{15} Z^{2}}{n^{3}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"43.234ex\" height=\"5.876ex\" role=\"img\" 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display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>15<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-129 preview-line 129 130\" data_line_start=\"129\" data_line_end=\"130\" data_line=\"129,131\" count_line=\"2\">\n<li>Wavelength of radiation in the transition from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">→<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">\u2192<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)rarrn_(1)<\/asciimath><latex style=\"display: none\">n_{2} \\rightarrow n_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.06ex\" height=\"1.495ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -511 3562.7 661\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 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186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"2192\" d=\"M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2559.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo stretchy=\"false\">\u2192<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=RZ^(2)[(1)\/(n_(1)^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R Z^{2}\\left[\\frac{1}{n_{1}^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.446ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 8595 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(249.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"612.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1130, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2185.8, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2944.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(781, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(4129.4, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M224 -649V1150H455V1099H275V-598H455V-649H224Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(472, 0)\"><g data-mml-node=\"mn\" transform=\"translate(398, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1843.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2844.1, 0)\"><g data-mml-node=\"mn\" transform=\"translate(398, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3993.7, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R<\/asciimath><latex style=\"display: none\">R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.048ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 704\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called Rydberg’s constant. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=((1)\/(4piepsi_(0)))(2pi^(2)me^(4))\/(ch^(3))=1.097 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">R=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right) \\frac{2 \\pi^{2} m e^{4}}{c h^{3}}=1.097 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.403ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 16089.9 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 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250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (A) Spectral series of hydrogen atom: When the electron in a <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom jumps from higher energy level to lower energy level, the difference of energies of the two energy levels is emitted as radiation of particular wavelength, known as spectral line. Spectral lines of different wavelengths are obtained for transition of electron between two different energy levels, which are found to fall in a number of spectral series given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-131 preview-line 131\" data_line_start=\"131\" data_line_end=\"131\" data_line=\"131,132\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-03.jpg?height=415&width=745&top_left_y=909&top_left_x=1041\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-133 preview-line 133\" data_line_start=\"133\" data_line_end=\"133\" data_line=\"133,134\" count_line=\"1\">Energy<\/div>\n<ul class=\"preview-paragraph-135 preview-line 135 136\" data_line_start=\"135\" data_line_end=\"136\" data_line=\"135,137\" count_line=\"2\">\n<li>Lyman series<\/li>\n<\/ul>\n<div class=\"preview-paragraph-137 preview-line 137\" data_line_start=\"137\" data_line_end=\"137\" data_line=\"137,138\" count_line=\"1\">Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>2<\/mn> \n <mo>,<\/mo> \n <mn>3<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=2,3,dots,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=2,3, \\ldots, \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.619ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7787.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4615.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5954.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(6398.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7398.8, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to first energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>1<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=1)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=1\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Lyman series.<\/div>\n<div class=\"preview-paragraph-139 preview-line 139\" data_line_start=\"139\" data_line_end=\"139\" data_line=\"139,140\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.606ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 7339.8 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(249.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 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563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2944.8, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M224 -649V1150H455V1099H275V-598H455V-649H224Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(472, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1773.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2773.4, 0)\"><g data-mml-node=\"mn\" transform=\"translate(398, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3923, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-141 preview-line 141\" data_line_start=\"141\" data_line_end=\"141\" data_line=\"141,142\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=2,3,4,dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=2,3,4, \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.025ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 9293.1 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4726.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5171.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6509.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7848.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8293.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-143 preview-line 143 144\" data_line_start=\"143\" data_line_end=\"144\" data_line=\"143,145\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of Lyman series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-145 preview-line 145 146 147\" data_line_start=\"145\" data_line_end=\"147\" data_line=\"145,148\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext> or <\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(oo^(2))]=R quad” or “quad lambda=(1)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{\\infty^{2}}\\right]=R \\quad \\text { or } \\quad \\lambda=\\frac{1}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.872ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 17181.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 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data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mtext>\u00a0or\u00a0<\/mtext><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-149 preview-line 149 150\" data_line_start=\"149\" data_line_end=\"150\" data_line=\"149,151\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Lyman series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-151 preview-line 151 152 153\" data_line_start=\"151\" data_line_end=\"153\" data_line=\"151,154\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext> or <\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(2^(2))]=(3R)\/(4)quad” or “quad lambda=(4)\/(3R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right]=\\frac{3 R}{4} \\quad \\text { or } \\quad \\lambda=\\frac{4}{3 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"40.998ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 18121.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 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21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1459\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><mn>4<\/mn><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mtext>\u00a0or\u00a0<\/mtext><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-155 preview-line 155 156 157 158 159 160 161 162\" data_line_start=\"155\" data_line_end=\"162\" data_line=\"155,163\" count_line=\"8\">\n<li>\n<div>Lyman series lie in the ultraviolet region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>Lyman series is obtained in emission as well<\/div>\n<\/li>\n<li>\n<div>Balmer series as in absorption spectrum.<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>3<\/mn> \n <mo>,<\/mo> \n <mn>4<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=3,4,dots oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=3,4, \\ldots \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.613ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7343.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 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120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5954.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6954.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to second energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>2<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=2)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=2\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g 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data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Balmer series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-163 preview-line 163 164 165\" data_line_start=\"163\" data_line_end=\"165\" data_line=\"163,166\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-167 preview-line 167\" data_line_start=\"167\" data_line_end=\"167\" data_line=\"167,168\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=3,4,5<\/asciimath><latex style=\"display: none\">n_{2}=3,4,5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.693ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 4726.4 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-169 preview-line 169 170\" data_line_start=\"169\" data_line_end=\"170\" data_line=\"169,171\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of Balmer series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-171 preview-line 171 172 173\" data_line_start=\"171\" data_line_end=\"173\" data_line=\"171,174\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>4<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>4<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(oo^(2))]=(R)\/(4)” or “lambda=(4)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{4} \\text { or } \\lambda=\\frac{4}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.342ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 15621.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" 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295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" 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315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 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199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(11113.7, 0)\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 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327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14422.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(349.5, 676)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>4<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-175 preview-line 175 176\" data_line_start=\"175\" data_line_end=\"176\" data_line=\"175,177\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Balmer series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-177 preview-line 177 178 179\" data_line_start=\"177\" data_line_end=\"179\" data_line=\"177,180\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>36<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>36<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5R)\/(36)” or “lambda=(36)\/(5R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5 R}{36} \\text { or } \\lambda=\\frac{36}{5 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.473ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16121.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><mn>36<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-181 preview-line 181 182 183 184 185 186 187 188\" data_line_start=\"181\" data_line_end=\"188\" data_line=\"181,189\" count_line=\"8\">\n<li>\n<div>Balmer series lie in the visible region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Paschen series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n 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153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4615.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5954.1, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6398.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6843.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(7288.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8288.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to third energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>3<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=3)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=3\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Paschen series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-189 preview-line 189 190 191\" data_line_start=\"189\" data_line_end=\"191\" data_line=\"189,192\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-193 preview-line 193\" data_line_start=\"193\" data_line_end=\"193\" data_line=\"193,194\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=4,5,6dots dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=4,5,6 \\ldots \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.425ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 10353.8 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4893.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6231.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7570.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8909.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9353.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-195 preview-line 195 196\" data_line_start=\"195\" data_line_end=\"196\" data_line=\"195,197\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of the Paschen series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-197 preview-line 197 198 199\" data_line_start=\"197\" data_line_end=\"199\" data_line=\"197,200\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>9<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>9<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(oo^(2))]=(R)\/(9)” or “lambda=(9)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{9} \\text { or } \\lambda=\\frac{9}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.342ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 15621.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(349.5, -686)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 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data-mml-node=\"mfrac\" transform=\"translate(14422.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(349.5, 676)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>9<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>9<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-201 preview-line 201\" data_line_start=\"201\" data_line_end=\"201\" data_line=\"201,202\" count_line=\"1\">The first line (longest wavelength) of the Paschen series is given by<\/div>\n<div class=\"preview-paragraph-203 preview-line 203 204 205\" data_line_start=\"203\" data_line_end=\"205\" data_line=\"203,206\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>144<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>144<\/mn>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>144<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>144<\/mn>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(4^(2))]=(7R)\/(144)” or “lambda=(144)\/(7R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{4^{2}}\\right]=\\frac{7 R}{144} \\text { or } \\lambda=\\frac{144}{7 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.564ex\" height=\"5.428ex\" 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160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(340.5, -686)\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1700\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>7<\/mn><mi>R<\/mi><\/mrow><mn>144<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>144<\/mn><mrow><mn>7<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-207 preview-line 207 208 209 210 211 212 213 214\" data_line_start=\"207\" data_line_end=\"214\" data_line=\"207,215\" count_line=\"8\">\n<li>\n<div>Paschen series lie in the infrared region of the electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Brackett Series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>5<\/mn> \n <mo>,<\/mo> \n <mn>6<\/mn> \n <mo>,<\/mo> \n <mn>7<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>.<\/mo> \n <mo>.<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=5,6,7,dots..,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=5,6,7, \\ldots . ., \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.769ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 9621.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4615.4, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5115.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5560.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6898.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7343.4, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7788.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8232.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9232.8, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to fourth energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>4<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=4)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=4\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Brackett series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-215 preview-line 215 216 217\" data_line_start=\"215\" data_line_end=\"217\" data_line=\"215,218\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-219 preview-line 219\" data_line_start=\"219\" data_line_end=\"219\" data_line=\"219,220\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=5,6,7dots dots dots..oo<\/asciimath><latex style=\"display: none\">n_{2}=5,6,7 \\ldots \\ldots \\ldots . . \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.431ex\" height=\"1.968ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 10798.4 870\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4893.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6231.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7570.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8909.1, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9353.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9798.4, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Series limit line (shortest wavelength) of Brackett series is given by<\/div>\n<div class=\"preview-paragraph-221 preview-line 221 222 223\" data_line_start=\"221\" data_line_end=\"223\" data_line=\"221,224\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>16<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>16<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>16<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>16<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(oo^(2))]=(R)\/( 16)” or “lambda=(16 )\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{16} \\text { or } \\lambda=\\frac{16}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.433ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16103.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2093.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3094, 0)\"><g data-mml-node=\"mn\" transform=\"translate(671.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1603.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4937.6, 0)\"><path data-c=\"5D\" d=\"M11 1388V1450H280V-949H11V-887H218V1388H11Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8858.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9914.7, 0)\"><g data-mml-node=\"mi\" transform=\"translate(340.5, 676)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -686)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(11354.7, 0)\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\" transform=\"translate(750, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1142, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(12746.7, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13607.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14663.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(340.5, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>16<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>16<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-225 preview-line 225 226\" data_line_start=\"225\" data_line_end=\"226\" data_line=\"225,227\" count_line=\"2\">\n<li>The first line (longest wavelength) of Brackett series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-227 preview-line 227 228 229\" data_line_start=\"227\" data_line_end=\"229\" data_line=\"227,230\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>400<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>400<\/mn>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>400<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>400<\/mn>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(5^(2))]=(9R)\/(400)” or “lambda=(400)\/(9R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{5^{2}}\\right]=\\frac{9 R}{400} \\text { or } \\lambda=\\frac{400}{9 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.564ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16603.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(340.5, -686)\"><g data-mml-node=\"mn\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1700\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>9<\/mn><mi>R<\/mi><\/mrow><mn>400<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>400<\/mn><mrow><mn>9<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-231 preview-line 231 232 233 234 235 236 237 238\" data_line_start=\"231\" data_line_end=\"238\" data_line=\"231,239\" count_line=\"8\">\n<li>\n<div>Brackett series lie in the infrared region of the electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Pfund series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mn>8<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>6<\/mn> \n <mo>,<\/mo> \n <mn>7<\/mn> \n <mo>,<\/mo> \n <mn>8<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>\u2026<\/mo> \n <mo>.<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=6,7,8,dots dots.,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=6,7,8, \\ldots \\ldots ., \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.791ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 10515.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" 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3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4615.4, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5115.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5560.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6898.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8237.4, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8682.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9126.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10126.8, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>,<\/mo><mn>8<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to fifth energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>5<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=5)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=5\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Pfund series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-239 preview-line 239 240 241\" data_line_start=\"239\" data_line_end=\"241\" data_line=\"239,242\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 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data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-243 preview-line 243\" data_line_start=\"243\" data_line_end=\"243\" data_line=\"243,244\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=6,7,dots dots dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=6,7, \\ldots \\ldots \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.945ex\" height=\"1.968ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 11025.8 870\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4226.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5565.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6903.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8242.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9581.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(10025.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-245 preview-line 245\" data_line_start=\"245\" data_line_end=\"245\" data_line=\"245,246\" count_line=\"1\">Series limit line (shortest wavelength) of Pfund series is given by<\/div>\n<div class=\"preview-paragraph-247 preview-line 247 248 249\" data_line_start=\"247\" data_line_end=\"249\" data_line=\"247,250\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>25<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>25<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>25<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>25<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(oo^(2))]=(R)\/( 25)” or “lambda=(25 )\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{25} \\text { or } \\lambda=\\frac{25}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.433ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16103.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2093.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3094, 0)\"><g data-mml-node=\"mn\" transform=\"translate(671.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 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174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(340.5, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>25<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>25<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-251 preview-line 251 252\" data_line_start=\"251\" data_line_end=\"252\" data_line=\"251,253\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Pfund series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-253 preview-line 253 254 255\" data_line_start=\"253\" data_line_end=\"255\" data_line=\"253,256\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>6<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>900<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>900<\/mn>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>6<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>900<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>900<\/mn>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(6^(2))]=(11 R)\/(900)” or “lambda=(900)\/(11 R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{6^{2}}\\right]=\\frac{11 R}{900} \\text { or } \\lambda=\\frac{900}{11 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" 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0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>6<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>11<\/mn><mi>R<\/mi><\/mrow><mn>900<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>900<\/mn><mrow><mn>11<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-257 preview-line 257 258 259 260 261 262\" data_line_start=\"257\" data_line_end=\"262\" data_line=\"257,263\" count_line=\"6\">\n<li>\n<div>Pfund series also lie in the infrared region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Number of spectral lines due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" 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0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit to lower orbit is<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-263 preview-line 263 264 265\" data_line_start=\"263\" data_line_end=\"265\" data_line=\"263,266\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N=(n(n-1))\/(2)<\/asciimath><latex style=\"display: none\">N=\\frac{n(n-1)}{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.552ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.394ex\" height=\"4.855ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1460 6362 2146\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 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data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1820.2, -686)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><rect width=\"3900.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>N<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mn>2<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-267 preview-line 267\" data_line_start=\"267\" data_line_end=\"267\" data_line=\"267,268\" count_line=\"1\">(B) Ionization energy and ionization potential Ionisation : The process of knocking an electron out of the atom is called ionisation. ionisation<\/div>\n<div class=\"preview-paragraph-269 preview-line 269 270 271\" data_line_start=\"269\" data_line_end=\"271\" data_line=\"269,272\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext> energy <\/mtext>\n <mo>=<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext>\u00a0energy\u00a0<\/mtext>\n <mo>=<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">” energy “=(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">\\text { energy }=\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.347ex\" height=\"4.857ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1342 8109.6 2146.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(694, 0)\"><\/path><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\" transform=\"translate(1250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 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216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(607.2, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1978\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6915.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtext>\u00a0energy\u00a0<\/mtext><mo>=<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-273 preview-line 273 274 275 276\" data_line_start=\"273\" data_line_end=\"276\" data_line=\"273,277\" count_line=\"4\">\n<li>\n<div>Ionisation energy : The energy required, to knock an electron completely out of the atom.<\/div>\n<\/li>\n<li>\n<div>Ionisation potential <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(13.6Z^(2))\/(n^(2))V<\/asciimath><latex style=\"display: none\">=\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{~V}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.386ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4590.6 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1055.8, 0)\"><g 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201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2294.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3590.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><mn>13.6<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ul>\n<h2 type=\"section\" class=\"section-title preview-paragraph-277 preview-line 277\" id=\"previous-years'-cbse-board-questions\" data_line_start=\"277\" data_line_end=\"277\" data_line=\"277,278\" count_line=\"1\">\n<span class=\"section-number\">1. <\/span>Previous Years’ CBSE Board Questions<\/h2>\n<div class=\"preview-paragraph-279 preview-line 279\" data_line_start=\"279\" data_line_end=\"279\" data_line=\"279,280\" count_line=\"1\">12.2 Alpha Particle scattering and Rutherford’s Nuclear Model of Atom<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-281 preview-line 281\" id=\"vsa-(1-mark)\" data_line_start=\"281\" data_line_end=\"281\" data_line=\"281,282\" count_line=\"1\">\n<span class=\"section-number\">2. <\/span>VSA (1 mark)<\/h2>\n<ol class=\"preview-paragraph-283 preview-line 283 284\" data_line_start=\"283\" data_line_end=\"284\" data_line=\"283,285\" count_line=\"2\">\n<li>Why is the classical (Rutherford) model for an atom of electron orbiting around the nucleus not able to explain the atomic structure?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-285 preview-line 285\" data_line_start=\"285\" data_line_end=\"285\" data_line=\"285,286\" count_line=\"1\">(Delhi 2012C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-287 preview-line 287\" id=\"sa-i-(-2-marks)\" data_line_start=\"287\" data_line_end=\"287\" data_line=\"287,288\" count_line=\"1\">\n<span class=\"section-number\">3. <\/span>SA I ( 2 marks)<\/h2>\n<ol start=\"2\" class=\"preview-paragraph-289 preview-line 289 290\" data_line_start=\"289\" data_line_end=\"290\" data_line=\"289,291\" count_line=\"2\">\n<li>Using Rutherford’s model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-291 preview-line 291\" data_line_start=\"291\" data_line_end=\"291\" data_line=\"291,292\" count_line=\"1\">(AI 2014)<\/div>\n<ol start=\"3\" class=\"preview-paragraph-293 preview-line 293 294\" data_line_start=\"293\" data_line_end=\"294\" data_line=\"293,295\" count_line=\"2\">\n<li>In an experiment on <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle scattering by a thin foil of gold, draw a plot showing the number of particles scattered versus the scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Why is it that a very small fraction of the particles are scattered at <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta > 90^(@)<\/asciimath><latex style=\"display: none\">\\theta>90^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.09ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.254ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 3206.1 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>><\/mo><msup><mn>90<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-295 preview-line 295\" data_line_start=\"295\" data_line_end=\"295\" data_line=\"295,296\" count_line=\"1\">Write two important conclusions that can be drawn regarding the structure of the atom from the study of this experiment.<\/div>\n<div class=\"preview-paragraph-297 preview-line 297\" data_line_start=\"297\" data_line_end=\"297\" data_line=\"297,298\" count_line=\"1\">(Foreign 2013)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-299 preview-line 299\" id=\"sa-ii-(3-marks)\" data_line_start=\"299\" data_line_end=\"299\" data_line=\"299,300\" count_line=\"1\">\n<span class=\"section-number\">4. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"4\" class=\"preview-paragraph-301 preview-line 301 302\" data_line_start=\"301\" data_line_end=\"302\" data_line=\"301,303\" count_line=\"2\">\n<li>Draw a schematic arrangement of the Geiger – Marsden experiment for studying <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle scattering by a thin foil of gold. Describe briefly, by drawing trajectories of the scattered <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles, how this study can be used to estimate the size of the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-303 preview-line 303\" data_line_start=\"303\" data_line_end=\"303\" data_line=\"303,304\" count_line=\"1\">(Foreign 2010, AI 2009)<\/div>\n<ol start=\"5\" class=\"preview-paragraph-305 preview-line 305 306\" data_line_start=\"305\" data_line_end=\"306\" data_line=\"305,307\" count_line=\"2\">\n<li>State the basic assumption of the Rutherford model of the atom. Explain, in brief, why this model cannot account for the stability of an atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-307 preview-line 307\" data_line_start=\"307\" data_line_end=\"307\" data_line=\"307,308\" count_line=\"1\">(Delhi 2010C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-309 preview-line 309\" id=\"la-%24%5Cquad(5%24-marks)\" data_line_start=\"309\" data_line_end=\"309\" data_line=\"309,310\" count_line=\"1\">\n<span class=\"section-number\">5. <\/span>LA <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(5<\/asciimath><latex style=\"display: none\">\\quad(5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.274ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> marks)<\/h2>\n<ol start=\"6\" class=\"preview-paragraph-311 preview-line 311 312\" data_line_start=\"311\" data_line_end=\"312\" data_line=\"311,313\" count_line=\"2\">\n<li>In Rutherford scattering experiment, draw the trajectory traced by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles in the coulomb field of target nucleus and explain how this led to estimate the size of the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-313 preview-line 313\" data_line_start=\"313\" data_line_end=\"313\" data_line=\"313,314\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(3\/\/5<\/asciimath><latex style=\"display: none\">(3 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.274ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(389, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, AI 2015C <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">)<\/asciimath><latex style=\"display: none\">)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<h3 type=\"subsection\" class=\"sub_section-title preview-paragraph-315 preview-line 315\" id=\"atomic-spectra\" data_line_start=\"315\" data_line_end=\"315\" data_line=\"315,316\" count_line=\"1\">\n<span class=\"section-number\">5.<\/span><span class=\"sub_section-number\">1.<\/span> Atomic Spectra<\/h3>\n<h2 type=\"section\" class=\"section-title preview-paragraph-317 preview-line 317\" id=\"sa-i-(2-marks)\" data_line_start=\"317\" data_line_end=\"317\" data_line=\"317,318\" count_line=\"1\">\n<span class=\"section-number\">6. <\/span>SA I (2 marks)<\/h2>\n<ol start=\"7\" class=\"preview-paragraph-319 preview-line 319 320\" data_line_start=\"319\" data_line_end=\"320\" data_line=\"319,321\" count_line=\"2\">\n<li>Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infrared, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-321 preview-line 321\" data_line_start=\"321\" data_line_end=\"321\" data_line=\"321,322\" count_line=\"1\">(AI 2015)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-323 preview-line 323\" id=\"sa-ii-(3-marks)-2\" data_line_start=\"323\" data_line_end=\"323\" data_line=\"323,324\" count_line=\"1\">\n<span class=\"section-number\">7. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"8\" class=\"preview-paragraph-325 preview-line 325 326\" data_line_start=\"325\" data_line_end=\"326\" data_line=\"325,327\" count_line=\"2\">\n<li>The second member of Lyman series in hydrogen spectrum has wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5400<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5400<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5400″\u212b”<\/asciimath><latex style=\"display: none\">5400 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.882ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2600 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2000, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5400<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> A. Find the wavelength of the first member.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-327 preview-line 327\" data_line_start=\"327\" data_line_end=\"327\" data_line=\"327,328\" count_line=\"1\">(Delhi 2008)<\/div>\n<h3 type=\"subsection\" class=\"sub_section-title preview-paragraph-329 preview-line 329\" id=\"bohr-model-of-hydrogen-atom\" data_line_start=\"329\" data_line_end=\"329\" data_line=\"329,330\" count_line=\"1\">\n<span class=\"section-number\">7.<\/span><span class=\"sub_section-number\">1.<\/span> Bohr Model of Hydrogen Atom<\/h3>\n<h2 type=\"section\" class=\"section-title preview-paragraph-331 preview-line 331\" id=\"vsa-(1-mark)-2\" data_line_start=\"331\" data_line_end=\"331\" data_line=\"331,332\" count_line=\"1\">\n<span class=\"section-number\">8. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"9\" class=\"preview-paragraph-333 preview-line 333 334\" data_line_start=\"333\" data_line_end=\"334\" data_line=\"333,335\" count_line=\"2\">\n<li>What is the ratio of radii of the orbits corresponding to first excited state and ground state in a hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-335 preview-line 335\" data_line_start=\"335\" data_line_end=\"335\" data_line=\"335,336\" count_line=\"1\">(Delhi 2010)<\/div>\n<ol start=\"10\" class=\"preview-paragraph-337 preview-line 337 338\" data_line_start=\"337\" data_line_end=\"338\" data_line=\"337,339\" count_line=\"2\">\n<li>Define ionisation energy. What is its value for a hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-339 preview-line 339\" data_line_start=\"339\" data_line_end=\"339\" data_line=\"339,340\" count_line=\"1\">(AI 2010)<\/div>\n<ol start=\"11\" class=\"preview-paragraph-341 preview-line 341 342\" data_line_start=\"341\" data_line_end=\"342\" data_line=\"341,343\" count_line=\"2\">\n<li>State Bohr’s quantisation condition for defining stationary orbits.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-343 preview-line 343\" data_line_start=\"343\" data_line_end=\"343\" data_line=\"343,344\" count_line=\"1\">(Foreign 2010)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-345 preview-line 345\" id=\"sa-i-(2-marks)-2\" data_line_start=\"345\" data_line_end=\"345\" data_line=\"345,346\" count_line=\"1\">\n<span class=\"section-number\">9. <\/span>SA I (2 marks)<\/h2>\n<ol start=\"12\" class=\"preview-paragraph-347 preview-line 347 348\" data_line_start=\"347\" data_line_end=\"348\" data_line=\"347,349\" count_line=\"2\">\n<li>State Bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-349 preview-line 349\" data_line_start=\"349\" data_line_end=\"349\" data_line=\"349,350\" count_line=\"1\">(Foreign 2016)<\/div>\n<ol start=\"13\" class=\"preview-paragraph-351 preview-line 351 352\" data_line_start=\"351\" data_line_end=\"352\" data_line=\"351,353\" count_line=\"2\">\n<li>Show that the radius of the orbit in hydrogen atom varies as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the principal quantum number of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-353 preview-line 353\" data_line_start=\"353\" data_line_end=\"353\" data_line=\"353,354\" count_line=\"1\">(Delhi 2015)<\/div>\n<ol start=\"14\" class=\"preview-paragraph-355 preview-line 355 356\" data_line_start=\"355\" data_line_end=\"356\" data_line=\"355,357\" count_line=\"2\">\n<li>Using Bohr’s postulates of the atomic model, derive the expression for the radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> electron orbit. Hence obtain the expression for Bohr’s radius.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-357 preview-line 357\" data_line_start=\"357\" data_line_end=\"357\" data_line=\"357,358\" count_line=\"1\">(AI 2014)<\/div>\n<ol start=\"15\" class=\"preview-paragraph-359 preview-line 359 360\" data_line_start=\"359\" data_line_end=\"360\" data_line=\"359,361\" count_line=\"2\">\n<li>In the ground state of hydrogen atom, its Bohr radius is given as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5.3 xx10^(-11)m<\/asciimath><latex style=\"display: none\">5.3 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.327ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5890.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4807.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The atom is excited such that the radius becomes <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>21.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>21.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">21.2 xx10^(-11)m<\/asciimath><latex style=\"display: none\">21.2 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.459ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 6390.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2000.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3000.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5307.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>21.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find (i) the value of the principal quantum number and (ii) the total energy of the atom in this excited state.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-361 preview-line 361\" data_line_start=\"361\" data_line_end=\"361\" data_line=\"361,362\" count_line=\"1\">(Delhi 2013C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-363 preview-line 363\" id=\"sa-ii-(3-marks)-3\" data_line_start=\"363\" data_line_end=\"363\" data_line=\"363,364\" count_line=\"1\">\n<span class=\"section-number\">10. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"16\" class=\"preview-paragraph-365 preview-line 365 366\" data_line_start=\"365\" data_line_end=\"366\" data_line=\"365,367\" count_line=\"2\">\n<li>(a) The radius of the innermost electron orbit of a hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5.3 xx10^(-11)m<\/asciimath><latex style=\"display: none\">5.3 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.327ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5890.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4807.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Calculate its radius in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-367 preview-line 367\" data_line_start=\"367\" data_line_end=\"367\" data_line=\"367,368\" count_line=\"1\">(b) The total energy of an electron in the first excited state of the hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">3.4eV<\/asciimath><latex style=\"display: none\">3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.593ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2472 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1278, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find out its (i) kinetic energy and (ii) potential energy in this state.<\/div>\n<div class=\"preview-paragraph-369 preview-line 369\" data_line_start=\"369\" data_line_end=\"369\" data_line=\"369,370\" count_line=\"1\">(Delhi 2014C)<\/div>\n<ol start=\"17\" class=\"preview-paragraph-371 preview-line 371 372\" data_line_start=\"371\" data_line_end=\"372\" data_line=\"371,373\" count_line=\"2\">\n<li>Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-373 preview-line 373\" data_line_start=\"373\" data_line_end=\"373\" data_line=\"373,374\" count_line=\"1\">(Delhi 2013)<\/div>\n<ol start=\"18\" class=\"preview-paragraph-375 preview-line 375 376\" data_line_start=\"375\" data_line_end=\"376\" data_line=\"375,377\" count_line=\"2\">\n<li>Using Bohr’s postulates for hydrogen atom, show that the total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in the stationary states can be expressed as the sum of kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(K)<\/asciimath><latex style=\"display: none\">(K)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.771ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1667 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1278, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>K<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(U)<\/asciimath><latex style=\"display: none\">(U)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.495ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1545 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1156, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>U<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mi>U<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <mi>U<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=-2U<\/asciimath><latex style=\"display: none\">K=-2 U<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.655ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4267.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1166.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2222.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3000.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3500.6, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mi>U<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Hence deduce the expression for the total energy in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> energy level of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-377 preview-line 377\" data_line_start=\"377\" data_line_end=\"377\" data_line=\"377,378\" count_line=\"1\">(Foreign 2012)<\/div>\n<ol start=\"19\" class=\"preview-paragraph-379 preview-line 379 380\" data_line_start=\"379\" data_line_end=\"380\" data_line=\"379,381\" count_line=\"2\">\n<li>The energy levels of a hypothetical atom are shown below. Which of the shown transitions will result in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-381 preview-line 381\" data_line_start=\"381\" data_line_end=\"381\" data_line=\"381,382\" count_line=\"1\">Which of these transitions correspond to emission of radiation of (i) maximum and (ii) minimum wavelength?<\/div>\n<div class=\"preview-paragraph-383 preview-line 383\" data_line_start=\"383\" data_line_end=\"383\" data_line=\"383,384\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-06.jpg?height=228&width=465&top_left_y=1856&top_left_x=424\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-385 preview-line 385\" data_line_start=\"385\" data_line_end=\"385\" data_line=\"385,386\" count_line=\"1\">(Delhi 2011)<\/div>\n<ol start=\"20\" class=\"preview-paragraph-387 preview-line 387 388\" data_line_start=\"387\" data_line_end=\"388\" data_line=\"387,389\" count_line=\"2\">\n<li>Using the postulates of Bohr’s model of hydrogen atom, obtain an expression for the frequency of radiation emitted when atom make a transition from the higher energy state with quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to the lower energy state with quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo><<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub> \n <mo><<\/mo> \n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)(n_(f) < n_(i))<\/asciimath><latex style=\"display: none\">n_{f}\\left(n_{f}<n_{i}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.501ex\" height=\"2.364ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 5083.3 1045\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1038.9, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1705.7, 0)\"><path data-c=\"3C\" d=\"M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2761.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3655.4, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo><<\/mo><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-389 preview-line 389\" data_line_start=\"389\" data_line_end=\"389\" data_line=\"389,390\" count_line=\"1\">(Foreign 2011)<\/div>\n<ol start=\"21\" class=\"preview-paragraph-391 preview-line 391 392\" data_line_start=\"391\" data_line_end=\"392\" data_line=\"391,393\" count_line=\"2\">\n<li>Using the relevant Bohr’s postulates, derive the expressions for the (a) speed of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-393 preview-line 393\" data_line_start=\"393\" data_line_end=\"393\" data_line=\"393,394\" count_line=\"1\">(b) radius of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of the electron, in hydrogen atom.<\/div>\n<div class=\"preview-paragraph-395 preview-line 395\" data_line_start=\"395\" data_line_end=\"395\" data_line=\"395,396\" count_line=\"1\">(Delhi 2010C)<\/div>\n<ol start=\"22\" class=\"preview-paragraph-397 preview-line 397 398\" data_line_start=\"397\" data_line_end=\"398\" data_line=\"397,399\" count_line=\"2\">\n<li>State any two postulates of Bohr’s theory of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-399 preview-line 399\" data_line_start=\"399\" data_line_end=\"399\" data_line=\"399,400\" count_line=\"1\">What is the maximum possible number of spectral lines observed when the hydrogen atom is in its second excited state? Justify your answer. Calculate the ratio of the maximum and minimum wavelengths of the radiations emitted in this process.<\/div>\n<ol start=\"23\" class=\"preview-paragraph-401 preview-line 401 402\" data_line_start=\"401\" data_line_end=\"402\" data_line=\"401,403\" count_line=\"2\">\n<li>(a) The energy levels of an atom are as shown below. Which of them will result in the transition of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-403 preview-line 403\" data_line_start=\"403\" data_line_end=\"403\" data_line=\"403,404\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-06.jpg?height=248&width=597&top_left_y=1064&top_left_x=1135\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-405 preview-line 405\" data_line_start=\"405\" data_line_end=\"405\" data_line=\"405,406\" count_line=\"1\">(b) Which transition corresponds to emission of radiation of maximum wavelength?<\/div>\n<div class=\"preview-paragraph-407 preview-line 407\" data_line_start=\"407\" data_line_end=\"407\" data_line=\"407,408\" count_line=\"1\">(Delhi 2009)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-409 preview-line 409\" id=\"la-(5-marks)\" data_line_start=\"409\" data_line_end=\"409\" data_line=\"409,410\" count_line=\"1\">\n<span class=\"section-number\">11. <\/span>LA (5 marks)<\/h2>\n<ol start=\"24\" class=\"preview-paragraph-411 preview-line 411 412\" data_line_start=\"411\" data_line_end=\"412\" data_line=\"411,413\" count_line=\"2\">\n<li>(a) Write two important limitations of Rutherford model which could not explain the observed features of atomic spectra. How were these explained in Bohr’s model of hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-413 preview-line 413\" data_line_start=\"413\" data_line_end=\"413\" data_line=\"413,414\" count_line=\"1\">(b) Using Bohr’s postulates, obtain the expression for the radius of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit in hydrogen atom. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>4<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>4<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(4\/\/5<\/asciimath><latex style=\"display: none\">\\quad(4 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.536ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, Delhi <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2015<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2015<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2015 C)<\/asciimath><latex style=\"display: none\">2015 C)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.124ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3149 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2000, 0)\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2760, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2015<\/mn><mi>C<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"25\" class=\"preview-paragraph-415 preview-line 415 416 417 418\" data_line_start=\"415\" data_line_end=\"418\" data_line=\"415,419\" count_line=\"4\">\n<li>\n<div>Using Bohr’s postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom. (3\/5, Foreign 2014)<\/div>\n<\/li>\n<li>\n<div>(a) Using Bohr’s theory of hydrogen atom, derive the expression for the total energy of the electron in the stationary states of the atom.<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-419 preview-line 419\" data_line_start=\"419\" data_line_end=\"419\" data_line=\"419,420\" count_line=\"1\">(b) If electron in the atom is replaced by a particle (muon) having the same charge but mass about 200 times as that of the electron to form a muonic atom, how would (i) the radius and (ii) the ground state energy of this be affected?<\/div>\n<div class=\"preview-paragraph-421 preview-line 421\" data_line_start=\"421\" data_line_end=\"421\" data_line=\"421,422\" count_line=\"1\">(3\/5, Delhi <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2012<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">C<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2012<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">C<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2012C)<\/asciimath><latex style=\"display: none\">2012 \\mathrm{C})<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.038ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3111 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2000, 0)\"><g data-mml-node=\"mi\"><path data-c=\"43\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q322 658 252 588Q173 509 173 342Q173 221 211 151Q232 111 263 84T328 45T384 29T428 24Q517 24 571 93T626 244Q626 251 632 257H660L666 251V236Q661 133 590 56T403 -21Q262 -21 159 83T56 342Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2722, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2012<\/mn><mrow><mi mathvariant=\"normal\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"27\" class=\"preview-paragraph-423 preview-line 423 424\" data_line_start=\"423\" data_line_end=\"424\" data_line=\"423,425\" count_line=\"2\">\n<li>(a) Using postulates of Bohr’s theory of hydrogen atom, show that<\/li>\n<\/ol>\n<div class=\"preview-paragraph-425 preview-line 425\" data_line_start=\"425\" data_line_end=\"425\" data_line=\"425,426\" count_line=\"1\">(i) the radii of orbits increase as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, and (ii) the total energy of the electron increase as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/n^(2)<\/asciimath><latex style=\"display: none\">1 \/ n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.533ex\" height=\"2.452ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 2003.6 1083.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1000, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the principal quantum number of the atom. (3\/5, AI 2011C)<\/div>\n<ol start=\"28\" class=\"preview-paragraph-427 preview-line 427 428\" data_line_start=\"427\" data_line_end=\"428\" data_line=\"427,429\" count_line=\"2\">\n<li>The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">102.7nm<\/asciimath><latex style=\"display: none\">102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.862ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3917 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2278, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-429 preview-line 429\" data_line_start=\"429\" data_line_end=\"429\" data_line=\"429,430\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=285&width=602&top_left_y=757&top_left_x=333\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-431 preview-line 431\" data_line_start=\"431\" data_line_end=\"431\" data_line=\"431,432\" count_line=\"1\">(Delhi 2008)<\/div>\n<div class=\"preview-paragraph-433 preview-line 433\" data_line_start=\"433\" data_line_end=\"433\" data_line=\"433,434\" count_line=\"1\">12.5 The Line Spectra of the Hydrogen Atom<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-435 preview-line 435\" id=\"vsa-(1-mark)-3\" data_line_start=\"435\" data_line_end=\"435\" data_line=\"435,436\" count_line=\"1\">\n<span class=\"section-number\">12. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"29\" class=\"preview-paragraph-437 preview-line 437 438\" data_line_start=\"437\" data_line_end=\"438\" data_line=\"437,439\" count_line=\"2\">\n<li>When is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line of the Balmer series in the emission spectrum of hydrogen atom obtained?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-439 preview-line 439\" data_line_start=\"439\" data_line_end=\"439\" data_line=\"439,440\" count_line=\"1\">(Delhi 2013C)<\/div>\n<ol start=\"30\" class=\"preview-paragraph-441 preview-line 441 442\" data_line_start=\"441\" data_line_end=\"442\" data_line=\"441,443\" count_line=\"2\">\n<li>What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state?<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-443 preview-line 443\" id=\"sai-(2-marks)\" data_line_start=\"443\" data_line_end=\"443\" data_line=\"443,444\" count_line=\"1\">\n<span class=\"section-number\">13. <\/span>SAI (2 marks)<\/h2>\n<ol start=\"31\" class=\"preview-paragraph-445 preview-line 445 446\" data_line_start=\"445\" data_line_end=\"446\" data_line=\"445,447\" count_line=\"2\">\n<li>Define ionization energy.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-447 preview-line 447\" data_line_start=\"447\" data_line_end=\"447\" data_line=\"447,448\" count_line=\"1\">How would the ionization energy change when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge?<\/div>\n<div class=\"preview-paragraph-449 preview-line 449\" data_line_start=\"449\" data_line_end=\"449\" data_line=\"449,450\" count_line=\"1\">(AI 2016)<\/div>\n<ol start=\"32\" class=\"preview-paragraph-451 preview-line 451 452\" data_line_start=\"451\" data_line_end=\"452\" data_line=\"451,453\" count_line=\"2\">\n<li>An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-453 preview-line 453\" data_line_start=\"453\" data_line_end=\"453\" data_line=\"453,454\" count_line=\"1\">(Foreign 2016)<\/div>\n<ol start=\"33\" class=\"preview-paragraph-455 preview-line 455 456\" data_line_start=\"455\" data_line_end=\"456\" data_line=\"455,457\" count_line=\"2\">\n<li>The figure shows energy level diagram of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-457 preview-line 457\" data_line_start=\"457\" data_line_end=\"457\" data_line=\"457,458\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=277&width=494&top_left_y=2169&top_left_x=381\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-459 preview-line 459\" data_line_start=\"459\" data_line_end=\"459\" data_line=\"459,460\" count_line=\"1\">(a) Find out the transition which results in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>496<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>496<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">496nm<\/asciimath><latex style=\"display: none\">496 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.581ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 3139 699\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>496<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. (b) Which transition corresponds to the emission of radiation of maximum wavelength? Justify your answer.<\/div>\n<div class=\"preview-paragraph-461 preview-line 461\" data_line_start=\"461\" data_line_end=\"461\" data_line=\"461,462\" count_line=\"1\">(AI 2015C)<\/div>\n<ol start=\"34\" class=\"preview-paragraph-463 preview-line 463 464\" data_line_start=\"463\" data_line_end=\"464\" data_line=\"463,465\" count_line=\"2\">\n<li>(i) In hydrogen atom, an electron undergoes transition from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2^(“nd “)<\/asciimath><latex style=\"display: none\">2^{\\text {nd }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.423ex\" height=\"1.932ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1513.1 853.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(556, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1112, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>2<\/mn><mrow><mtext>nd\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> excited state to the first excited state and then to the ground state. Identify the spectral series to which these transitions belong. (ii) Find out the ratio of the wavelengths of the emitted radiations in the two cases. (AI 2012C)<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-465 preview-line 465\" id=\"sa-ii-(3-marks)-4\" data_line_start=\"465\" data_line_end=\"465\" data_line=\"465,466\" count_line=\"1\">\n<span class=\"section-number\">14. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"35\" class=\"preview-paragraph-467 preview-line 467 468 469 470\" data_line_start=\"467\" data_line_end=\"470\" data_line=\"467,471\" count_line=\"4\">\n<li>\n<div>Using Rydberg formula, calculate the longest wavelength belonging to Lyman and Balmer series of hydrogen spectrum. In which region these transitions lie? <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(3\/\/5<\/asciimath><latex style=\"display: none\">\\quad(3 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.536ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, Foreign 2015)<\/div>\n<\/li>\n<li>\n<div>A <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">12.5eV<\/asciimath><latex style=\"display: none\">12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.724ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2972 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1778, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the hydrogen atoms would be excited?<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-471 preview-line 471\" data_line_start=\"471\" data_line_end=\"471\" data_line=\"471,472\" count_line=\"1\">Calculate the wavelengths of the first member of Lyman and first member of Balmer series.<\/div>\n<div class=\"preview-paragraph-473 preview-line 473\" data_line_start=\"473\" data_line_end=\"473\" data_line=\"473,474\" count_line=\"1\">(Delhi 2014)<\/div>\n<ol start=\"37\" class=\"preview-paragraph-475 preview-line 475 476\" data_line_start=\"475\" data_line_end=\"476\" data_line=\"475,477\" count_line=\"2\">\n<li>The value of ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-477 preview-line 477\" data_line_start=\"477\" data_line_end=\"477\" data_line=\"477,478\" count_line=\"1\">(i) Find the energy required to move an electron from the ground state to the first excited state of the atom.<\/div>\n<div class=\"preview-paragraph-479 preview-line 479\" data_line_start=\"479\" data_line_end=\"479\" data_line=\"479,480\" count_line=\"1\">(ii) Determine (a) the kinetic energy and (b) orbital radius in the first excited state of the atom.<\/div>\n<div class=\"preview-paragraph-481 preview-line 481\" data_line_start=\"481\" data_line_end=\"481\" data_line=\"481,482\" count_line=\"1\">(Given the value of Bohr radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.53<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.53<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=0.53″\u212b”<\/asciimath><latex style=\"display: none\">=0.53 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.769ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3433.8 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2833.8, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>0.53<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-483 preview-line 483\" data_line_start=\"483\" data_line_end=\"483\" data_line=\"483,484\" count_line=\"1\">(AI 2014C)<\/div>\n<ol start=\"38\" class=\"preview-paragraph-485 preview-line 485 486\" data_line_start=\"485\" data_line_end=\"486\" data_line=\"485,487\" count_line=\"2\">\n<li>(a) The energy levels of a hypothetical hydrogen-like atom are shown in the figure. Find out the transition, from the ones shown in the figure, which will result in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-487 preview-line 487\" data_line_start=\"487\" data_line_end=\"487\" data_line=\"487,488\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=306&width=599&top_left_y=2080&top_left_x=1111\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-489 preview-line 489\" data_line_start=\"489\" data_line_end=\"489\" data_line=\"489,490\" count_line=\"1\">(b) Which of these transitions corresponds to the emission of radiation of (i) maximum and (ii) minimum wavelength? (Foreign 2013) 39. The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?<\/div>\n<div class=\"preview-paragraph-491 preview-line 491\" data_line_start=\"491\" data_line_end=\"491\" data_line=\"491,492\" count_line=\"1\">(1\/3, Delhi 2012)<\/div>\n<ol start=\"40\" class=\"preview-paragraph-493 preview-line 493 494\" data_line_start=\"493\" data_line_end=\"494\" data_line=\"493,495\" count_line=\"2\">\n<li>The ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. If an electron makes a transition from an energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-0.85eV<\/asciimath><latex style=\"display: none\">-0.85 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-3.4eV<\/asciimath><latex style=\"display: none\">-3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.353ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3250 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2056, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-495 preview-line 495\" data_line_start=\"495\" data_line_end=\"495\" data_line=\"495,496\" count_line=\"1\">(AI 2012)<\/div>\n<ol start=\"41\" class=\"preview-paragraph-497 preview-line 497 498\" data_line_start=\"497\" data_line_end=\"498\" data_line=\"497,499\" count_line=\"2\">\n<li>The electron in a given Bohr orbit has a total energy of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-1.5eV<\/asciimath><latex style=\"display: none\">-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.353ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3250 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2056, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Calculate its<\/li>\n<\/ol>\n<div class=\"preview-paragraph-499 preview-line 499\" data_line_start=\"499\" data_line_end=\"499\" data_line=\"499,500\" count_line=\"1\">(i) kinetic energy.<\/div>\n<div class=\"preview-paragraph-501 preview-line 501\" data_line_start=\"501\" data_line_end=\"501\" data_line=\"501,502\" count_line=\"1\">(ii) potential energy.<\/div>\n<div class=\"preview-paragraph-503 preview-line 503\" data_line_start=\"503\" data_line_end=\"503\" data_line=\"503,504\" count_line=\"1\">(iii) wavelength of radiation emitted, when this electron makes a transition to the ground state. [Given : Energy in the ground state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-13.6eV<\/asciimath><latex style=\"display: none\">=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.873ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4805.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3611.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and Rybderg’s constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=1.09 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">=1.09 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.96ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 7496.5 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3056, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(4056.2, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(5459.8, 0)\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ]<\/div>\n<div class=\"preview-paragraph-505 preview-line 505\" data_line_start=\"505\" data_line_end=\"505\" data_line=\"505,506\" count_line=\"1\">(Delhi 2011C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-507 preview-line 507\" id=\"la-(5-marks)-2\" data_line_start=\"507\" data_line_end=\"507\" data_line=\"507,508\" count_line=\"1\">\n<span class=\"section-number\">15. <\/span>LA (5 marks)<\/h2>\n<ol start=\"42\" class=\"preview-paragraph-509 preview-line 509 510\" data_line_start=\"509\" data_line_end=\"510\" data_line=\"509,511\" count_line=\"2\">\n<li>Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-511 preview-line 511\" data_line_start=\"511\" data_line_end=\"511\" data_line=\"511,512\" count_line=\"1\">(2\/5, Foreign 2014)<\/div>\n<ol start=\"43\" class=\"preview-paragraph-513 preview-line 513 514\" data_line_start=\"513\" data_line_end=\"514\" data_line=\"513,515\" count_line=\"2\">\n<li>Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ) to the lower state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(f))<\/asciimath><latex style=\"display: none\">\\left(n_{f}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.111ex\" height=\"2.364ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1816.9 1045\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1427.9, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. When electron in hydrogen atom jumps from energy state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=4<\/asciimath><latex style=\"display: none\">n_{i}=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2727.5 834.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=3,2,1<\/asciimath><latex style=\"display: none\">n_{f}=3,2,1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.773ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 4761.8 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2872.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3317.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3817.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4261.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Identify the spectral series to which the emission lines belong.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-515 preview-line 515\" data_line_start=\"515\" data_line_end=\"515\" data_line=\"515,516\" count_line=\"1\">(AI 2013)<\/div>\n<ol start=\"44\" class=\"preview-paragraph-517 preview-line 517 518\" data_line_start=\"517\" data_line_end=\"518\" data_line=\"517,519\" count_line=\"2\">\n<li>Calculate the wavelength of the first spectral line in the corresponding Lyman series of this atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-519 preview-line 519\" data_line_start=\"519\" data_line_end=\"519\" data_line=\"519,520\" count_line=\"1\">(2\/5, Delhi 2012C)<\/div>\n<ol start=\"45\" class=\"preview-paragraph-521 preview-line 521 522\" data_line_start=\"521\" data_line_end=\"522\" data_line=\"521,523\" count_line=\"2\">\n<li>Calculate the wavlength of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line in Balmer series of hydrogen atom, given Rydberg constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=1.097 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">R=1.097 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.437ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 9033.2 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2092.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 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358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5593, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(6996.6, 0)\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-523 preview-line 523\" data_line_start=\"523\" data_line_end=\"523\" data_line=\"523,524\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mi>A<\/mi>\n <mi>I<\/mi>\n <mn>2011<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mi>A<\/mi>\n <mi>I<\/mi>\n <mn>2011<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(2\/\/5,AI 2011 C)<\/asciimath><latex style=\"display: none\">(2 \/ 5, A I 2011 C)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.241ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 6736.7 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(389, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1889, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2333.7, 0)\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3083.7, 0)\"><path data-c=\"49\" d=\"M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3587.7, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5587.7, 0)\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6347.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><mo>,<\/mo><mi>A<\/mi><mi>I<\/mi><mn>2011<\/mn><mi>C<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-525 preview-line 525\" data_line_start=\"525\" data_line_end=\"525\" data_line=\"525,526\" count_line=\"1\">12.6 de Broglie’s Explanation of Bohr’s Second Postulate of Quantisation<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-527 preview-line 527\" id=\"vsa-(1-mark)-4\" data_line_start=\"527\" data_line_end=\"527\" data_line=\"527,528\" count_line=\"1\">\n<span class=\"section-number\">16. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"46\" class=\"preview-paragraph-529 preview-line 529 530\" data_line_start=\"529\" data_line_end=\"530\" data_line=\"529,531\" count_line=\"2\">\n<li>State de-Broglie hypothesis.<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-531 preview-line 531\" id=\"sai-(2-marks)-2\" data_line_start=\"531\" data_line_end=\"531\" data_line=\"531,532\" count_line=\"1\">\n<span class=\"section-number\">17. <\/span>SAI (2 marks)<\/h2>\n<ol start=\"47\" class=\"preview-paragraph-533 preview-line 533 534\" data_line_start=\"533\" data_line_end=\"534\" data_line=\"533,535\" count_line=\"2\">\n<li>Calculate the de-Broglie wavelength of the electron orbiting in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-535 preview-line 535\" data_line_start=\"535\" data_line_end=\"535\" data_line=\"535,536\" count_line=\"1\">(AI 2016)<\/div>\n<ol start=\"48\" class=\"preview-paragraph-537 preview-line 537 538\" data_line_start=\"537\" data_line_end=\"538\" data_line=\"537,539\" count_line=\"2\">\n<li>Use de-Broglie’s hypothesis to write the relation for the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> radius of Bohr orbit in terms of Bohr’s quantization condition of orbital angular momentum.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-539 preview-line 539\" data_line_start=\"539\" data_line_end=\"539\" data_line=\"539,540\" count_line=\"1\">(Foreign 2016)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-541 preview-line 541\" id=\"sa-ii-(3-marks)-5\" data_line_start=\"541\" data_line_end=\"541\" data_line=\"541,542\" count_line=\"1\">\n<span class=\"section-number\">18. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"49\" class=\"preview-paragraph-543 preview-line 543 544\" data_line_start=\"543\" data_line_end=\"544\" data_line=\"543,545\" count_line=\"2\">\n<li>(i) State Bohr’s quantization condition for defining stationary orbits. How does de Broglie hypothesis explain the stationary orbits ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-545 preview-line 545\" data_line_start=\"545\" data_line_end=\"545\" data_line=\"545,546\" count_line=\"1\">(ii) Find the relation between the three wavelengths <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1),lambda_(2)<\/asciimath><latex style=\"display: none\">\\lambda_{1}, \\lambda_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.47ex\" height=\"2.009ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 2417.8 888\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(986.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1431.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(3)<\/asciimath><latex style=\"display: none\">\\lambda_{3}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.945ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 859.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from the energy level diagram shown below.<\/div>\n<div class=\"preview-paragraph-547 preview-line 547\" data_line_start=\"547\" data_line_end=\"547\" data_line=\"547,548\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-08.jpg?height=317&width=534&top_left_y=1195&top_left_x=1161\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-549 preview-line 549\" data_line_start=\"549\" data_line_end=\"549\" data_line=\"549,550\" count_line=\"1\">(Delhi 2016)<\/div>\n<ol start=\"50\" class=\"preview-paragraph-551 preview-line 551 552\" data_line_start=\"551\" data_line_end=\"552\" data_line=\"551,553\" count_line=\"2\">\n<li>The kinetic energy of the electron orbiting in the first excited state of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">3.4eV<\/asciimath><latex style=\"display: none\">3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.593ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2472 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1278, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Determine the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-553 preview-line 553\" data_line_start=\"553\" data_line_end=\"553\" data_line=\"553,554\" count_line=\"1\">(Foreign 2015)<\/div>\n<ol start=\"51\" class=\"preview-paragraph-555 preview-line 555 556\" data_line_start=\"555\" data_line_end=\"556\" data_line=\"555,557\" count_line=\"2\">\n<li>An electron is revolving around the nucleus with a constant speed of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2.2 xx10^(8)m\/\/s<\/asciimath><latex style=\"display: none\">2.2 \\times 10^{8} \\mathrm{~m} \/ \\mathrm{s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.305ex\" height=\"2.52ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5881 1114\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3904, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4987, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5487, 0)\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\/<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-557 preview-line 557\" data_line_start=\"557\" data_line_end=\"557\" data_line=\"557,558\" count_line=\"1\">(AI 2014C)<\/div>\n<ol start=\"52\" class=\"preview-paragraph-559 preview-line 559 560\" data_line_start=\"559\" data_line_end=\"560\" data_line=\"559,561\" count_line=\"2\">\n<li>Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbital state in hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-561 preview-line 561\" data_line_start=\"561\" data_line_end=\"561\" data_line=\"561,562\" count_line=\"1\">(2\/3, Delhi 2012)<\/div>\n<ol start=\"53\" class=\"preview-paragraph-563 preview-line 563 564\" data_line_start=\"563\" data_line_end=\"564\" data_line=\"563,565\" count_line=\"2\">\n<li>(a) Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-565 preview-line 565\" data_line_start=\"565\" data_line_end=\"565\" data_line=\"565,566\" count_line=\"1\">(b) The ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. What are the kinetic and potential energies of the electron in this state? (AI 2011)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-567 preview-line 567\" id=\"detailed-solutions\" data_line_start=\"567\" data_line_end=\"567\" data_line=\"567,568\" count_line=\"1\">\n<span class=\"section-number\">19. <\/span>Detailed Solutions<\/h2>\n<ol class=\"preview-paragraph-569 preview-line 569 570 571 572\" data_line_start=\"569\" data_line_end=\"572\" data_line=\"569,573\" count_line=\"4\">\n<li>\n<div>According to electromagnetic theory, electron revolving around the nucleus are continuously accelerated. Since an accelerated charge emits energy, the radius of the circular path of a revolving electron should go on decreasing and ultimately it should fall into the nucleus. So, it could not explain the structure of the atom. As matter is stable, we cannot expect the atoms to collapse.<\/div>\n<\/li>\n<li>\n<div>An electron revolving in an orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, has both kinetic energy and electrostatic potential energy. Kinetic energy of the electron revolving in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(K)=(1)\/(2)mv^(2)<\/asciimath><latex style=\"display: none\">E_{K}=\\frac{1}{2} m v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.781ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.014ex\" height=\"2.737ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 5310.3 1209.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 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422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-573 preview-line 573\" data_line_start=\"573\" data_line_end=\"573\" data_line=\"573,574\" count_line=\"1\">Since, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))(e^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.324ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5889 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-575 preview-line 575 576 577\" data_line_start=\"575\" data_line_end=\"577\" data_line=\"575,578\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext> or <\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadE_(K)=(1)\/(2)xx(1)\/(4piepsi_(0))(e^(2))\/(r)” or “E_(K)=(1)\/(4piepsi_(0))(e^(2))\/(2r)<\/asciimath><latex style=\"display: none\">\\therefore \\quad E_{K}=\\frac{1}{2} \\times \\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r} \\text { or } E_{K}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.763ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 18459.2 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 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429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1151\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-579 preview-line 579\" data_line_start=\"579\" data_line_end=\"579\" data_line=\"579,580\" count_line=\"1\">Electrostatic potential energy of electron of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> revolving around the nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in an orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-581 preview-line 581 582 583\" data_line_start=\"581\" data_line_end=\"583\" data_line=\"581,584\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo>+<\/mo>\n <mi>e<\/mi>\n <mo>×<\/mo>\n <mo>−<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext> or <\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo>+<\/mo>\n <mi>e<\/mi>\n <mo>\u00d7<\/mo>\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(P)=(1)\/(4piepsi_(0))(+e xx-e)\/(r)” or “E_(P)=(-1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">E_{P}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{+e \\times-e}{r} \\text { or } E_{P}=\\frac{-1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.272ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 16916.3 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 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186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1849.7, -686)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"3910.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(9182.6, 0)\"><path data-c=\"A0\" 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186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(429.3, -686)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1069.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>E<\/mi><mrow><mi>P<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mo>+<\/mo><mi>e<\/mi><mo>\u00d7<\/mo><mo>\u2212<\/mo><mi>e<\/mi><\/mrow><mi>r<\/mi><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><msub><mi>E<\/mi><mrow><mi>P<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-585 preview-line 585\" data_line_start=\"585\" data_line_end=\"585\" data_line=\"585,586\" count_line=\"1\">So, total energy of electron in orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-587 preview-line 587 588 589\" data_line_start=\"587\" data_line_end=\"589\" data_line=\"587,590\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mtext> or <\/mtext>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(K)+E_(P)” or “E=(1)\/(4piepsi_(0))(e^(2))\/(2r)-(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">E=E_{K}+E_{P} \\text { or } E=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.238ex\" 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591\" data_line_start=\"591\" data_line_end=\"591\" data_line=\"591,592\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-1)\/(4piepsi_(0))(e^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E=\\frac{-1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.361ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5021.5 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(453.9, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3909, 0)\"><g data-mml-node=\"msup\" transform=\"translate(248.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"872.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-593 preview-line 593\" data_line_start=\"593\" data_line_end=\"593\" data_line=\"593,594\" count_line=\"1\">The -ve sign of the energy of electron indicates that the electron and nucleus together form a bound system i.e., electron is bound to the nucleus.<\/div>\n<div class=\"preview-paragraph-595 preview-line 595\" data_line_start=\"595\" data_line_end=\"595\" data_line=\"595,596\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-09.jpg?height=456&width=528&top_left_y=1985&top_left_x=250\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-597 preview-line 597\" data_line_start=\"597\" data_line_end=\"597\" data_line=\"597,598\" count_line=\"1\">A very small fraction of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles are scattered at <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta > 90^(@)<\/asciimath><latex style=\"display: none\">\\theta>90^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.09ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.254ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 3206.1 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>><\/mo><msup><mn>90<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> because the size of nucleus is very small nearly <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/8000<\/asciimath><latex style=\"display: none\">1 \/ 8000<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.787ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3000 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1000, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>8000<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the size of atom. So, a few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles experience a strong repulsive force and turn back. Conclusions :<\/div>\n<div class=\"preview-paragraph-599 preview-line 599\" data_line_start=\"599\" data_line_end=\"599\" data_line=\"599,600\" count_line=\"1\">(i) Entire positive charge and most of the mass of the atom is concentrated in the nucleus with the electrons some distance away.<\/div>\n<div class=\"preview-paragraph-601 preview-line 601\" data_line_start=\"601\" data_line_end=\"601\" data_line=\"601,602\" count_line=\"1\">(ii) Size of the nucleus is about <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-15)m<\/asciimath><latex style=\"display: none\">10^{-15} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>14<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>14<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-14)m<\/asciimath><latex style=\"display: none\">10^{-14} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.022ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.8 3390.2 893.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>14<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, while size of the atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-10)m<\/asciimath><latex style=\"display: none\">10^{-10} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so the electrons are at distance <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(4)m<\/asciimath><latex style=\"display: none\">10^{4} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.626ex\" height=\"2.022ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.8 2486.6 893.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1403.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mn>4<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>5<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>5<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(5)m<\/asciimath><latex style=\"display: none\">10^{5} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.626ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 2486.6 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1403.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mn>5<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from the nucleus, and being large empty space in the atom, most <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particles go through the empty space.<\/div>\n<ol start=\"4\" class=\"preview-paragraph-603 preview-line 603 604\" data_line_start=\"603\" data_line_end=\"604\" data_line=\"603,605\" count_line=\"2\">\n<li><\/li>\n<\/ol>\n<div class=\"preview-paragraph-605 preview-line 605\" data_line_start=\"605\" data_line_end=\"605\" data_line=\"605,606\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-09.jpg?height=462&width=741&top_left_y=1134&top_left_x=1040\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-607 preview-line 607\" data_line_start=\"607\" data_line_end=\"607\" data_line=\"607,608\" count_line=\"1\">Only a small fraction of the number of incident <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles (1 in 8000) rebound back. This shows that the number of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles undergoing head on collision is small. This implies that the entire positive charge of the atom is concentrated in a small volume.<\/div>\n<div class=\"preview-paragraph-609 preview-line 609\" data_line_start=\"609\" data_line_end=\"609\" data_line=\"609,610\" count_line=\"1\">So, this experiment is an important way to determine an upper limit on the size of nucleus.<\/div>\n<ol start=\"5\" class=\"preview-paragraph-611 preview-line 611 612\" data_line_start=\"611\" data_line_end=\"612\" data_line=\"611,613\" count_line=\"2\">\n<li>Assumptions of Rutherford’s atomic model :<\/li>\n<\/ol>\n<div class=\"preview-paragraph-613 preview-line 613\" data_line_start=\"613\" data_line_end=\"613\" data_line=\"613,614\" count_line=\"1\">(i) Every atom consists of a tiny central core called the atomic nucleus, in which the entire positive charge and atmost entire mass of the atom are concentrated.<\/div>\n<div class=\"preview-paragraph-615 preview-line 615\" data_line_start=\"615\" data_line_end=\"615\" data_line=\"615,616\" count_line=\"1\">(ii) The size of nucleus is of the order of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-15)m<\/asciimath><latex style=\"display: none\">10^{-15} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, which is very small as compared to the size of the atom which is of the order of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-10)m<\/asciimath><latex style=\"display: none\">10^{-10} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-617 preview-line 617\" data_line_start=\"617\" data_line_end=\"617\" data_line=\"617,618\" count_line=\"1\">(iii) The atomic nucleus is surrounded by certain number of electrons. As atom on the whole is electrically neutral, the total negative charge of electrons surrounding the nucleus is equal to total positive charge on the nucleus. (iv) The electrons revolve around the nucleus in various circular orbits.<\/div>\n<div class=\"preview-paragraph-619 preview-line 619\" data_line_start=\"619\" data_line_end=\"619\" data_line=\"619,620\" count_line=\"1\">Refer to answer 1.<\/div>\n<ol start=\"6\" class=\"preview-paragraph-621 preview-line 621 622\" data_line_start=\"621\" data_line_end=\"622\" data_line=\"621,623\" count_line=\"2\">\n<li><\/li>\n<\/ol>\n<div class=\"preview-paragraph-623 preview-line 623\" data_line_start=\"623\" data_line_end=\"623\" data_line=\"623,624\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-10.jpg?height=349&width=554&top_left_y=605&top_left_x=340\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-625 preview-line 625\" data_line_start=\"625\" data_line_end=\"625\" data_line=\"625,626\" count_line=\"1\">The size of the nucleus can be obtained by finding impact parameter <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b<\/asciimath><latex style=\"display: none\">b<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.971ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 429 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> using trajectories of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle. The impact parameter is the perpendicular distance of the initial velocity vector of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle from the central line of nucleus, when it is far away from the atom. Rutherford calculated impact parameter as<\/div>\n<div class=\"preview-paragraph-627 preview-line 627\" data_line_start=\"627\" data_line_end=\"627\" data_line=\"627,628\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b=(1)\/(4piepsi_(0))*(Ze^(2)cot(theta\/\/2))\/(E)<\/asciimath><latex style=\"display: none\">b=\\frac{1}{4 \\pi \\varepsilon_{0}} \\cdot \\frac{Z e^{2} \\cot (\\theta \/ 2)}{E}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.258ex\" height=\"3.549ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1106.5 8511.9 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210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4950.2, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1837.6, -345) scale(0.707)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><rect width=\"3975.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo>\u22c5<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>cot<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mi>E<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-629 preview-line 629\" data_line_start=\"629\" data_line_end=\"629\" data_line=\"629,630\" count_line=\"1\">where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=KE<\/asciimath><latex style=\"display: none\">E=K E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.485ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2986.6, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle<\/div>\n<div class=\"preview-paragraph-631 preview-line 631\" data_line_start=\"631\" data_line_end=\"631\" data_line=\"631,632\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta=<\/asciimath><latex style=\"display: none\">\\theta=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.45ex\" height=\"1.781ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 1524.8 787\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> scattering angle<\/div>\n<div class=\"preview-paragraph-633 preview-line 633\" data_line_start=\"633\" data_line_end=\"633\" data_line=\"633,634\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=<\/asciimath><latex style=\"display: none\">Z=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.024ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1778.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> atomic number of atom<\/div>\n<div class=\"preview-paragraph-635 preview-line 635\" data_line_start=\"635\" data_line_end=\"635\" data_line=\"635,636\" count_line=\"1\">The size of the nucleus is smaller than the impact parameter.<\/div>\n<ol start=\"7\" class=\"preview-paragraph-637 preview-line 637 638\" data_line_start=\"637\" data_line_end=\"638\" data_line=\"637,639\" count_line=\"2\">\n<li>Wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>λ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03bb<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda)<\/asciimath><latex style=\"display: none\">(\\lambda)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.079ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1361 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(972, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>\u03bb<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of Balmer series is given by<\/li>\n<\/ol>\n<div class=\"preview-paragraph-639 preview-line 639 640 641\" data_line_start=\"639\" data_line_end=\"641\" data_line=\"639,642\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mtext> where <\/mtext>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mtext>\u00a0where\u00a0<\/mtext>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R_(H)[(1)\/(2^(2))-(1)\/(n_(i)^(2))]” where “n_(i)=3,4,5,dots<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R_{H}\\left[\\frac{1}{2^{2}}-\\frac{1}{n_{i}^{2}}\\right] \\text { where } n_{i}=3,4,5, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.313ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 18260.5 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2356.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 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data-mml-node=\"mo\" transform=\"translate(16643.9, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(17088.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><msub><mi>R<\/mi><mrow><mi>H<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mtext>\u00a0where\u00a0<\/mtext><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-643 preview-line 643\" data_line_start=\"643\" data_line_end=\"643\" data_line=\"643,644\" count_line=\"1\">For shortest wavelength, when transition of electrons take place from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=oo<\/asciimath><latex style=\"display: none\">n_{i}=\\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.302ex\" height=\"1.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 3227.5 740.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 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214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=2<\/asciimath><latex style=\"display: none\">n_{f}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.499ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2872.5 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, wavelength of emitted photon is shortest.<\/div>\n<div class=\"preview-paragraph-645 preview-line 645 646 647 648 649 650\" data_line_start=\"645\" data_line_end=\"650\" data_line=\"645,651\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi mathvariant=\"normal\">∞<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.646<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3646<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.646<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3646<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[(1)\/(lambda_(min))=R_(H)[(1)\/(2^(2))-(1)\/(oo)]=(1.097 xx10^(7))\/(4)],[:.quadlambda_(min)=3.646 xx10^(-7)m=3646″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\frac{1}{\\lambda_{\\min }}=R_{H}\\left[\\frac{1}{2^{2}}-\\frac{1}{\\infty}\\right]=\\frac{1.097 \\times 10^{7}}{4} \\\\\n&\\therefore \\quad \\lambda_{\\min }=3.646 \\times 10^{-7} \\mathrm{~m}=3646 \\AA\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.889ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.923ex\" height=\"8.909ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2218.8 16761.8 3937.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 671.7)\"><g data-mml-node=\"mtd\"><\/g><g data-mml-node=\"mtd\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(875.9, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 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transform=\"translate(15238.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><msub><mi>R<\/mi><mrow><mi>H<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mi mathvariant=\"normal\">\u221e<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>4<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>3.646<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>3646<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-652 preview-line 652\" data_line_start=\"652\" data_line_end=\"652\" data_line=\"652,653\" count_line=\"1\">This wavelength lies in visible region of electromagnetic spectrum.<\/div>\n<ol start=\"8\" class=\"preview-paragraph-654 preview-line 654 655\" data_line_start=\"654\" data_line_end=\"655\" data_line=\"654,656\" count_line=\"2\">\n<li>For Lyman series,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-656 preview-line 656 657 658\" data_line_start=\"656\" data_line_end=\"658\" data_line=\"656,659\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">[<\/mo>\n <mo>∴<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2234<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R((1)\/(1^(2))-(1)\/(n^(2)))quad[:.n=2,3,4,dots]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{n^{2}}\\right) \\quad[\\therefore n=2,3,4, \\ldots]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.546ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 17037.4 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(736, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2301.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3302, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4745.6, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z\"><\/path><\/g><\/g><g data-mml-node=\"mstyle\" transform=\"translate(8597.1, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(9597.1, 0)\"><path data-c=\"5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9875.1, 0)\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(10819.9, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11697.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(12753.4, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13253.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(13698.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14198.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(14642.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(15142.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(15587.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(16759.4, 0)\"><path data-c=\"5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">[<\/mo><mo>\u2234<\/mo><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo stretchy=\"false\">]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-660 preview-line 660\" data_line_start=\"660\" data_line_end=\"660\" data_line=\"660,661\" count_line=\"1\">Let <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1)<\/asciimath><latex style=\"display: none\">\\lambda_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)<\/asciimath><latex style=\"display: none\">\\lambda_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be the wavelength of the first and second line respectively, then<\/div>\n<div class=\"preview-paragraph-662 preview-line 662 663 664\" data_line_start=\"662\" data_line_end=\"664\" data_line=\"662,665\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1<\/mn>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1<\/mn> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mn>4<\/mn>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(1))=R((1)\/(1^(2))-(1)\/(2^(2)))=R(1-(1)\/(4))=(3)\/(4)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{1}}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right)=R\\left(1-\\frac{1}{4}\\right)=\\frac{3}{4} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.086ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 18160.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(463.3, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -686)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) 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43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3519.1, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(736, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g 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285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4645.6, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(9178.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(10234.2, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 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display=\"block\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-666 preview-line 666\" data_line_start=\"666\" data_line_end=\"666\" data_line=\"666,667\" count_line=\"1\">and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1<\/mn>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1<\/mn> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mn>9<\/mn>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(2))=R((1)\/(1^(2))-(1)\/(3^(2)))=R(1-(1)\/(9))=(8)\/(9)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{2}}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right)=R\\left(1-\\frac{1}{9}\\right)=\\frac{8}{9} 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682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>9<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>8<\/mn><mn>9<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-668 preview-line 668\" data_line_start=\"668\" data_line_end=\"668\" data_line=\"668,669\" count_line=\"1\">Dividing (ii) by (i), we get<\/div>\n<div class=\"preview-paragraph-670 preview-line 670\" data_line_start=\"670\" data_line_end=\"670\" data_line=\"670,671\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <mrow>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mn>3<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <mrow>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mn>3<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">((1)\/(lambda_(2)))\/((1)\/(lambda_(1)))=((8)\/(9)R)\/((3)\/(4)R)=>(1)\/(lambda_(2))xx(lambda_(1))\/(1)=(8)\/(9)xx(4)\/(3)<\/asciimath><latex style=\"display: none\">\\frac{\\frac{1}{\\lambda_{2}}}{\\frac{1}{\\lambda_{1}}}=\\frac{\\frac{8}{9} R}{\\frac{3}{4} R} \\Rightarrow \\frac{1}{\\lambda_{2}} \\times \\frac{\\lambda_{1}}{1}=\\frac{8}{9} \\times \\frac{4}{3}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.284ex\" height=\"4.985ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1351.8 13385.3 2203.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mfrac\" transform=\"translate(220, 740.2) scale(0.707)\"><g 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622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><rect width=\"553.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><\/mfrac><mo>=<\/mo><mfrac><mrow><mfrac><mn>8<\/mn><mn>9<\/mn><\/mfrac><mi>R<\/mi><\/mrow><mrow><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mi>R<\/mi><\/mrow><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>\u00d7<\/mo><mfrac><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mn>1<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>8<\/mn><mn>9<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-672 preview-line 672\" data_line_start=\"672\" data_line_end=\"672\" data_line=\"672,673\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(1))\/(lambda_(2))=(32)\/(27)<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{1}}{\\lambda_{2}}=\\frac{32}{27}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.186ex\" height=\"3.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -936.8 3618.3 1387.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"msub\" transform=\"translate(220, 446.1) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"897.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1415.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2471.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-674 preview-line 674\" data_line_start=\"674\" data_line_end=\"674\" data_line=\"674,675\" count_line=\"1\">As <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5400<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5400<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=5400<\/asciimath><latex style=\"display: none\">\\lambda_{2}=5400<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.774ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4320.1 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1264.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2320.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5400<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-676 preview-line 676\" data_line_start=\"676\" data_line_end=\"676\" data_line=\"676,677\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mn>5400<\/mn>\n <mo>=<\/mo>\n <mn>6400<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mn>5400<\/mn>\n <mo>=<\/mo>\n <mn>6400<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadlambda_(1)=(32)\/(27)xxlambda_(2)=(32)\/(27)xx5400=6400″\u212b”<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\lambda_{1}=\\frac{32}{27} \\times \\lambda_{2}=\\frac{32}{27} \\times 5400=6400 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.044ex\" height=\"2.773ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 17257.7 1225.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 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0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(16657.7, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><mo>\u00d7<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>5400<\/mn><mo>=<\/mo><mn>6400<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"9\" class=\"preview-paragraph-678 preview-line 678 679\" data_line_start=\"678\" data_line_end=\"679\" data_line=\"678,680\" count_line=\"2\">\n<li>Since <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r propn^(2)<\/asciimath><latex style=\"display: none\">r \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.308ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 2788.1 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-680 preview-line 680\" data_line_start=\"680\" data_line_end=\"680\" data_line=\"680,681\" count_line=\"1\">For ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(1)=1<\/asciimath><latex style=\"display: none\">n_{1}=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.419ex\" height=\"1.846ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2837.1 816\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-682 preview-line 682\" data_line_start=\"682\" data_line_end=\"682\" data_line=\"682,683\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mtext>st <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mtext>st\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1^(“st “)<\/asciimath><latex style=\"display: none\">1^{\\text {st }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.897ex\" height=\"1.805ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -797.9 1280.4 797.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\" transform=\"translate(394, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(783, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>1<\/mn><mrow><mtext>st\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> excited state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=2<\/asciimath><latex style=\"display: none\">n_{2}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.419ex\" height=\"1.846ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2837.1 816\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-684 preview-line 684\" data_line_start=\"684\" data_line_end=\"684\" data_line=\"684,685\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Required ratio of radii of the orbits<\/div>\n<div class=\"preview-paragraph-686 preview-line 686 687 688\" data_line_start=\"686\" data_line_end=\"688\" data_line=\"686,689\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>:<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>:<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(r_(2))\/(r_(1))=(n_(2)^(2))\/(n_(1)^(2))=(2^(2))\/(1)=4:1<\/asciimath><latex style=\"display: none\">\\frac{r_{2}}{r_{1}}=\\frac{n_{2}^{2}}{n_{1}^{2}}=\\frac{2^{2}}{1}=4: 1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.448ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.434ex\" height=\"6.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1581.9 9915.9 2663.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"msub\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -686)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><rect width=\"1054.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1572.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2628.1, 0)\"><g data-mml-node=\"msubsup\" transform=\"translate(220, 747.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 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370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9415.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><msub><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msubsup><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>=<\/mo><mfrac><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><mn>1<\/mn><\/mfrac><mo>=<\/mo><mn>4<\/mn><mo>:<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"10\" class=\"preview-paragraph-690 preview-line 690 691\" data_line_start=\"690\" data_line_end=\"691\" data_line=\"690,692\" count_line=\"2\">\n<li>Ionisation energy for an atom is defined as the energy required to remove an electron completely from the outermost shell of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-692 preview-line 692\" data_line_start=\"692\" data_line_end=\"692\" data_line=\"692,693\" count_line=\"1\">For hydrogen atom,<\/div>\n<div class=\"preview-paragraph-694 preview-line 694 695 696\" data_line_start=\"694\" data_line_end=\"696\" data_line=\"694,697\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi mathvariant=\"normal\">∞<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(oo)-E_(1)=0-(-13.6)eV=13.6eV<\/asciimath><latex style=\"display: none\">E=E_{\\infty}-E_{1}=0-(-13.6) \\mathrm{eV}=13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"40.376ex\" height=\"2.262ex\" role=\"img\" 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620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi mathvariant=\"normal\">\u221e<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"11\" class=\"preview-paragraph-698 preview-line 698 699\" data_line_start=\"698\" data_line_end=\"699\" data_line=\"698,700\" count_line=\"2\">\n<li>Quantum condition : The stationary orbits are those in which angular momentum of electron is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi)<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.707ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 1196.6 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e.,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-700 preview-line 700 701 702\" data_line_start=\"700\" data_line_end=\"702\" data_line=\"700,703\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=n(h)\/(2pi),n=1,2,3,dots<\/asciimath><latex style=\"display: none\">m v r=n \\frac{h}{2 \\pi}, n=1,2,3, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.339ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 11641.8 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 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685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 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340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9080.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9525.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10025.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10469.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-704 preview-line 704\" data_line_start=\"704\" data_line_end=\"704\" data_line=\"704,705\" count_line=\"1\">Integer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called the principal quantum number. This equation is called Bohr’s quantum condition.<\/div>\n<ol start=\"12\" class=\"preview-paragraph-706 preview-line 706 707\" data_line_start=\"706\" data_line_end=\"707\" data_line=\"706,708\" count_line=\"2\">\n<li>Frequency condition : An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-708 preview-line 708 709 710\" data_line_start=\"708\" data_line_end=\"710\" data_line=\"708,711\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">h v=E_{i}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.181ex\" height=\"2.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 5825.9 989\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1338.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2394.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3648.7, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4649, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-712 preview-line 712\" data_line_start=\"712\" data_line_end=\"712\" data_line=\"712,713\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is frequency of radiation emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies associated with stationary orbits of principal quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> respectively <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(:}<\/asciimath><latex style=\"display: none\">\\left(\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(389, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i) > n_(f)<\/asciimath><latex style=\"display: none\">n_{i}>n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.39ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -540 3266.4 835\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2227.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>><\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-714 preview-line 714\" data_line_start=\"714\" data_line_end=\"714\" data_line=\"714,715\" count_line=\"1\">13 According to Bohr’s theory, a hydrogen atom consists of a nucleus with a positive charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Ze<\/asciimath><latex style=\"display: none\">Z e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.69ex\" height=\"1.57ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1189 694\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(723, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, and a single electron of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, which revolves around it in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-716 preview-line 716\" data_line_start=\"716\" data_line_end=\"716\" data_line=\"716,717\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-11.jpg?height=217&width=285&top_left_y=557&top_left_x=491\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-718 preview-line 718\" data_line_start=\"718\" data_line_end=\"718\" data_line=\"718,719\" count_line=\"1\">Here <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z<\/asciimath><latex style=\"display: none\">Z<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.636ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 723 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the atomic number and for hydrogen <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The electrostatic force of attraction between the hydrogen nucleus and the electron is<\/div>\n<div class=\"preview-paragraph-720 preview-line 720\" data_line_start=\"720\" data_line_end=\"720\" data_line=\"720,721\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>e<\/mi>\n <mo>⋅<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>e<\/mi>\n <mo>\u22c5<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"[\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">F=(ke*e)\/(r^(2))=(ke^(2))\/(r^(2))quad[:}<\/asciimath><latex style=\"display: none\">F=\\frac{k e \\cdot e}{r^{2}}=\\frac{k e^{2}}{r^{2}} \\quad\\left[\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.605ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 7781.4 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1026.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2082.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(987, 0)\"><path data-c=\"22C5\" d=\"M78 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239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1424\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4024.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5080.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(6503.4, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(7503.4, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(278, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>F<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>e<\/mi><mo>\u22c5<\/mo><mi>e<\/mi><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <mi>k<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"\" close=\"]\" separators=\"|\">\n <mrow>\n <mi>k<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:k=(1)\/(4piepsi_(0))]<\/asciimath><latex style=\"display: none\">\\left.k=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.362ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 4138 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><\/g><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1854.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 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1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><mi>k<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-722 preview-line 722\" data_line_start=\"722\" data_line_end=\"722\" data_line=\"722,723\" count_line=\"1\">To keep the electron in its orbit, the centripetal force on the electron must be equal to the electrostatic attraction. Therefore,<\/div>\n<div class=\"preview-paragraph-724 preview-line 724\" data_line_start=\"724\" data_line_end=\"724\" data_line=\"724,725\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(ke^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.059ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4446 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) 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data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-726 preview-line 726\" data_line_start=\"726\" data_line_end=\"726\" data_line=\"726,727\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.234ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4523.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2044.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3100.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 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316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-728 preview-line 728\" data_line_start=\"728\" data_line_end=\"728\" data_line=\"728,729\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(ke^(2))\/(mv^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{k e^{2}}{m v^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.859ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 3473.7 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-730 preview-line 730\" data_line_start=\"730\" data_line_end=\"730\" data_line=\"730,731\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the mass of the electron, and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, its speed in an orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-732 preview-line 732\" data_line_start=\"732\" data_line_end=\"732\" data_line=\"732,733\" count_line=\"1\">Bohr’s quantisation condition for angular momentum is<\/div>\n<div class=\"preview-paragraph-734 preview-line 734\" data_line_start=\"734\" data_line_end=\"734\" data_line=\"734,735\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">L=m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.556ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6433.7 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(958.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2014.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2892.6, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3377.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4106.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5162.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi mv)<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.925ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3944.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-736 preview-line 736\" data_line_start=\"736\" data_line_end=\"736\" data_line=\"736,737\" count_line=\"1\">From equation (ii) and (iii), we get<\/div>\n<div class=\"preview-paragraph-738 preview-line 738\" data_line_start=\"738\" data_line_end=\"738\" data_line=\"738,739\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(ke^(2))\/(mv^(2))=(nh)\/(2pi mv)quad<\/asciimath><latex style=\"display: none\">\\frac{k e^{2}}{m v^{2}}=\\frac{n h}{2 \\pi m v} \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.989ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6183.1 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(352.9, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(5183.1, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad v=(2pi ke^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\quad v=\\frac{2 \\pi k e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.309ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4998.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1000, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1591, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(674.2, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"1939.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-740 preview-line 740\" data_line_start=\"740\" data_line_end=\"740\" data_line=\"740,741\" count_line=\"1\">Substituting this value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (iii), we get<\/div>\n<div class=\"preview-paragraph-742 preview-line 742\" data_line_start=\"742\" data_line_end=\"742\" data_line=\"742,743\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi m)*(nh)\/(2pi ke^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m} \\cdot \\frac{n h}{2 \\pi k e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.716ex\" height=\"2.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6504.3 1322.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(492.9, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1577.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3824.2, 0)\"><path data-c=\"22C5\" d=\"M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4324.4, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(674.2, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1591, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1939.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><\/mrow><\/mfrac><mo>\u22c5<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-744 preview-line 744\" data_line_start=\"744\" data_line_end=\"744\" data_line=\"744,745\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>r=(n^(2)h^(2))\/(4pi^(2)mke^(2))quad:.r propn^(2)<\/asciimath><latex style=\"display: none\">\\Rightarrow r=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k e^{2}} \\quad \\therefore r \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.247ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 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157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"14\" class=\"preview-paragraph-746 preview-line 746 747\" data_line_start=\"746\" data_line_end=\"747\" data_line=\"746,748\" count_line=\"2\">\n<li>Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of hydrogen atom : In <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, an electron having charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> revolves around the nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, such that necessary centripetal force is provided by the electrostatic force of attraction between the electron and nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-748 preview-line 748\" data_line_start=\"748\" data_line_end=\"748\" data_line=\"748,749\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-11.jpg?height=242&width=374&top_left_y=453&top_left_x=1224\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-750 preview-line 750\" data_line_start=\"750\" data_line_end=\"750\" data_line=\"750,751\" count_line=\"1\">i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>e<\/mi>\n <mo>.<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>e<\/mi>\n <mo>.<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))(e.e)\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e . e}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.868ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6129.8 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 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411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 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61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(744, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(345.7, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1055.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>e<\/mi><mo>.<\/mo><mi>e<\/mi><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.499ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5966.4 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(368, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"814.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-752 preview-line 752\" data_line_start=\"752\" data_line_end=\"752\" data_line=\"752,753\" count_line=\"1\">From Bohr’s quantization condition<\/div>\n<div class=\"preview-paragraph-754 preview-line 754\" data_line_start=\"754\" data_line_end=\"754\" data_line=\"754,755\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container 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147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-756 preview-line 756\" data_line_start=\"756\" data_line_end=\"756\" data_line=\"756,757\" count_line=\"1\">Using equation (ii) in (i), we get<\/div>\n<div class=\"preview-paragraph-758 preview-line 758\" data_line_start=\"758\" data_line_end=\"758\" data_line=\"758,759\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>⋅<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>\u22c5<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m*((nh)\/(2pi mr))^(2)=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">m \\cdot\\left(\\frac{n h}{2 \\pi m r}\\right)^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.942ex\" height=\"3.495ex\" role=\"img\" focusable=\"false\" 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <mo>⋅<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <mo>\u22c5<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m*n^(2)h^(2))\/(4pi^(2)m^(2)r^(2))=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">\\frac{m \\cdot n^{2} h^{2}}{4 \\pi^{2} m^{2} r^{2}}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.272ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 7192.3 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(386.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><mo>\u22c5<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>m<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-760 preview-line 760\" data_line_start=\"760\" data_line_end=\"760\" data_line=\"760,761\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(n^(2)h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n^{2} h^{2} \\varepsilon_{0}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.597ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4241.7 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 457.1) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1003.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(1983.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(409.2, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2217.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-762 preview-line 762\" data_line_start=\"762\" data_line_end=\"762\" data_line=\"762,763\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,2,3,dots<\/asciimath><latex style=\"display: none\">n=1,2,3, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.438ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 5939.6 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2878.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3378.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3822.9, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4322.9, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4767.6, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is principal quantum number. Equation (iii), gives the radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom. So the radii of the orbits increase proportionally with <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mi>r<\/mi> \n <mo>\u221d<\/mo> \n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">[r propn^(2)]<\/asciimath><latex style=\"display: none\">\\left[r \\propto n^{2}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.195ex\" height=\"2.713ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -849.5 3622.1 1199\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M202 -349V850H394V810H242V-309H394V-349H202Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(417, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1145.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2201.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3205.1, 0)\"><path data-c=\"5D\" d=\"M22 810V850H214V-349H22V-309H174V810H22Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Radius of first orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom is called Bohr radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)<\/asciimath><latex style=\"display: none\">a_{0}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.11ex\" height=\"1.372ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -441 932.6 606.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and is given by<\/div>\n<div class=\"preview-paragraph-764 preview-line 764\" data_line_start=\"764\" data_line_end=\"764\" data_line=\"764,765\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)=(h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">a_{0}=\\frac{h^{2} \\varepsilon_{0}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.83ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4344.9 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1210.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2266.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(385.6, 457.1) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(979.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 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435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1838.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> for <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)=0.529″\u212b”<\/asciimath><latex style=\"display: none\">a_{0}=0.529 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.638ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 5144.1 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1210.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2266.1, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4544.1, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>0.529<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-766 preview-line 766\" data_line_start=\"766\" data_line_end=\"766\" data_line=\"766,767\" count_line=\"1\">So, radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom then becomes<\/div>\n<div class=\"preview-paragraph-768 preview-line 768\" data_line_start=\"768\" data_line_end=\"768\" data_line=\"768,769\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=n^(2)xx0.529″\u212b”<\/asciimath><latex style=\"display: none\">r=n^{2} \\times 0.529 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.585ex\" height=\"2.339ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 6888.6 1033.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3010.3, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4010.6, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6288.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>0.529<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"15\" class=\"preview-paragraph-770 preview-line 770 771\" data_line_start=\"770\" data_line_end=\"771\" data_line=\"770,772\" count_line=\"2\">\n<li>(i) Since, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>;<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>g<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>;<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>g<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r propn^(2);(r_(n))\/(r_(g))=(n^(2))\/(1^(2))<\/asciimath><latex style=\"display: none\">r \\propto n^{2} ; \\frac{r_{n}}{r_{g}}=\\frac{n^{2}}{1^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.252ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.408ex\" height=\"3.478ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6810.2 1537.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2788.1, 0)\"><path data-c=\"3B\" d=\"M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 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data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(250.8, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><\/g><\/g><\/g><rect width=\"854.3\" 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285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(255.4, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>;<\/mo><mfrac><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mi>g<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-772 preview-line 772\" data_line_start=\"772\" data_line_end=\"772\" data_line=\"772,773\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mn>21.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mn>21.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(21.2 xx10^(-11))\/(5.3 xx10^(-11))=(n^(2))\/(1)<\/asciimath><latex style=\"display: none\">\\frac{21.2 \\times 10^{-11}}{5.3 \\times 10^{-11}}=\\frac{n^{2}}{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.394ex\" height=\"3.329ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1004.9 6362 1471.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 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387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(398, -345) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mn>21.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mn>1<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-774 preview-line 774\" data_line_start=\"774\" data_line_end=\"774\" data_line=\"774,775\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>212<\/mn>\n <mn>53<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">⇒<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>212<\/mn>\n <mn>53<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(212)\/(53)=n^(2)=>n^(2)=4quad<\/asciimath><latex style=\"display: none\">\\frac{212}{53}=n^{2} \\Rightarrow n^{2}=4 \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.883ex\" height=\"2.773ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 9230.4 1225.5\" aria-hidden=\"true\"><g 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383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(6674.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(7730.4, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(8230.4, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>212<\/mn><mn>53<\/mn><\/mfrac><mo>=<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">\u21d2<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mn>4<\/mn><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <msqrt>\n <mn>4<\/mn>\n <\/msqrt>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <msqrt>\n <mn>4<\/mn>\n <\/msqrt>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad n=sqrt4=2<\/asciimath><latex style=\"display: none\">\\quad n=\\sqrt{4}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.213ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.846ex\" height=\"2.398ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -966 6120.1 1060\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1000, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msqrt\" transform=\"translate(2933.6, 0)\"><g transform=\"translate(853, 0)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(0, 106)\"><path data-c=\"221A\" d=\"M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z\"><\/path><\/g><rect width=\"500\" height=\"60\" x=\"853\" y=\"846\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4564.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5620.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>n<\/mi><mo>=<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-776 preview-line 776\" data_line_start=\"776\" data_line_end=\"776\" data_line=\"776,777\" count_line=\"1\">(ii) We know that <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-13.6)\/(n^(2))=(-13.6)\/(4)=-3.4eV<\/asciimath><latex style=\"display: none\">E=\\frac{-13.6}{n^{2}}=\\frac{-13.6}{4}=-3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.302ex\" height=\"2.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 12509.4 1306.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><mn>4<\/mn><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"16\" class=\"preview-paragraph-778 preview-line 778 779\" data_line_start=\"778\" data_line_end=\"779\" data_line=\"778,780\" count_line=\"2\">\n<li>(a) Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)propn^(2)<\/asciimath><latex style=\"display: none\">r_{n} \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.381ex\" height=\"2.244ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 3262.4 991.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1203, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2258.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-780 preview-line 780\" data_line_start=\"780\" data_line_end=\"780\" data_line=\"780,781\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>9<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>9<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>(r_(3))\/(r_(1))=(3^(2))\/(1^(2))=9<\/asciimath><latex style=\"display: none\">\\Rightarrow \\frac{r_{3}}{r_{1}}=\\frac{3^{2}}{1^{2}}=9<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.86ex\" height=\"3.246ex\" role=\"img\" focusable=\"false\" viewBox=\"0 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400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 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429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5012.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(6068.1, 0)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><msub><mi>r<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mn>9<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-782 preview-line 782\" data_line_start=\"782\" data_line_end=\"782\" data_line=\"782,783\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <mo>×<\/mo>\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(3)=9r_(1)=9xx5.3 xx10^(-11)<\/asciimath><latex style=\"display: none\">r_{3}=9 r_{1}=9 \\times 5.3 \\times 10^{-11}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.806ex\" height=\"2.329ex\" role=\"img\" 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count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>47.7<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4.77<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>47.7<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4.77<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>47.7<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>4.77<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-786 preview-line 786\" data_line_start=\"786\" data_line_end=\"786\" data_line=\"786,787\" count_line=\"1\">(b) (i) Kinetic Energy,<\/div>\n<div class=\"preview-paragraph-788 preview-line 788\" data_line_start=\"788\" data_line_end=\"788\" data_line=\"788,789\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>×<\/mo>\n <mn>1<\/mn>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1<\/mn>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=-E=-(-3.4)xx1=3.4eV<\/asciimath><latex style=\"display: none\">E_{k}=-E=-(-3.4) \\times 1=3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.818ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14505.5 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 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data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13311.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mn>1<\/mn><mo>=<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-790 preview-line 790\" data_line_start=\"790\" data_line_end=\"790\" data_line=\"790,791\" count_line=\"1\">(ii) Potential Energy,<\/div>\n<div class=\"preview-paragraph-792 preview-line 792\" data_line_start=\"792\" data_line_end=\"792\" data_line=\"792,793\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>6.8<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>6.8<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=2E=-3.4 xx2=-6.8eV<\/asciimath><latex style=\"display: none\">E_{p}=2 E=-3.4 \\times 2=-6.8 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.4ex\" height=\"2.195ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 13436.8 970.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 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183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2977.2, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4019, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5074.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5852.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 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417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(12242.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>6.8<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> 17. (i) According to Bohr’s postulates, in a hydrogen atom, as single electron revolves around a nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. For an electron moving with a uniform speed in a circular orbit of a given radius, the centripetal force is provided by coulomb force of attraction between the electron and the nucleus. The gravitational attraction may be neglected as the mass of electron and proton is very small.<\/div>\n<div class=\"preview-paragraph-794 preview-line 794\" data_line_start=\"794\" data_line_end=\"794\" data_line=\"794,795\" count_line=\"1\">So, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(ke^(2))\/(r^(2))quad(:}<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}} \\quad\\left(\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.201ex\" 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41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(4446, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(5446, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(389, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <mi>k<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"\" close=\")\" separators=\"|\">\n <mrow>\n <mi>k<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:k=(1)\/(4piepsi_(0)))<\/asciimath><latex style=\"display: none\">\\left.k=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.645ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 4263 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><\/g><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1854.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3666, 0)\"><path data-c=\"29\" d=\"M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><mi>k<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-796 preview-line 796\" data_line_start=\"796\" data_line_end=\"796\" data_line=\"796,797\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.234ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4523.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2044.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3100.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-798 preview-line 798\" data_line_start=\"798\" data_line_end=\"798\" data_line=\"798,799\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m=<\/asciimath><latex style=\"display: none\">m=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.375ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1933.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1155.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> mass of electron<\/div>\n<div class=\"preview-paragraph-800 preview-line 800\" data_line_start=\"800\" data_line_end=\"800\" data_line=\"800,801\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=<\/asciimath><latex style=\"display: none\">r=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.409ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1506.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> radius of electronic orbit<\/div>\n<div class=\"preview-paragraph-802 preview-line 802\" data_line_start=\"802\" data_line_end=\"802\" data_line=\"802,803\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=<\/asciimath><latex style=\"display: none\">v=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.486ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1540.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> velocity of electron<\/div>\n<div class=\"preview-paragraph-804 preview-line 804\" data_line_start=\"804\" data_line_end=\"804\" data_line=\"804,805\" count_line=\"1\">Again, by Bohr’s second postulates<\/div>\n<div class=\"preview-paragraph-806 preview-line 806\" data_line_start=\"806\" data_line_end=\"806\" data_line=\"806,807\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-808 preview-line 808\" data_line_start=\"808\" data_line_end=\"808\" data_line=\"808,809\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,2,3dots dots<\/asciimath><latex style=\"display: none\">n=1,2,3 \\ldots \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.838ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 7000.2 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2878.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3378.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3822.9, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4489.6, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5828.2, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-810 preview-line 810\" data_line_start=\"810\" data_line_end=\"810\" data_line=\"810,811\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.948ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3954.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(652.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-812 preview-line 812\" data_line_start=\"812\" data_line_end=\"812\" data_line=\"812,813\" count_line=\"1\">Putting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in eq. (i)<\/div>\n<div class=\"preview-paragraph-814 preview-line 814\" data_line_start=\"814\" data_line_end=\"814\" data_line=\"814,815\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m((nh)\/(2pi mr))^(2)=(ke^(2))\/(r)=>r=(n^(2)h^(2))\/(4pi^(2)kme^(2))<\/asciimath><latex style=\"display: none\">m\\left(\\frac{n h}{2 \\pi m r}\\right)^{2}=\\frac{k e^{2}}{r} \\Rightarrow r=\\frac{n^{2} h^{2}}{4 \\pi^{2} k m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.581ex\" height=\"3.439ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1082.7 13516.9 1520.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path 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415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>k<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-816 preview-line 816\" data_line_start=\"816\" data_line_end=\"816\" data_line=\"816,817\" count_line=\"1\">Kinetic energy of electron,<\/div>\n<div class=\"preview-paragraph-818 preview-line 818\" data_line_start=\"818\" data_line_end=\"818\" data_line=\"818,819\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>∵<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2235<\/mo> \n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac> \n <mo>=<\/mo> \n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=(1)\/(2)mv^(2)=(ke^(2))\/(2r)quad(:'(mv^(2))\/(r)=(ke^(2))\/(r^(2)))<\/asciimath><latex style=\"display: none\">E_{k}=\\frac{1}{2} m v^{2}=\\frac{k e^{2}}{2 r} \\quad\\left(\\because \\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.823ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" 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29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(4161.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g 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206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5987.7, 0)\"><path data-c=\"29\" d=\"M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo>\u2235<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-820 preview-line 820\" data_line_start=\"820\" data_line_end=\"820\" data_line=\"820,821\" count_line=\"1\">Using eq. (ii) we get<\/div>\n<div class=\"preview-paragraph-822 preview-line 822\" data_line_start=\"822\" data_line_end=\"822\" data_line=\"822,823\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=(ke^(2))\/(2)(4pi^(2)kme^(2))\/(n^(2)h^(2))=(2pi^(2)k^(2)me^(4))\/(n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{k}=\\frac{k e^{2}}{2} \\frac{4 \\pi^{2} k m e^{2}}{n^{2} h^{2}}=\\frac{2 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.48ex\" 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383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1003.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3131.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mn>2<\/mn><\/mfrac><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>k<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-824 preview-line 824\" data_line_start=\"824\" data_line_end=\"824\" data_line=\"824,825\" count_line=\"1\">Potential energy of electron,<\/div>\n<div class=\"preview-paragraph-826 preview-line 826\" data_line_start=\"826\" data_line_end=\"826\" data_line=\"826,827\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>×<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u00d7<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=-(k(e)xx(e))\/(r)=-(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">E_{p}=-\\frac{k(e) \\times(e)}{r}=-\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.416ex\" height=\"3.167ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1047.1 9907.9 1399.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g 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347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2477.2, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3255.2, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 516.8) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(521, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(910, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1376, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1765, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2543, 0)\"><path 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-250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1399.5, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"2877.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(6650.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7706.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(8484.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>k<\/mi><mo stretchy=\"false\">(<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-828 preview-line 828\" data_line_start=\"828\" data_line_end=\"828\" data_line=\"828,829\" count_line=\"1\">Using eq. (ii), we get<\/div>\n<div class=\"preview-paragraph-830 preview-line 830\" data_line_start=\"830\" data_line_end=\"830\" data_line=\"830,831\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=-ke^(2)xx(4pi^(2)kme^(2))\/(n^(2)h^(2))=-(4pik^(2)me^(4))\/(n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{p}=-k e^{2} \\times \\frac{4 \\pi^{2} k m e^{2}}{n^{2} h^{2}}=-\\frac{4 \\pi k^{2} m e^{4}}{n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.018ex\" height=\"3.228ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 14151.9 1426.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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count_line=\"1\">Hence, total energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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<mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-(4pi^(2)k^(2)me^(4))\/(n^(2)h^(2))+(2pi^(2)k^(2)me^(4))\/(n^(2)h^(2))<\/asciimath><latex style=\"display: none\">=-\\frac{4 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}+\\frac{2 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.17ex\" height=\"3.228ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 9799.1 1426.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-836 preview-line 836\" data_line_start=\"836\" data_line_end=\"836\" data_line=\"836,837\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-(2pi^(2)k^(2)me^(4))\/(n^(2)h^(2))=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">=-\\frac{2 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.095ex\" 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mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> When the electron in a hydrogen atom jumps from higher energy level to the lower energy level, the difference of energies of the two energy levels is emitted as a radiation of particular wavelength. It is called a spectral line.<\/div>\n<div class=\"preview-paragraph-838 preview-line 838\" data_line_start=\"838\" data_line_end=\"838\" data_line=\"838,839\" count_line=\"1\">(ii) In <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, when an electron jumps form the orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, the wavelength of the emitted radiation is given by<\/div>\n<div class=\"preview-paragraph-840 preview-line 840 841 842\" data_line_start=\"840\" data_line_end=\"842\" data_line=\"840,843\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>;<\/mo>\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>;<\/mo>\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))];R=1.09 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right] ; R=1.09 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.376ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 17404.4 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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-21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9907.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(10963.7, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(12963.9, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(13964.1, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 413) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(15367.7, 0)\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 413) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>;<\/mo><mi>R<\/mi><mo>=<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-844 preview-line 844\" data_line_start=\"844\" data_line_end=\"844\" data_line=\"844,845\" count_line=\"1\">For Balmar series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=2<\/asciimath><latex style=\"display: none\">n_{f}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.499ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2872.5 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3,4,5,dots dots<\/asciimath><latex style=\"display: none\">n_{i}=3,4,5, \\ldots \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.132ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 7572.2 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2727.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3172.2, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3672.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4116.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4616.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5061.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6400.2, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-846 preview-line 846 847 848\" data_line_start=\"846\" data_line_end=\"848\" data_line=\"846,849\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R((1)\/(2^(2))-(1)\/(n_(i)^(2)))<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left(\\frac{1}{2^{2}}-\\frac{1}{n_{i}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.704ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8709.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(792, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2357.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3358, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4801.6, 0)\"><path data-c=\"29\" d=\"M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-850 preview-line 850\" data_line_start=\"850\" data_line_end=\"850\" data_line=\"850,851\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3,4,5,dots<\/asciimath><latex style=\"display: none\">n_{i}=3,4,5, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.103ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 6233.5 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2727.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3172.2, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3672.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4116.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4616.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5061.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-852 preview-line 852\" data_line_start=\"852\" data_line_end=\"852\" data_line=\"852,853\" count_line=\"1\">These spectral lines lie on the visible region.<\/div>\n<div class=\"preview-paragraph-854 preview-line 854\" data_line_start=\"854\" data_line_end=\"854\" data_line=\"854,855\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-12.jpg?height=498&width=611&top_left_y=1213&top_left_x=1131\" alt=\"\"><\/div>\n<ol start=\"18\" class=\"preview-paragraph-856 preview-line 856 857\" data_line_start=\"856\" data_line_end=\"857\" data_line=\"856,858\" count_line=\"2\">\n<li>According to Bohr’s postulates for hydrogen atom, electron revolves in a circular orbit around the heavy positively charged nucleus. These are the stationary (orbits) states of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-858 preview-line 858\" data_line_start=\"858\" data_line_end=\"858\" data_line=\"858,859\" count_line=\"1\">For a particular orbit, electron moves there, so it has kinetic energy.<\/div>\n<div class=\"preview-paragraph-860 preview-line 860\" data_line_start=\"860\" data_line_end=\"860\" data_line=\"860,861\" count_line=\"1\">Also, there is potential energy due to charge on electron and heavy positively charged nucleus.<\/div>\n<div class=\"preview-paragraph-862 preview-line 862\" data_line_start=\"862\" data_line_end=\"862\" data_line=\"862,863\" count_line=\"1\">Hence, total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of atom is sum of kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(K)<\/asciimath><latex style=\"display: none\">(K)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.771ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1667 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1278, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>K<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(U)<\/asciimath><latex style=\"display: none\">(U)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.495ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1545 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1156, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>U<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-864 preview-line 864\" data_line_start=\"864\" data_line_end=\"864\" data_line=\"864,865\" count_line=\"1\">i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mo>+<\/mo>\n <mi>U<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mo>+<\/mo>\n <mi>U<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=K+U<\/asciimath><latex style=\"display: none\">E=K+U<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.258ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4976 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3208.8, 0)\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4209, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mo>+<\/mo><mi>U<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-866 preview-line 866\" data_line_start=\"866\" data_line_end=\"866\" data_line=\"866,867\" count_line=\"1\">Let us assume that the nucleus has positive charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Ze<\/asciimath><latex style=\"display: none\">Z e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.69ex\" height=\"1.57ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1189 694\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(723, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. An electron moving with a constant speed <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> along a circle of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> with centre at the nucleus.<\/div>\n<div class=\"preview-paragraph-868 preview-line 868 869 870\" data_line_start=\"868\" data_line_end=\"870\" data_line=\"868,871\" count_line=\"3\">Force acting on electron due to nucleus is given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">F=(Ze^(2))\/(4piepsi_(0)r^(2))<\/asciimath><latex style=\"display: none\">F=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.237ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.177ex\" height=\"3.463ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4498.3 1530.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1026.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2082.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(644.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1939.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2175.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>F<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><br>\nThe acceleration of electron <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(v^(2))\/(r)<\/asciimath><latex style=\"display: none\">=\\frac{v^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.806ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 2124.1 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1055.8, 0)\"><g data-mml-node=\"msup\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(374.7, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"828.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (towards the<br>\ncentre).<\/div>\n<div class=\"preview-paragraph-872 preview-line 872\" data_line_start=\"872\" data_line_end=\"872\" data_line=\"872,873\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m=<\/asciimath><latex style=\"display: none\">m=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.375ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1933.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1155.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> mass of an electron, then from Newton’s second law<\/div>\n<div class=\"preview-paragraph-874 preview-line 874 875 876 877 878 879\" data_line_start=\"874\" data_line_end=\"879\" data_line=\"874,880\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[F=m((v^(2))\/(r))],[=>(Ze^(2))\/(4piepsi_(0)r^(2))=m((v^(2))\/(r))=>r=(Ze^(2))\/(4piepsi_(0)mv^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&F=m\\left(\\frac{v^{2}}{r}\\right) \\\\\n&\\Rightarrow \\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r^{2}}=m\\left(\\frac{v^{2}}{r}\\right) \\Rightarrow r=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} m v^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.349ex\" 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308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2817.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3906.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>F<\/mi><mo>=<\/mo><mi>m<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mi>m<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-881 preview-line 881\" data_line_start=\"881\" data_line_end=\"881\" data_line=\"881,882\" count_line=\"1\">From Bohr’s quantisation rules,<\/div>\n<div class=\"preview-paragraph-883 preview-line 883 884 885\" data_line_start=\"883\" data_line_end=\"885\" data_line=\"883,886\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.895ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 5257.6 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3147.6, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3747.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(467, 676)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-887 preview-line 887\" data_line_start=\"887\" data_line_end=\"887\" data_line=\"887,888\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is a positive integer<\/div>\n<div class=\"preview-paragraph-889 preview-line 889\" data_line_start=\"889\" data_line_end=\"889\" data_line=\"889,890\" count_line=\"1\">Substituting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from eq. (i), we get<\/div>\n<div class=\"preview-paragraph-891 preview-line 891 892 893\" data_line_start=\"891\" data_line_end=\"893\" data_line=\"891,894\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>m<\/mi> \n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv*(Ze^(2))\/(4piepsi_(0)(mv^(2)))=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v \\cdot \\frac{Z e^{2}}{4 \\pi \\varepsilon_{0}\\left(m v^{2}\\right)}=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.622ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.962ex\" height=\"6.038ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 10591.1 2668.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1585.2, 0)\"><path data-c=\"22C5\" d=\"M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 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48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1939.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M152 251Q152 646 388 850H416Q422 844 422 841Q422 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342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1336, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 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d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mo>\u22c5<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-895 preview-line 895 896 897 898 899\" data_line_start=\"895\" data_line_end=\"899\" data_line=\"895,900\" count_line=\"5\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:v=(Ze^(2))\/(2epsi_(0)hn):}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n& v=\\frac{Z e^{2}}{2 \\varepsilon_{0} h n}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.106ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.869ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1430.7 4804.1 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, -79.2)\"><g data-mml-node=\"mtd\"><\/g><g data-mml-node=\"mtd\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(696.5, 676)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 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130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"2745.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>h<\/mi><mi>n<\/mi><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-901 preview-line 901\" data_line_start=\"901\" data_line_end=\"901\" data_line=\"901,902\" count_line=\"1\">So, kinetic energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(2)mv^(2)=(Z^(2)e^(4))\/(8epsi_(0)^(2)h^(2)n^(2))<\/asciimath><latex style=\"display: none\">K=\\frac{1}{2} m v^{2}=\\frac{Z^{2} e^{4}}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.197ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 8926.9 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 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345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2570.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-903 preview-line 903\" data_line_start=\"903\" data_line_end=\"903\" data_line=\"903,904\" count_line=\"1\">Potential energy of the atom,<\/div>\n<div class=\"preview-paragraph-905 preview-line 905 906 907\" data_line_start=\"905\" data_line_end=\"907\" data_line=\"905,908\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">U=-(Ze^(2))\/(4piepsi_(0)r)<\/asciimath><latex style=\"display: none\">U=-\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.917ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 5709.1 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1044.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2100.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2878.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(619, 676)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"2590.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>U<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-909 preview-line 909\" data_line_start=\"909\" data_line_end=\"909\" data_line=\"909,910\" count_line=\"1\">Using eq. (iii) in eq. (i), we get<\/div>\n<div class=\"preview-paragraph-911 preview-line 911 912 913 914 915 916\" data_line_start=\"911\" data_line_end=\"916\" data_line=\"911,917\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <mfrac>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <mfrac>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>Z<\/mi> \n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>2<\/mn> \n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub> \n <mi>h<\/mi> \n <mi>n<\/mi> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>4<\/mn> \n <mi>\u03c0<\/mi> \n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[r=(Ze^(2))\/(4piepsi_(0)m((Ze^(2))^(2))\/((2epsi_(0)hn)^(2)))=(4epsi_(0)^(2)h^(2)n^(2))\/((4piepsi_(0))mZe^(2))],[r=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&r=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} m \\frac{\\left(Z e^{2}\\right)^{2}}{\\left(2 \\varepsilon_{0} h n\\right)^{2}}}=\\frac{4 \\varepsilon_{0}^{2} h^{2} n^{2}}{\\left(4 \\pi \\varepsilon_{0}\\right) m Z e^{2}} \\\\\n&r=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -6.434ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.116ex\" height=\"13.998ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -3343.6 15079.2 6187.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3240.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>m<\/mi><mfrac><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>2<\/mn><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>h<\/mi><mi>n<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-918 preview-line 918\" data_line_start=\"918\" data_line_end=\"918\" data_line=\"918,919\" count_line=\"1\">Using value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in eq. ( <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">v<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">v<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v)<\/asciimath><latex style=\"display: none\">\\mathrm{v})<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.075ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 917 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M338 431Q344 429 422 429Q479 429 503 431H508V385H497Q439 381 423 345Q421 341 356 172T288 -2Q283 -11 263 -11Q244 -11 239 -2Q99 359 98 364Q93 378 82 381T43 385H19V431H25L33 430Q41 430 53 430T79 430T104 429T122 428Q217 428 232 431H240V385H226Q187 384 184 370Q184 366 235 234L286 102L377 341V349Q377 363 367 372T349 383T335 385H331V431H338Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(528, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">v<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, we get<\/div>\n<div class=\"preview-paragraph-920 preview-line 920 921 922\" data_line_start=\"920\" data_line_end=\"922\" data_line=\"920,923\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">U=(-Ze^(2))\/(4piepsi_(0)((epsi_(0)h^(2)n^(2))\/(pi mZe^(2))))=(-Z^(2)e^(4)m)\/(4epsi_(0)^(2)h^(2)n^(2))<\/asciimath><latex style=\"display: none\">U=\\frac{-Z e^{2}}{4 \\pi \\varepsilon_{0}\\left(\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\\right)}=\\frac{-Z^{2} e^{4} m}{4 \\varepsilon_{0}^{2} h^{2} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.98ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"31.104ex\" height=\"7.413ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1517.7 13747.8 3276.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path 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221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -1109.5)\"><g 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11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1939.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(597, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(286.4, 457.1) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(869.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1849.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1448, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 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309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3910.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>U<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-924 preview-line 924\" data_line_start=\"924\" data_line_end=\"924\" data_line=\"924,925\" count_line=\"1\">So, the total energy,<\/div>\n<div class=\"preview-paragraph-926 preview-line 926 927 928 929 930 931\" data_line_start=\"926\" data_line_end=\"931\" data_line=\"926,932\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" 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<\/mrow>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E=K+U],[=+(mZ^(2)e^(4))\/(8epsi_(0)^(2)h^(2)n^(2))-(mZ^(2)e^(4))\/(4epsi_(0)^(2)h^(2)n^(2))=-(Z^(2)e^(4)m)\/(8epsi_(0)^(2)h^(2)n^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&E=K+U \\\\\n&=+\\frac{m Z^{2} e^{4}}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}-\\frac{m Z^{2} e^{4}}{4 \\varepsilon_{0}^{2} h^{2} n^{2}}=-\\frac{Z^{2} e^{4} m}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.863ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.062ex\" height=\"8.858ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2207.6 16823.5 3915.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3552.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mo>+<\/mo><mi>U<\/mi><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mo>+<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>\u2212<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-933 preview-line 933\" data_line_start=\"933\" data_line_end=\"933\" data_line=\"933,934\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so the total energy of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 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class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom.<\/div>\n<div class=\"preview-paragraph-935 preview-line 935 936 937\" data_line_start=\"935\" data_line_end=\"937\" data_line=\"935,938\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(me^(4))\/(8n^(2)epsi_(0)^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{m e^{4}}{8 n^{2} \\varepsilon_{0}^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.483ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.101ex\" height=\"5.917ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1517.7 7116.5 2615.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2545.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3323.8, 0)\"><g 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data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 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147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(2373.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3552.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-939 preview-line 939\" data_line_start=\"939\" data_line_end=\"939\" data_line=\"939,940\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-13.jpg?height=240&width=583&top_left_y=451&top_left_x=1042\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-941 preview-line 941\" data_line_start=\"941\" data_line_end=\"941\" data_line=\"941,942\" count_line=\"1\">The wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=4)<\/asciimath><latex style=\"display: none\">(n=4)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2822.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to the state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=2)<\/asciimath><latex style=\"display: none\">(n=2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2822.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-943 preview-line 943 944 945 946 947 948\" data_line_start=\"943\" data_line_end=\"948\" data_line=\"943,949\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>4.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>2.75<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>4.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>2.75<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda=(hc)\/((E_(4)-E_(2)))=(6.6 xx10^(-34)xx3xx10^(8))\/([0-(-4.5)]xx1.6 xx10^(-19))],[=2.75 xx10^(-7)m=275 xx10^(-9)m=275nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\lambda=\\frac{h c}{\\left(E_{4}-E_{2}\\right)}=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{[0-(-4.5)] \\times 1.6 \\times 10^{-19}} \\\\\n&=2.75 \\times 10^{-7} \\mathrm{~m}=275 \\times 10^{-9} \\mathrm{~m}=275 \\mathrm{~nm}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" 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122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(14741.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(15796.9, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17296.9, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>4<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4.5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>2.75<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>275<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-950 preview-line 950\" data_line_start=\"950\" data_line_end=\"950\" data_line=\"950,951\" count_line=\"1\">…(ii) Hence, transition shown by arrow <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">B<\/asciimath><latex style=\"display: none\">B<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>B<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to emission of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=275nm<\/asciimath><latex style=\"display: none\">=275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.49ex\" height=\"1.715ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 4194.8 758\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2555.8, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-952 preview-line 952\" data_line_start=\"952\" data_line_end=\"952\" data_line=\"952,953\" count_line=\"1\">(i) The maximum wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4<\/asciimath><latex style=\"display: none\">n=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.717ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2433.6 759\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-954 preview-line 954 955 956 957 958 959\" data_line_start=\"954\" data_line_end=\"959\" data_line=\"954,960\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.18<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.18<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda=(hc)\/([0-(-2)]eV)=>lambda=(6.6 xx10^(-34)xx3xx10^(8))\/(2xx1.6 xx10^(-19))],[=6.18 xx10^(-7)m=618 xx10^(-9)m=618nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\lambda=\\frac{h c}{[0-(-2)] \\mathrm{eV}} \\Rightarrow \\lambda=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{2 \\times 1.6 \\times 10^{-19}} \\\\\n&=6.18 \\times 10^{-7} \\mathrm{~m}=618 \\times 10^{-9} \\mathrm{~m}=618 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194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10426.5, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(11426.7, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 413) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13380.4, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(14741.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(15796.9, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17296.9, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mrow><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6.18<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>618<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>618<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-961 preview-line 961\" data_line_start=\"961\" data_line_end=\"961\" data_line=\"961,962\" count_line=\"1\">Hence transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to maximum wavelength.<\/div>\n<div class=\"preview-paragraph-963 preview-line 963\" data_line_start=\"963\" data_line_end=\"963\" data_line=\"963,964\" count_line=\"1\">(ii) The minimum wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-965 preview-line 965\" data_line_start=\"965\" data_line_end=\"965\" data_line=\"965,966\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(6.6 xx10^(-34)xx3xx10^(8))\/([-2eV-(-10eV)])=(6.6 xx10^(-34)xx3xx10^(8))\/(8xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{[-2 \\mathrm{eV}-(-10 \\mathrm{eV})]}=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{8 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.374ex\" height=\"3.524ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 15193.2 1557.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>10<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-967 preview-line 967\" data_line_start=\"967\" data_line_end=\"967\" data_line=\"967,968\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.55<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>155<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.55<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>155<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1.55 xx10^(-7)m=155nm<\/asciimath><latex style=\"display: none\">\\lambda=1.55 \\times 10^{-7} \\mathrm{~m}=155 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.114ex\" height=\"2.156ex\" 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82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(10787.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1.55<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>155<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-969 preview-line 969\" data_line_start=\"969\" data_line_end=\"969\" data_line=\"969,970\" count_line=\"1\">Hence transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to minimum wavelength.<\/div>\n<ol start=\"20\" class=\"preview-paragraph-971 preview-line 971 972\" data_line_start=\"971\" data_line_end=\"972\" data_line=\"971,973\" count_line=\"2\">\n<li>Suppose <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be the mass of an electron and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be its speed in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The centripetal force for revolution is produced by electrostatic attraction between electron and nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-973 preview-line 973 974 975\" data_line_start=\"973\" data_line_end=\"975\" data_line=\"973,976\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))((Ze)(e))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{(Z e)(e)}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.653ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 9570.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 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<mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(1)\/(4piepsi_(0))(Ze^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.655ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6477.7 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" 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292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-979 preview-line 979\" data_line_start=\"979\" data_line_end=\"979\" data_line=\"979,980\" count_line=\"1\">So, kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(2)mv^(2)<\/asciimath><latex style=\"display: none\">K=\\frac{1}{2} m v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.781ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.821ex\" height=\"2.737ex\" role=\"img\" focusable=\"false\" viewBox=\"0 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301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1166.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2222.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path 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145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3894.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-981 preview-line 981 982 983\" data_line_start=\"981\" data_line_end=\"983\" data_line=\"981,984\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">K=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.011ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 6634.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(540.8, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1792.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-985 preview-line 985\" data_line_start=\"985\" data_line_end=\"985\" data_line=\"985,986\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-13.jpg?height=274&width=259&top_left_y=2025&top_left_x=1521\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-987 preview-line 987\" data_line_start=\"987\" data_line_end=\"987\" data_line=\"987,988\" count_line=\"1\">Potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(1)\/(4piepsi_(0))((Ze)(-e))\/(r)=-(1)\/(4piepsi_(0))(Ze^(2))\/(r)<\/asciimath><latex style=\"display: none\">=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{(Z e)(-e)}{r}=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" 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671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 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data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(623.6, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>Z<\/mi><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Total energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=<\/asciimath><latex style=\"display: none\">E=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.117ex\" height=\"1.724ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1819.8 762\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> K.E. + P.E.<\/div>\n<div class=\"preview-paragraph-989 preview-line 989\" data_line_start=\"989\" data_line_end=\"989\" data_line=\"989,990\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(1)\/(4piepsi_(0))(Ze^(2))\/(2r)+(-(1)\/(4piepsi_(0))(Ze^(2))\/(r))<\/asciimath><latex style=\"display: none\">=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}+\\left(-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.899ex\" 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=-(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.147ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6253.1 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2097.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2875.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4687, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(446.8, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-991 preview-line 991\" data_line_start=\"991\" data_line_end=\"991\" data_line=\"991,992\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E<\/asciimath><latex style=\"display: none\">E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.729ex\" height=\"1.538ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 764 680\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> can be written as<\/div>\n<div class=\"preview-paragraph-993 preview-line 993\" data_line_start=\"993\" data_line_end=\"993\" data_line=\"993,994\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.162ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6701.4 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path 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186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-995 preview-line 995\" data_line_start=\"995\" data_line_end=\"995\" data_line=\"995,996\" count_line=\"1\">Again from Bohr’s postulate for quantization of angular momentum.<\/div>\n<div class=\"preview-paragraph-997 preview-line 997\" data_line_start=\"997\" data_line_end=\"997\" data_line=\"997,998\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-999 preview-line 999\" data_line_start=\"999\" data_line_end=\"999\" data_line=\"999,1000\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.948ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3954.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 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0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1001 preview-line 1001\" data_line_start=\"1001\" data_line_end=\"1001\" data_line=\"1001,1002\" count_line=\"1\">Substituting this value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (i), we get<\/div>\n<div class=\"preview-paragraph-1003 preview-line 1003\" data_line_start=\"1003\" data_line_end=\"1003\" data_line=\"1003,1004\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <msup>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m)\/(r)[(nh)\/(2pi mr)]^(2)=(1)\/(4piepsi_(0))(Ze^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m}{r}\\left[\\frac{n h}{2 \\pi m r}\\right]^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.692ex\" height=\"3.495ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1082.7 9145.9 1544.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(371, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"820.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"msup\" transform=\"translate(1060.8, 0)\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M202 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442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2553.3, 0)\"><path data-c=\"5D\" d=\"M22 810V850H214V-349H22V-309H174V810H22Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(2970.3, 611.8) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4712.5, 0)\"><path 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211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mfrac\" transform=\"translate(7579.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 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data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(480.9, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>m<\/mi><mi>r<\/mi><\/mfrac><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1005 preview-line 1005\" data_line_start=\"1005\" data_line_end=\"1005\" data_line=\"1005,1006\" count_line=\"1\">or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.897ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4374.6 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 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385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2350\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.97ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4848.8 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1203, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2258.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(286.4, 457.1) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" 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469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1448, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2171, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2350\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1007 preview-line 1007\" data_line_start=\"1007\" data_line_end=\"1007\" data_line=\"1007,1008\" count_line=\"1\">Substituting value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)<\/asciimath><latex style=\"display: none\">r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.093ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 925.3 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (ii), we get<\/div>\n<div class=\"preview-paragraph-1009 preview-line 1009\" data_line_start=\"1009\" data_line_end=\"1009\" data_line=\"1009,1010\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(1)\/(2xx4piepsi_(0))(Ze^(2))\/(((epsi_(0)h^(2)n^(2))\/(pi mZe^(2))))=(mZ^(2)e^(4)xx ch)\/(8epsi_(0)^(2)ch^(3)n^(2))<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{1}{2 \\times 4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{\\left(\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\\right)}=\\frac{m Z^{2} e^{4} \\times c h}{8 \\varepsilon_{0}^{2} c h^{3} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.476ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"33.003ex\" height=\"5.714ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 14587.4 2525.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 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data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(500, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 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358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2348, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mi>c<\/mi><mi>h<\/mi><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1011 preview-line 1011\" data_line_start=\"1011\" data_line_end=\"1011\" data_line=\"1011,1012\" count_line=\"1\">or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>,<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>,<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(Z^(2)Rhc)\/(n^(2)),quad<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{Z^{2} R h c}{n^{2}}, \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.507ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 7296.3 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2545.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3323.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(781, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1184.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1943.6, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2519.6, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(909.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2287.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5851.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(6296.3, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>,<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=(me^(4))\/(8epsi_(0)^(2)ch^(3))<\/asciimath><latex style=\"display: none\">R=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} c h^{3}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.181ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4499.8 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2092.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(585.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1369.6, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2167.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1013 preview-line 1013\" data_line_start=\"1013\" data_line_end=\"1013\" data_line=\"1013,1014\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R<\/asciimath><latex style=\"display: none\">R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.048ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 704\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called Rydberg constant. For hydrogen atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1015 preview-line 1015\" data_line_start=\"1015\" data_line_end=\"1015\" data_line=\"1015,1016\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=(-Rch)\/(n^(2))<\/asciimath><latex style=\"display: none\">E_{n}=\\frac{-R c h}{n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.828ex\" height=\"3ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4786.1 1326.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2545.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(765.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1017 preview-line 1017\" data_line_start=\"1017\" data_line_end=\"1017\" data_line=\"1017,1018\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the quantum numbers of initial and final states and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are energies of electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom in initial and final state, we have<\/div>\n<div class=\"preview-paragraph-1019 preview-line 1019\" data_line_start=\"1019\" data_line_end=\"1019\" data_line=\"1019,1020\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)=(-Rch)\/(n_(i)^(2))<\/asciimath><latex style=\"display: none\">E_{i}=\\frac{-R c h}{n_{i}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.44ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.42ex\" height=\"3.45ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4605.8 1525\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1309.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2365.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(765.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)=(-Rch)\/(n_(f)^(2))<\/asciimath><latex style=\"display: none\">E_{f}=\\frac{-R c h}{n_{f}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.709ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.748ex\" height=\"3.719ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4750.8 1644\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1454.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2510.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(752.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -315.5) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1021 preview-line 1021\" data_line_start=\"1021\" data_line_end=\"1021\" data_line=\"1021,1022\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the frequency of emitted radiation.<\/div>\n<div class=\"preview-paragraph-1023 preview-line 1023 1024\" data_line_start=\"1023\" data_line_end=\"1024\" data_line=\"1023,1025\" count_line=\"2\">we get <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(E_(i)-E_(f))\/(h)<\/asciimath><latex style=\"display: none\">v=\\frac{E_{i}-E_{f}}{h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.888ex\" height=\"3.127ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1029.4 4370.6 1382.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 548.6) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1032, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1810, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1072.4, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"2312\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/mrow><mi>h<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><br>\nfrom eq. (i)<\/div>\n<div class=\"preview-paragraph-1026 preview-line 1026\" data_line_start=\"1026\" data_line_end=\"1026\" data_line=\"1026,1027\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>h<\/mi>\n <\/mfrac>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>h<\/mi>\n <\/mfrac>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>+<\/mo> \n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(1)\/(h)((-Rch)\/(n_(i)^(2))+(Rch)\/(n_(f)^(2)))<\/asciimath><latex style=\"display: none\">v=\\frac{1}{h}\\left(\\frac{-R c h}{n_{i}^{2}}+\\frac{R c h}{n_{f}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.02ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 9290.8 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(246.9, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"607.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mrow\" transform=\"translate(2665.8, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(736, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" 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17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -315.5) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><rect width=\"1450.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5888.9, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mi>h<\/mi><\/mfrac><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>+<\/mo><mfrac><mrow><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1028 preview-line 1028\" data_line_start=\"1028\" data_line_end=\"1028\" data_line=\"1028,1029\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=Rc[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))]<\/asciimath><latex style=\"display: none\">v=R c\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.225ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 7613.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4074.7, 0)\"><path data-c=\"5D\" d=\"M11 1388V1450H280V-949H11V-887H218V1388H11Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mi>R<\/mi><mi>c<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"21\" class=\"preview-paragraph-1030 preview-line 1030 1031\" data_line_start=\"1030\" data_line_end=\"1031\" data_line=\"1030,1032\" count_line=\"2\">\n<li>(a) Speed of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit : The centripetal force required for revolution is provided by the electrostatic force of attraction between the electron and the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1032 preview-line 1032 1033 1034 1035 1036 1037\" data_line_start=\"1032\" data_line_end=\"1037\" data_line=\"1032,1038\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>∴<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mtext> where, <\/mtext>\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>\u2234<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mtext>\u00a0where,\u00a0<\/mtext> \n <mi>K<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[:.(mv^(2))\/(r)=(KZe^(2))\/(r^(2))quad[” where, “K=(1)\/(4piepsi_(0))]],[=>r=(KZe^(2))\/(mv^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\therefore \\frac{m v^{2}}{r}=\\frac{K Z e^{2}}{r^{2}} \\quad\\left[\\text { where, } K=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right] \\\\\n&\\Rightarrow r=\\frac{K Z e^{2}}{m v^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.175ex\" 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369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2681.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>\u2234<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mtext>\u00a0where,\u00a0<\/mtext><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1039 preview-line 1039\" data_line_start=\"1039\" data_line_end=\"1039\" data_line=\"1039,1040\" count_line=\"1\">The angular momentum for any permitted (stationary) orbit is<\/div>\n<div class=\"preview-paragraph-1041 preview-line 1041\" data_line_start=\"1041\" data_line_end=\"1041\" data_line=\"1041,1042\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1043 preview-line 1043\" data_line_start=\"1043\" data_line_end=\"1043\" data_line=\"1043,1044\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is any positive integer.<\/div>\n<div class=\"preview-paragraph-1045 preview-line 1045\" data_line_start=\"1045\" data_line_end=\"1045\" data_line=\"1045,1046\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi mv)<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.925ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3944.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1047 preview-line 1047\" data_line_start=\"1047\" data_line_end=\"1047\" data_line=\"1047,1048\" count_line=\"1\">From (i) and (ii), we get<\/div>\n<div class=\"preview-paragraph-1049 preview-line 1049\" data_line_start=\"1049\" data_line_end=\"1049\" data_line=\"1049,1050\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>∴<\/mo>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u2234<\/mo>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(KZe^(2))\/(mv^(2))=(nh)\/(2pi mv):.v=(2pi KZe^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\frac{K Z e^{2}}{m v^{2}}=\\frac{n h}{2 \\pi m v} \\therefore v=\\frac{2 \\pi K Z e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.428ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 11681.1 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 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388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"2711.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mo>\u2234<\/mo><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1051 preview-line 1051\" data_line_start=\"1051\" data_line_end=\"1051\" data_line=\"1051,1052\" count_line=\"1\">For hydrogen atom, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1053 preview-line 1053\" data_line_start=\"1053\" data_line_end=\"1053\" data_line=\"1053,1054\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>ν<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>K<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bd<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>K<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad nu=(2pi Ke^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\nu=\\frac{2 \\pi K e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.137ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6248.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"3BD\" d=\"M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2752.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3808.3, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1959, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(804.3, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"2200.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bd<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>K<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1055 preview-line 1055\" data_line_start=\"1055\" data_line_end=\"1055\" data_line=\"1055,1056\" count_line=\"1\">(b) Refer to answer 14.<\/div>\n<ol start=\"22\" class=\"preview-paragraph-1057 preview-line 1057 1058\" data_line_start=\"1057\" data_line_end=\"1058\" data_line=\"1057,1059\" count_line=\"2\">\n<li>Bohr’s postulates of atomic model : Bohr introduced three postulates and laid the foundations of quantum mechanics.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1059 preview-line 1059\" data_line_start=\"1059\" data_line_end=\"1059\" data_line=\"1059,1060\" count_line=\"1\">(i) In a hydrogen atom, an electron revolves in certain stable orbits called stationary orbits without the emission of radiant energy.<\/div>\n<div class=\"preview-paragraph-1061 preview-line 1061\" data_line_start=\"1061\" data_line_end=\"1061\" data_line=\"1061,1062\" count_line=\"1\">(ii) The angular momentum in the stationary orbits is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi)<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.707ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 1196.6 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(394.7, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1063 preview-line 1063\" data_line_start=\"1063\" data_line_end=\"1063\" data_line=\"1063,1064\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad L=mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">\\therefore \\quad L=m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.956ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 8378.4 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2903.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3959.3, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4837.3, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5322.3, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6051.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(7106.9, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1065 preview-line 1065\" data_line_start=\"1065\" data_line_end=\"1065\" data_line=\"1065,1066\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is an integer called a quantum number.<\/div>\n<div class=\"preview-paragraph-1067 preview-line 1067\" data_line_start=\"1067\" data_line_end=\"1067\" data_line=\"1067,1068\" count_line=\"1\">In second excited state i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, three spectral lines can be obtained corresponding to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,n=3<\/asciimath><latex style=\"display: none\">n=1, n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.018ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 5311.8 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2878.2, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3756, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4811.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1069 preview-line 1069\" data_line_start=\"1069\" data_line_end=\"1069\" data_line=\"1069,1070\" count_line=\"1\">For Lyman series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for minimum wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>9<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>9<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(min))=R[(1)\/(1^(2))-(1)\/(3^(2))]=(8R)\/(9)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\min }}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{8 R}{9}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.438ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10801.7 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(683.8, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><rect width=\"1481.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1998.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3054.7, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3813.7, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M224 -649V1150H455V1099H275V-598H455V-649H224Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(472, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1773.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2773.4, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3852.3, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8415.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9471.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(488.3, -345) scale(0.707)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><rect width=\"1090.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>8<\/mn><mi>R<\/mi><\/mrow><mn>9<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1071 preview-line 1071\" data_line_start=\"1071\" data_line_end=\"1071\" data_line=\"1071,1072\" count_line=\"1\">For Balmer series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for maximum wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(max))=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\max }}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.961ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 11474.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(732.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 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-22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mi\" transform=\"translate(10715.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Dividing eq. (i) by (ii), we get<\/div>\n<div class=\"preview-paragraph-1073 preview-line 1073\" data_line_start=\"1073\" data_line_end=\"1073\" data_line=\"1073,1074\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>9<\/mn>\n <\/mrow>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>36<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>5<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>9<\/mn>\n <\/mrow>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>36<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>5<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(max))\/(lambda_(min))=(8R\/\/9)\/(5R\/\/36)=(32)\/(5)<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{\\max }}{\\lambda_{\\min }}=\\frac{8 R \/ 9}{5 R \/ 36}=\\frac{32}{5}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.152ex\" height=\"3.607ex\" 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movablelimits=\"true\">max<\/mo><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>8<\/mn><mi>R<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>9<\/mn><\/mrow><mrow><mn>5<\/mn><mi>R<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>36<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>32<\/mn><mn>5<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1075 preview-line 1075\" data_line_start=\"1075\" data_line_end=\"1075\" data_line=\"1075,1076\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>:<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>32<\/mn>\n <mo>:<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>:<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>32<\/mn>\n <mo>:<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(max):lambda_(min)=32:5<\/asciimath><latex style=\"display: none\">\\lambda_{\\max }: \\lambda_{\\min }=32: 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.691ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 8261.3 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4872, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5927.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7205.6, 0)\"><path data-c=\"3A\" d=\"M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(7761.3, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>:<\/mo><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>32<\/mn><mo>:<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"23\" class=\"preview-paragraph-1077 preview-line 1077 1078 1079 1080\" data_line_start=\"1077\" data_line_end=\"1080\" data_line=\"1077,1081\" count_line=\"4\">\n<li>\n<div>Refer to answer 19.<\/div>\n<\/li>\n<li>\n<div>(a) Limitation of Rutherford’s model:<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1081 preview-line 1081\" data_line_start=\"1081\" data_line_end=\"1081\" data_line=\"1081,1082\" count_line=\"1\">(i) Rutherford’s atomic model is inconsistent with classical physics. According to electromagnetic theory, an electron is a charged particle moving in the circular orbit around the nucleus and<\/div>\n<div class=\"preview-paragraph-1083 preview-line 1083 1084\" data_line_start=\"1083\" data_line_end=\"1084\" data_line=\"1083,1085\" count_line=\"2\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-15.jpg?height=254&width=251&top_left_y=770&top_left_x=751\" alt=\"\"><br>\nis accelerated, so it should emit radiation continuously and thereby loose energy. Due to this, radius of the electron would decrease continuously and also the atom should then produce continuous spectrum, and ultimately electron will fall into the nucleus and atom will collapse in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-8)s<\/asciimath><latex style=\"display: none\">10^{-8} \\mathrm{~s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.877ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 2597.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1953.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. But the atom is fairly stable and it emits line spectrum.<\/div>\n<div class=\"preview-paragraph-1086 preview-line 1086\" data_line_start=\"1086\" data_line_end=\"1086\" data_line=\"1086,1087\" count_line=\"1\">(ii) Rutherford’s model is not able to explain the spectrum of even most simplest H-spectrum.<\/div>\n<div class=\"preview-paragraph-1088 preview-line 1088\" data_line_start=\"1088\" data_line_end=\"1088\" data_line=\"1088,1089\" count_line=\"1\">Bohr’s postulates to resolve observed features of atomic spectrum :<\/div>\n<div class=\"preview-paragraph-1090 preview-line 1090\" data_line_start=\"1090\" data_line_end=\"1090\" data_line=\"1090,1091\" count_line=\"1\">(i) Quantum condition: Of all the possible circular orbits allowed by the classical theory, the electrons are permitted to circulate only in those orbits in which the angular momentum of an electron is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi),h<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}, h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.016ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 2217.3 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(394.7, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1196.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1641.3, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> being Planck’s constant. Therefore, for any permitted orbit,<\/div>\n<div class=\"preview-paragraph-1092 preview-line 1092 1093 1094\" data_line_start=\"1092\" data_line_end=\"1094\" data_line=\"1092,1095\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=mvr=(nh)\/(2pi),n=1,2,3dots dots,<\/asciimath><latex style=\"display: none\">L=m v r=\\frac{n h}{2 \\pi}, n=1,2,3 \\ldots \\ldots,<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"33.185ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 14667.7 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(958.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2014.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2892.6, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3377.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4106.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5162.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(273, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1376\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(6778.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(7222.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8100.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9156.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9656.3, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(10101, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10601, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(11045.7, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11712.3, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13051, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14389.7, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1096 preview-line 1096\" data_line_start=\"1096\" data_line_end=\"1096\" data_line=\"1096,1097\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called the principal quantum number, and this equation is called Bohr’s quantisation condition.<\/div>\n<div class=\"preview-paragraph-1098 preview-line 1098\" data_line_start=\"1098\" data_line_end=\"1098\" data_line=\"1098,1099\" count_line=\"1\">(ii) Stationary orbits: While resolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.<\/div>\n<div class=\"preview-paragraph-1100 preview-line 1100\" data_line_start=\"1100\" data_line_end=\"1100\" data_line=\"1100,1101\" count_line=\"1\">(iii) Frequency condition: An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.<\/div>\n<div class=\"preview-paragraph-1102 preview-line 1102 1103 1104\" data_line_start=\"1102\" data_line_end=\"1104\" data_line=\"1102,1105\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mrow>\n <mi mathvariant=\"normal\">i<\/mi>\n <\/mrow>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mrow>\n <mi mathvariant=\"normal\">i<\/mi>\n <\/mrow>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">h v=E_{\\mathrm{i}}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.073ex\" height=\"2.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 5778.5 989\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1338.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2394.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3601.4, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4601.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mrow><mi mathvariant=\"normal\">i<\/mi><\/mrow><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1106 preview-line 1106\" data_line_start=\"1106\" data_line_end=\"1106\" data_line=\"1106,1107\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is frequency of radiation emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies associated with stationary orbits of principal quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> respectively (where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i) > n_(f)<\/asciimath><latex style=\"display: none\">n_{i}>n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.39ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -540 3266.4 835\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2227.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>><\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-1108 preview-line 1108\" data_line_start=\"1108\" data_line_end=\"1108\" data_line=\"1108,1109\" count_line=\"1\">(b) Refer to answer 13.<\/div>\n<ol start=\"25\" class=\"preview-paragraph-1110 preview-line 1110 1111 1112 1113\" data_line_start=\"1110\" data_line_end=\"1113\" data_line=\"1110,1114\" count_line=\"4\">\n<li>\n<div>Refer to answer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">17(i)<\/asciimath><latex style=\"display: none\">17(i)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.803ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2123 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1389, 0)\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1734, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>17<\/mn><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<\/li>\n<li>\n<div>(a) Refer to answer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">17(i)<\/asciimath><latex style=\"display: none\">17(i)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.803ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2123 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1389, 0)\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1734, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>17<\/mn><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1114 preview-line 1114\" data_line_start=\"1114\" data_line_end=\"1114\" data_line=\"1114,1115\" count_line=\"1\">(b) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:’<\/asciimath><latex style=\"display: none\">\\because<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2235<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(n^(2)h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n^{2} h^{2} \\varepsilon_{0}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.597ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4241.7 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 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369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2217.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>m<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>m<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r prop(1)\/(m)<\/asciimath><latex style=\"display: none\">r \\propto \\frac{1}{m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.438ex\" height=\"2.755ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 2845.4 1217.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(353.6, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"820.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><mfrac><mn>1<\/mn><mi>m<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1116 preview-line 1116\" data_line_start=\"1116\" data_line_end=\"1116\" data_line=\"1116,1117\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> when we increase the mass 200 times, the radius reduces to 200 times.<\/div>\n<div class=\"preview-paragraph-1118 preview-line 1118\" data_line_start=\"1118\" data_line_end=\"1118\" data_line=\"1118,1119\" count_line=\"1\">Similarly, ground state energy for hydrogen, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-me^(4))\/(8epsi_(0)^(2)n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E=\\frac{-m e^{4}}{8 \\varepsilon_{0}^{2} n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.105ex\" height=\"3.705ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -993.2 4908.2 1637.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(512.4, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1656, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(2373.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2570.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1120 preview-line 1120\" data_line_start=\"1120\" data_line_end=\"1120\" data_line=\"1120,1121\" count_line=\"1\">i.e. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>∝<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>\u221d<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E prop m<\/asciimath><latex style=\"display: none\">E \\propto m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.732ex\" height=\"1.563ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 2975.6 691\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>\u221d<\/mo><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1122 preview-line 1122\" data_line_start=\"1122\" data_line_end=\"1122\" data_line=\"1122,1123\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.<\/asciimath><latex style=\"display: none\">\\therefore<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> when we increase the mass 200 times, the ground state energy also increases by a factor 200.<\/div>\n<ol start=\"27\" class=\"preview-paragraph-1124 preview-line 1124 1125 1126 1127\" data_line_start=\"1124\" data_line_end=\"1127\" data_line=\"1124,1128\" count_line=\"4\">\n<li>\n<div>Refer to answer 17(i).<\/div>\n<\/li>\n<li>\n<div>For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1128 preview-line 1128\" data_line_start=\"1128\" data_line_end=\"1128\" data_line=\"1128,1129\" count_line=\"1\">Ground state energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-13.6eV<\/asciimath><latex style=\"display: none\">E_{1}=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.084ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 6225.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2475.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3253.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5031.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1130 preview-line 1130\" data_line_start=\"1130\" data_line_end=\"1130\" data_line=\"1130,1131\" count_line=\"1\">Excited state energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(2)=-1.5eV<\/asciimath><latex style=\"display: none\">E_{2}=-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.953ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 5725.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2475.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3253.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4531.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1132 preview-line 1132\" data_line_start=\"1132\" data_line_end=\"1132\" data_line=\"1132,1133\" count_line=\"1\">Energy of photon emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(2)-E_(1)<\/asciimath><latex style=\"display: none\">E=E_{2}-E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.677ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 5603.1 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3461.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4461.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1134 preview-line 1134\" data_line_start=\"1134\" data_line_end=\"1134\" data_line=\"1134,1135\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-1.5-(-13.6)=-1.5+13.6=12.1eV<\/asciimath><latex style=\"display: none\">=-1.5-(-13.6)=-1.5+13.6=12.1 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.547ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 18363.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3334, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4334.2, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4723.2, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5501.2, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 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data-mml-node=\"mo\" transform=\"translate(7946, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9001.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9779.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11280, 0)\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(12280.2, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14336, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(15391.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17169.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>+<\/mo><mn>13.6<\/mn><mo>=<\/mo><mn>12.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1136 preview-line 1136\" data_line_start=\"1136\" data_line_end=\"1136\" data_line=\"1136,1137\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.<\/asciimath><latex style=\"display: none\">\\therefore<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Wavelength of photon emitted,<\/div>\n<div class=\"preview-paragraph-1138 preview-line 1138\" data_line_start=\"1138\" data_line_end=\"1138\" data_line=\"1138,1139\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>19.36<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>19.36<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/(E)=(6.62 xx10^(-34)xx3xx10^(8))\/(12.1 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(19.36)<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{E}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{12.1 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{19.36}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.3ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 16044.6 1476.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 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414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1778, 0)\"><\/path><\/g><rect width=\"3742.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>E<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>12.1<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>19.36<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1140 preview-line 1140\" data_line_start=\"1140\" data_line_end=\"1140\" data_line=\"1140,1141\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.027<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.027<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=1.027 xx10^(-7)=102.7nm<\/asciimath><latex style=\"display: none\">=1.027 \\times 10^{-7}=102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.607ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 11760.5 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" 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402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>1.027<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mo>=<\/mo><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1142 preview-line 1142\" data_line_start=\"1142\" data_line_end=\"1142\" data_line=\"1142,1143\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>C<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>C<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">C<\/asciimath><latex style=\"display: none\">C<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.719ex\" height=\"1.645ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 760 727\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>C<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1144 preview-line 1144\" data_line_start=\"1144\" data_line_end=\"1144\" data_line=\"1144,1145\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-3.4eV,E_(2)=-1.5eV<\/asciimath><latex style=\"display: none\">E_{1}=-3.4 \\mathrm{eV}, E_{2}=-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.912ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 11894.9 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2475.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3253.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4531.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path 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599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(7589.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8644.9, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9422.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(10700.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1146 preview-line 1146\" data_line_start=\"1146\" data_line_end=\"1146\" data_line=\"1146,1147\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-1.5-(-3.4)=-1.5+3.4=1.9eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-1.5-(-3.4)=-1.5+3.4=1.9 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"44.91ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 19850.3 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2986.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4042.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4820.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 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display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>+<\/mo><mn>3.4<\/mn><mo>=<\/mo><mn>1.9<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1148 preview-line 1148\" data_line_start=\"1148\" data_line_end=\"1148\" data_line=\"1148,1149\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>3.04<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>3.04<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(1.9 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(3.04)<\/asciimath><latex style=\"display: none\">\\therefore \\lambda=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{1.9 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{3.04}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.811ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 14502.4 1476.9\" aria-hidden=\"true\"><g 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transform=\"translate(778, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(1278, 0)\"><\/path><\/g><rect width=\"3742.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>1.9<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>3.04<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1150 preview-line 1150\" data_line_start=\"1150\" data_line_end=\"1150\" data_line=\"1150,1151\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.539<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>653.9<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.539<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>653.9<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=6.539 xx10^(-7)m=653.9nm<\/asciimath><latex style=\"display: none\">=6.539 \\times 10^{-7} \\mathrm{~m}=653.9 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" 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472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>6.539<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>653.9<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1152 preview-line 1152\" data_line_start=\"1152\" data_line_end=\"1152\" data_line=\"1152,1153\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">B<\/asciimath><latex style=\"display: none\">B<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-3.4eV,E_(2)=-0.85eV<\/asciimath><latex style=\"display: none\">E_{1}=-3.4 \\mathrm{eV}, E_{2}=-0.85 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.043ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 12394.9 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 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mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1156 preview-line 1156\" data_line_start=\"1156\" data_line_end=\"1156\" data_line=\"1156,1157\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>2.55<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>2.55<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-0.85-(-3.4)=-0.85+3.4=2.55eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-0.85-(-3.4)=-0.85+3.4=2.55 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" 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<mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2.55<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4.08<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2.55<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4.08<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(2.55 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(4.08)<\/asciimath><latex style=\"display: none\">\\therefore \\lambda=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{2.55 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{4.08}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.811ex\" height=\"3.341ex\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2.55<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>4.08<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1160 preview-line 1160\" data_line_start=\"1160\" data_line_end=\"1160\" data_line=\"1160,1161\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.867<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>486.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.867<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>486.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=4.867 xx10^(-7)m=486.7nm<\/asciimath><latex style=\"display: none\">=4.867 \\times 10^{-7} \\mathrm{~m}=486.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" 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mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1162 preview-line 1162\" data_line_start=\"1162\" data_line_end=\"1162\" data_line=\"1162,1163\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1164 preview-line 1164\" data_line_start=\"1164\" data_line_end=\"1164\" data_line=\"1164,1165\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-1.5eV,E_(2)=-0.85eV<\/asciimath><latex style=\"display: none\">E_{1}=-1.5 \\mathrm{eV}, E_{2}=-0.85 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.043ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 12394.9 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 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311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11200.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1166 preview-line 1166\" data_line_start=\"1166\" data_line_end=\"1166\" data_line=\"1166,1167\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>1.5<\/mn>\n <mo>=<\/mo>\n <mn>0.65<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>1.5<\/mn>\n <mo>=<\/mo>\n <mn>0.65<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-0.85-(-1.5)=-0.85+1.5=0.65<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-0.85-(-1.5)=-0.85+1.5=0.65<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"45.603ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 20156.3 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mo>+<\/mo><mn>1.5<\/mn><mo>=<\/mo><mn>0.65<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1168 preview-line 1168 1169 1170 1171 1172 1173\" data_line_start=\"1168\" data_line_end=\"1173\" data_line=\"1168,1174\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>0.65<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>1.04<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>19.096<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1909.6<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>0.65<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>1.04<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>19.096<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1909.6<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[:.quad lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(0.65 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(1.04)],[=19.096 xx10^(-7)m=1909.6nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n\\therefore \\quad \\lambda &=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{0.65 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{1.04} \\\\\n&=19.096 \\times 10^{-7} \\mathrm{~m}=1909.6 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d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(7287.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8648.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9704.2, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 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431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>0.65<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>1.04<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>19.096<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>1909.6<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1175 preview-line 1175\" data_line_start=\"1175\" data_line_end=\"1175\" data_line=\"1175,1176\" count_line=\"1\">The element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to a spectral line of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">102.7nm<\/asciimath><latex style=\"display: none\">102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.862ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3917 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2278, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<ol start=\"29\" class=\"preview-paragraph-1177 preview-line 1177 1178 1179 1180\" data_line_start=\"1177\" data_line_end=\"1180\" data_line=\"1177,1181\" count_line=\"4\">\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line of the Balmer series in the emission spectrum of hydrogen atoms obtained when the transition occurs from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state.<\/div>\n<\/li>\n<li>\n<div>Number of spectral lines obtained due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd <\/mtext>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd\u00a0<\/mtext>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4(3^(“rd “):}<\/asciimath><latex style=\"display: none\">n=4\\left(3^{\\text {rd }}\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.703ex\" height=\"2.722ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 4288.7 1203.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2433.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M152 251Q152 646 388 850H416Q422 844 422 841Q422 837 403 816T357 753T302 649T255 482T236 250Q236 124 255 19T301 -147T356 -251T403 -315T422 -340Q422 -343 416 -349H388Q359 -325 332 -296T271 -213T212 -97T170 56T152 251Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(458, 0)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(392, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(948, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1855.1, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msup><mn>3<\/mn><mrow><mtext>rd\u00a0<\/mtext><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state) to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (ground state) is<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1181 preview-line 1181\" data_line_start=\"1181\" data_line_end=\"1181\" data_line=\"1181,1182\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=314&width=714&top_left_y=997&top_left_x=288\" alt=\"\"><\/div>\n<ol start=\"31\" class=\"preview-paragraph-1183 preview-line 1183 1184\" data_line_start=\"1183\" data_line_end=\"1184\" data_line=\"1183,1185\" count_line=\"2\">\n<li>The minimum energy, required to free the electron from the ground state of the hydrogen atom, is known as ionization energy of that atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1185 preview-line 1185\" data_line_start=\"1185\" data_line_end=\"1185\" data_line=\"1185,1186\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(0)=(me^(4))\/(8epsi_(0)^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{0}=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.353ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4576.2 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2475.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(432.7, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1861.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e..<span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(0)prop m<\/asciimath><latex style=\"display: none\">E_{0} \\propto m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.586ex\" height=\"1.913ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 3353.1 845.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2475.1, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>\u221d<\/mo><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron, ionization energy increases by 200 times.<\/div>\n<ol start=\"32\" class=\"preview-paragraph-1187 preview-line 1187 1188\" data_line_start=\"1187\" data_line_end=\"1188\" data_line=\"1187,1189\" count_line=\"2\">\n<li>Number of spectral lines obtained due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd <\/mtext>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd\u00a0<\/mtext>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4(3^(“rd “):}<\/asciimath><latex style=\"display: none\">n=4\\left(3^{\\text {rd }}\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.703ex\" height=\"2.722ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 4288.7 1203.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2433.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M152 251Q152 646 388 850H416Q422 844 422 841Q422 837 403 816T357 753T302 649T255 482T236 250Q236 124 255 19T301 -147T356 -251T403 -315T422 -340Q422 -343 416 -349H388Q359 -325 332 -296T271 -213T212 -97T170 56T152 251Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(458, 0)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(392, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(948, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1855.1, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msup><mn>3<\/mn><mrow><mtext>rd\u00a0<\/mtext><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state) to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (ground state) is<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1189 preview-line 1189\" data_line_start=\"1189\" data_line_end=\"1189\" data_line=\"1189,1190\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=314&width=699&top_left_y=1805&top_left_x=290\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1191 preview-line 1191\" data_line_start=\"1191\" data_line_end=\"1191\" data_line=\"1191,1192\" count_line=\"1\">These lines correspond to Lyman series.<\/div>\n<ol start=\"33\" class=\"preview-paragraph-1193 preview-line 1193 1194\" data_line_start=\"1193\" data_line_end=\"1194\" data_line=\"1193,1195\" count_line=\"2\">\n<li>(a) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=496nm=496 xx10^(-9)m<\/asciimath><latex style=\"display: none\">\\lambda=496 \\mathrm{~nm}=496 \\times 10^{-9} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.485ex\" height=\"2.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 12148.2 946\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3416.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(5333.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(6389.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8111.3, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(9111.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11065.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>496<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1195 preview-line 1195 1196 1197 1198 1199 1200\" data_line_start=\"1195\" data_line_end=\"1200\" data_line=\"1195,1201\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mi>E<\/mi>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>496<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>496<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>2.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <mi>E<\/mi>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n 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<\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>2.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E=(hc)\/(lambda)=(6.62 xx10^(-34)xx3xx10^(8))\/(496 xx10^(-9))J],[=(6.6 xx10^(-34)xx3xx10^(8))\/(496 xx10^(-9)xx1.6 xx10^(-19))=2.5eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nE &=\\frac{h c}{\\lambda}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{496 \\times 10^{-9}} \\mathrm{~J} \\\\\n&=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{496 \\times 10^{-9} \\times 1.6 \\times 10^{-19}}=2.5 \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.189ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.573ex\" height=\"11.51ex\" role=\"img\" focusable=\"false\" 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rowspacing=\"3pt\"><mtr><mtd><mi>E<\/mi><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>2.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1202 preview-line 1202\" data_line_start=\"1202\" data_line_end=\"1202\" data_line=\"1202,1203\" count_line=\"1\">This energy corresponds to the transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A(n=4<\/asciimath><latex style=\"display: none\">A(n=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.083ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3572.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(750, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1139, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2016.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3072.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3)<\/asciimath><latex style=\"display: none\">n=3)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.386ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2822.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> for which the energy change <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2eV<\/asciimath><latex style=\"display: none\">=2 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.221ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2749.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1555.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (b) Energy of emitted photon is given by,<\/div>\n<div class=\"preview-paragraph-1204 preview-line 1204 1205 1206\" data_line_start=\"1204\" data_line_end=\"1206\" data_line=\"1204,1207\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(hc)\/(lambda)quad:.lambda_(max)prop(1)\/(E_(min))<\/asciimath><latex style=\"display: none\">E=\\frac{h c}{\\lambda} \\quad \\therefore \\lambda_{\\max } \\propto \\frac{1}{E_{\\min }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.891ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.924ex\" height=\"4.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 11458.3 2206\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 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257L296 236L358 151Q424 61 429 57T446 50Q464 46 499 46H516V0H510H502Q494 1 482 1T457 2T432 2T414 3Q403 3 377 3T327 1L304 0H295V46H298Q309 46 320 51T331 63Q331 65 291 120L250 175Q249 174 219 133T185 88Q181 83 181 74Q181 63 188 55T206 46Q208 46 208 23V0H201Z\" transform=\"translate(1333, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(7995.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9051.6, 0)\"><g 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625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><rect width=\"2166.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>\u221d<\/mo><mfrac><mn>1<\/mn><msub><mi>E<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1208 preview-line 1208\" data_line_start=\"1208\" data_line_end=\"1208\" data_line=\"1208,1209\" count_line=\"1\">Transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for which the energy emission is minimum, corresponds to the emission of radiation of maximum wavelength.<\/div>\n<ol start=\"34\" class=\"preview-paragraph-1210 preview-line 1210 1211\" data_line_start=\"1210\" data_line_end=\"1211\" data_line=\"1210,1212\" count_line=\"2\">\n<li>(i) An electron undergoes transition from 2nd excited state to the first excited state is Balmer series and then to the ground state is Lyman series.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1212 preview-line 1212\" data_line_start=\"1212\" data_line_end=\"1212\" data_line=\"1212,1213\" count_line=\"1\">(ii) The wavelength of the emitted radiations in the two cases.<\/div>\n<div class=\"preview-paragraph-1214 preview-line 1214\" data_line_start=\"1214\" data_line_end=\"1214\" data_line=\"1214,1215\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=540&width=605&top_left_y=961&top_left_x=1134\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1216 preview-line 1216\" data_line_start=\"1216\" data_line_end=\"1216\" data_line=\"1216,1217\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"REL\">\n <mover>\n <mrow data-mjx-texclass=\"OP\">\n <mo stretchy=\"false\">⟶<\/mo>\n <\/mrow>\n <mrow>\n <mi>λ<\/mi>\n <\/mrow>\n <\/mover>\n <\/mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"REL\">\n <mover accent=\"true\" accentunder=\"false\">\n <mrow data-mjx-texclass=\"OP\">\n <mo stretchy=\"false\">\u27f6<\/mo>\n <\/mrow>\n <mrow>\n <mi>\u03bb<\/mi>\n <\/mrow>\n <\/mover>\n <\/mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)longrightarrow^(lambda)n_(1)<\/asciimath><latex style=\"display: none\">n_{2} \\stackrel{\\lambda}{\\longrightarrow} n_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.504ex\" height=\"3.284ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1301.7 4200.7 1451.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"REL\" transform=\"translate(1281.3, 0)\"><g data-mml-node=\"mover\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"OP\"><g data-mml-node=\"mo\"><path data-c=\"27F6\" d=\"M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(612.9, 711) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(3197.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"REL\"><mover><mrow data-mjx-texclass=\"OP\"><mo stretchy=\"false\">\u27f6<\/mo><\/mrow><mrow><mi>\u03bb<\/mi><\/mrow><\/mover><\/mrow><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1218 preview-line 1218\" data_line_start=\"1218\" data_line_end=\"1218\" data_line=\"1218,1219\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>10.20<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>10.20<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=(-3.40+13.6)=10.20eV<\/asciimath><latex style=\"display: none\">\\Delta E=(-3.40+13.6)=10.20 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"31.834ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14070.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 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mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1220 preview-line 1220\" data_line_start=\"1220\" data_line_end=\"1220\" data_line=\"1220,1221\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.626<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.626<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=(6.626 xx10^(-34)xx3xx10^(8))\/(10.2 xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda_{2}=\\frac{6.626 \\times 10^{-34} \\times 3 \\times 10^{8}}{10.2 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" 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65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"6438.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>6.626<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>10.2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1222 preview-line 1222\" data_line_start=\"1222\" data_line_end=\"1222\" data_line=\"1222,1223\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.218<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1218<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.218<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1218<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=(19.878 xx10^(-7))\/(10.2 xx1.6)=1.218 xx10^(-7)m=1218″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda_{2}=\\frac{19.878 \\times 10^{-7}}{10.2 \\times 1.6}=1.218 \\times 10^{-7} \\mathrm{~m}=1218 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.765ex\" height=\"3.101ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1009.9 18460.3 1370.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>19.878<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>10.2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>1.218<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>1218<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1224 preview-line 1224\" data_line_start=\"1224\" data_line_end=\"1224\" data_line=\"1224,1225\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">→<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">\u2192<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(3)rarrn_(2)<\/asciimath><latex style=\"display: none\">n_{3} \\rightarrow n_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.06ex\" height=\"1.531ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -511 3562.7 676.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 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149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><mo stretchy=\"false\">\u2192<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1226 preview-line 1226\" data_line_start=\"1226\" data_line_end=\"1226\" data_line=\"1226,1227\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=(-1.5+3.4)=1.9eV<\/asciimath><latex style=\"display: none\">\\Delta E=(-1.5+3.4)=1.9 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.309ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12070.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 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mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1228 preview-line 1228\" data_line_start=\"1228\" data_line_end=\"1228\" data_line=\"1228,1229\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>6.538<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>6538<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>6.538<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>6538<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1)=(19.878 xx10^(-7))\/(1.9 xx1.6)=6.538 xx10^(-7)m=6538″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda_{1}=\\frac{19.878 \\times 10^{-7}}{1.9 \\times 1.6}=6.538 \\times 10^{-7} \\mathrm{~m}=6538 \\AA<\/latex><mjx-container 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625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17860.3, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>19.878<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>1.9<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>6.538<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>6538<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1230 preview-line 1230\" data_line_start=\"1230\" data_line_end=\"1230\" data_line=\"1230,1231\" count_line=\"1\">The ratio <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>6538<\/mn>\n <mn>1218<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>5.36<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>6538<\/mn>\n <mn>1218<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>5.36<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(1))\/(lambda_(2))=(6538)\/(1218)=5.36<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{1}}{\\lambda_{2}}=\\frac{6538}{1218}=5.36<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.826ex\" height=\"3.14ex\" role=\"img\" focusable=\"false\" 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630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>6538<\/mn><mn>1218<\/mn><\/mfrac><mo>=<\/mo><mn>5.36<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"35\" class=\"preview-paragraph-1232 preview-line 1232 1233\" data_line_start=\"1232\" data_line_end=\"1233\" data_line=\"1232,1234\" count_line=\"2\">\n<li>For longest wavelength of Lyman series <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=2<\/asciimath><latex style=\"display: none\">n_{i}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.864ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2727.5 823.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1234 preview-line 1234 1235 1236 1237 1238 1239 1240\" data_line_start=\"1234\" data_line_end=\"1240\" data_line=\"1234,1241\" count_line=\"7\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1215<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1215<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[(1)\/(lambda_(max))=R((1)\/(1^(2))-(1)\/(2^(2)))=(3R)\/(4)],[lambda_(max)=(4)\/(3R)=(4)\/(3xx1.097 xx10^(7))=1.215 xx10^(-7)m],[lambda_(max)=1215″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\frac{1}{\\lambda_{\\max }}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right)=\\frac{3 R}{4} \\\\\n&\\lambda_{\\max }=\\frac{4}{3 R}=\\frac{4}{3 \\times 1.097 \\times 10^{7}}=1.215 \\times 10^{-7} \\mathrm{~m} \\\\\n&\\lambda_{\\max }=1215 \\AA\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -6.454ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.082ex\" height=\"14.039ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -3352.5 21252.2 6205.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g 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304Q329 345 329 358Q329 364 327 369T322 376T317 380T310 384L307 385H302V431H309Q324 428 408 428Q487 428 493 431H499V385H492Q443 385 411 368Q394 360 377 341T312 257L296 236L358 151Q424 61 429 57T446 50Q464 46 499 46H516V0H510H502Q494 1 482 1T457 2T432 2T414 3Q403 3 377 3T327 1L304 0H295V46H298Q309 46 320 51T331 63Q331 65 291 120L250 175Q249 174 219 133T185 88Q181 83 181 74Q181 63 188 55T206 46Q208 46 208 23V0H201Z\" transform=\"translate(1333, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2226.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3282.5, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 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22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5282.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><mn>4<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>1.215<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>1215<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1242 preview-line 1242\" data_line_start=\"1242\" data_line_end=\"1242\" data_line=\"1242,1243\" count_line=\"1\">The lines of the Lyman series are found in ultraviolet region. (ii) For longest wavelength of Balmer series <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3<\/asciimath><latex style=\"display: none\">n_{i}=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.861ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2727.5 822.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1244 preview-line 1244\" data_line_start=\"1244\" data_line_end=\"1244\" data_line=\"1244,1245\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(max))=R((1)\/(2^(2))-(1)\/(3^(2)))=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\max }}=R\\left(\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right)=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.526ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 11724.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" 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686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1246 preview-line 1246\" data_line_start=\"1246\" data_line_end=\"1246\" data_line=\"1246,1247\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>×<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.563<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6563<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.563<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6563<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda_(max)=(36)\/(5R)=(36)\/(5xx1.097 xx10^(7))=6.563 xx10^(-7)m],[=6563″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned} \\lambda_{\\max }=\\frac{36}{5 R}=\\frac{36}{5 \\times 1.097 \\times 10^{7}} &=6.563 \\times 10^{-7} \\mathrm{~m} \\\\ &=6563 \\AA \\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.388ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.082ex\" height=\"7.907ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1997.5 21252.2 3495.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 655.5)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" 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361Q302 397 257 397Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3333.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6.563<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6563<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1248 preview-line 1248\" data_line_start=\"1248\" data_line_end=\"1248\" data_line=\"1248,1249\" count_line=\"1\">Balmer series lie in the visible region of electromagnetic spectrum.<\/div>\n<ol start=\"36\" class=\"preview-paragraph-1250 preview-line 1250 1251\" data_line_start=\"1250\" data_line_end=\"1251\" data_line=\"1250,1252\" count_line=\"2\">\n<li>Here, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=12.5eV<\/asciimath><latex style=\"display: none\">\\Delta E=12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.354ex\" height=\"1.805ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 5902.6 798\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2930.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4708.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1252 preview-line 1252\" data_line_start=\"1252\" data_line_end=\"1252\" data_line=\"1252,1253\" count_line=\"1\">Energy of an electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of hydrogen atom is, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.061ex\" height=\"2.947ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 6215.1 1302.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2545.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3323.8, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(493.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1457.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5021.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1254 preview-line 1254\" data_line_start=\"1254\" data_line_end=\"1254\" data_line=\"1254,1255\" count_line=\"1\">In ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1256 preview-line 1256\" data_line_start=\"1256\" data_line_end=\"1256\" data_line=\"1256,1257\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-13.6eV<\/asciimath><latex style=\"display: none\">E_{1}=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.084ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 6225.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 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117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5031.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1258 preview-line 1258\" data_line_start=\"1258\" data_line_end=\"1258\" data_line=\"1258,1259\" count_line=\"1\">Energy of an electron in the excited state after absorbing a photon of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">12.5eV<\/asciimath><latex style=\"display: none\">12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.724ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2972 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1778, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> energy will be<\/div>\n<div class=\"preview-paragraph-1260 preview-line 1260\" data_line_start=\"1260\" data_line_end=\"1260\" data_line=\"1260,1261\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo>+<\/mo>\n <mn>12.5<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo>+<\/mo>\n <mn>12.5<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-13.6+12.5=-1.1eV<\/asciimath><latex style=\"display: none\">E_{n}=-13.6+12.5=-1.1 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.701ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 12685.8 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 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d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo>+<\/mo><mn>12.5<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>1.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1262 preview-line 1262\" data_line_start=\"1262\" data_line_end=\"1262\" data_line=\"1262,1263\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1.1<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>12.36<\/mn>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3.5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1.1<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>12.36<\/mn>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3.5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadn^(2)=(-13.6)\/(E_(n))=(-13.6)\/(-1.1)=12.36=>n=3.5<\/asciimath><latex style=\"display: none\">\\therefore \\quad n^{2}=\\frac{-13.6}{E_{n}}=\\frac{-13.6}{-1.1}=12.36 \\Rightarrow n=3.5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.83ex\" height=\"2.999ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 18488.8 1325.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13999.5, 0)\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(15277.3, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(16155.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(17210.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><mrow><mo>\u2212<\/mo><mn>1.1<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>12.36<\/mn><mo stretchy=\"false\">\u21d2<\/mo><mi>n<\/mi><mo>=<\/mo><mn>3.5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1264 preview-line 1264\" data_line_start=\"1264\" data_line_end=\"1264\" data_line=\"1264,1265\" count_line=\"1\">Here, state of electron cannot be fraction.<\/div>\n<div class=\"preview-paragraph-1266 preview-line 1266\" data_line_start=\"1266\" data_line_end=\"1266\" data_line=\"1266,1267\" count_line=\"1\">So, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ( <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2^(“nd “)<\/asciimath><latex style=\"display: none\">2^{\\text {nd }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.423ex\" height=\"1.932ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1513.1 853.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(556, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1112, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>2<\/mn><mrow><mtext>nd\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">)<\/asciimath><latex style=\"display: none\">)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1268 preview-line 1268\" data_line_start=\"1268\" data_line_end=\"1268\" data_line=\"1268,1269\" count_line=\"1\">The wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda<\/asciimath><latex style=\"display: none\">\\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.027ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.319ex\" height=\"1.597ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 583 706\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the first member of Lyman series is given by<\/div>\n<div class=\"preview-paragraph-1270 preview-line 1270\" data_line_start=\"1270\" data_line_end=\"1270\" data_line=\"1270,1271\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(2^(2))]=(3)\/(4)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right]=\\frac{3}{4} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.975ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10155.2 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" 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46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1272 preview-line 1272\" data_line_start=\"1272\" data_line_end=\"1272\" data_line=\"1272,1273\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda=(4)\/(3R)=(4)\/(3xx1.09 xx10^(7))=>lambda=1.215 xx10^(-7)m<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda=\\frac{4}{3 R}=\\frac{4}{3 \\times 1.09 \\times 10^{7}} \\Rightarrow \\lambda=1.215 \\times 10^{-7} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.067ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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class=\"preview-paragraph-1274 preview-line 1274\" data_line_start=\"1274\" data_line_end=\"1274\" data_line=\"1274,1275\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda=121 xx10^(-9)m=>lambda=121nm<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda=121 \\times 10^{-9} \\mathrm{~m} \\Rightarrow \\lambda=121 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.214ex\" height=\"2.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 15564.6 946\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path 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54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13925.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>121<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>121<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1276 preview-line 1276\" data_line_start=\"1276\" data_line_end=\"1276\" data_line=\"1276,1277\" count_line=\"1\">The wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda^(‘)<\/asciimath><latex style=\"display: none\">\\lambda^{\\prime}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.027ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.872ex\" height=\"1.744ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -759 827.5 771\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"2032\" d=\"M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>\u03bb<\/mi><mrow><mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the first member of the Balmer series is given by<\/div>\n<div class=\"preview-paragraph-1278 preview-line 1278\" data_line_start=\"1278\" data_line_end=\"1278\" data_line=\"1278,1279\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda^(‘))=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda^{\\prime}}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.166ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10681.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(335.8, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -376.7) 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566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mi\" transform=\"translate(9922.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msup><mi>\u03bb<\/mi><mrow><mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1280 preview-line 1280\" data_line_start=\"1280\" data_line_end=\"1280\" data_line=\"1280,1281\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>×<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>\u00d7<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1.09<\/mn> \n <mo>\u00d7<\/mo> \n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda^(‘)=(36)\/(5R)=(36)\/(5xx(1.09 xx10^(7)))<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda^{\\prime}=\\frac{36}{5 R}=\\frac{36}{5 \\times\\left(1.09 \\times 10^{7}\\right)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" 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662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4417.6, 0)\"><path data-c=\"29\" d=\"M305 251Q305 -145 69 -349H56Q43 -349 39 -347T35 -338Q37 -333 60 -307T108 -239T160 -136T204 27T221 250T204 473T160 636T108 740T60 807T35 839Q35 850 50 850H56H69Q197 743 256 566Q305 425 305 251Z\"><\/path><\/g><\/g><\/g><rect width=\"4551.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><msup><mi>\u03bb<\/mi><mrow><mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1282 preview-line 1282\" data_line_start=\"1282\" data_line_end=\"1282\" data_line=\"1282,1283\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.56<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.56<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=6.56 xx10^(-7)m=656 xx10^(-9)m=656nm<\/asciimath><latex style=\"display: none\">=6.56 \\times 10^{-7} \\mathrm{~m}=656 \\times 10^{-9} \\mathrm{~m}=656 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"42.213ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 18658.1 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3056, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 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210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10148.7, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(11148.9, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 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343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(14463.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(15519.1, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17019.1, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>6.56<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>656<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>656<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"37\" class=\"preview-paragraph-1284 preview-line 1284 1285\" data_line_start=\"1284\" data_line_end=\"1285\" data_line=\"1284,1286\" count_line=\"2\">\n<li>(i) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:’E_(n)=(-13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">\\because E_{n}=\\frac{-13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.683ex\" height=\"2.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 6932 1306.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 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mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1286 preview-line 1286\" data_line_start=\"1286\" data_line_end=\"1286\" data_line=\"1286,1287\" count_line=\"1\">Energy of the photon emitted during a transition of the electron from the first excited state to its ground state is,<\/div>\n<div class=\"preview-paragraph-1288 preview-line 1288\" data_line_start=\"1288\" data_line_end=\"1288\" data_line=\"1288,1289\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=E_(2)-E_(1)<\/asciimath><latex style=\"display: none\">\\Delta E=E_{2}-E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.561ex\" height=\"1.959ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 6436.1 866\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 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0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 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<\/mrow>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(-13.6)\/(2^(2))-((-13.6)\/(1^(2)))=(-13.6)\/(4)+(13.6)\/(1)=-3.40+13.6<\/asciimath><latex style=\"display: none\">=\\frac{-13.6}{2^{2}}-\\left(\\frac{-13.6}{1^{2}}\\right)=\\frac{-13.6}{4}+\\frac{13.6}{1}=-3.40+13.6<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.32ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 21357.6 1799\" aria-hidden=\"true\"><g 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573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2833.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>10.2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1294 preview-line 1294\" data_line_start=\"1294\" data_line_end=\"1294\" data_line=\"1294,1295\" count_line=\"1\">This transition lies in the region of Lyman series. (ii) (a) The energy levels of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom are given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(Rhc)\/(n^(2))=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{R h c}{n^{2}}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.662ex\" height=\"2.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 10016.8 1322.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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transform=\"translate(2545.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3323.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(759, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1335, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(490.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" 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366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" 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186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1457.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(8822.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1296 preview-line 1296\" data_line_start=\"1296\" data_line_end=\"1296\" data_line=\"1296,1297\" count_line=\"1\">For first excited state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1298 preview-line 1298\" data_line_start=\"1298\" data_line_end=\"1298\" data_line=\"1298,1299\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(2)=-(13.6)\/((2)^(2))eV=-3.4eV<\/asciimath><latex style=\"display: none\">E_{2}=-\\frac{13.6}{(2)^{2}} \\mathrm{eV}=-3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.372ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.271ex\" height=\"3.329ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 10727.9 1471.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 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126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1300 preview-line 1300\" data_line_start=\"1300\" data_line_end=\"1300\" data_line=\"1300,1301\" count_line=\"1\">Kinetic energy of electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=2)<\/asciimath><latex style=\"display: none\">(n=2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2822.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state is<\/div>\n<div class=\"preview-paragraph-1302 preview-line 1302\" data_line_start=\"1302\" data_line_end=\"1302\" data_line=\"1302,1303\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K_(2)=-E_(2)=+3.4eV<\/asciimath><latex style=\"display: none\">K_{2}=-E_{2}=+3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.564ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 9089.2 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(7895.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>K<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>+<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1304 preview-line 1304\" data_line_start=\"1304\" data_line_end=\"1304\" data_line=\"1304,1305\" count_line=\"1\">(b) Radius in the first excited state<\/div>\n<div class=\"preview-paragraph-1306 preview-line 1306\" data_line_start=\"1306\" data_line_end=\"1306\" data_line=\"1306,1307\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">(<\/mo>\n <mn>0.53<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">(<\/mo>\n <mn>0.53<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(1)=(2)^(2)(0.53)”\u212b”<\/asciimath><latex style=\"display: none\">r_{1}=(2)^{2}(0.53) \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.895ex\" height=\"2.452ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 7025.7 1083.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 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429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3869.7, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4258.7, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6036.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6425.7, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mrow><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>0.53<\/mn><mo stretchy=\"false\">)<\/mo><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1308 preview-line 1308\" data_line_start=\"1308\" data_line_end=\"1308\" data_line=\"1308,1309\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2.12<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2.12<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(1)=2.12″\u212b”<\/asciimath><latex style=\"display: none\">r_{1}=2.12 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.331ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 4566.1 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2188.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3966.1, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2.12<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"38\" class=\"preview-paragraph-1310 preview-line 1310 1311 1312 1313 1314 1315\" data_line_start=\"1310\" data_line_end=\"1315\" data_line=\"1310,1316\" count_line=\"6\">\n<li>\n<div>Refer to answer 19.<\/div>\n<\/li>\n<li>\n<div>Refer to answer 32.<\/div>\n<\/li>\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=(hc)\/(lambda)=(E_(2)-E_(1))<\/asciimath><latex style=\"display: none\">h v=\\frac{h c}{\\lambda}=\\left(E_{2}-E_{1}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.8ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.736ex\" height=\"2.801ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 9165.1 1238.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" 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440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3894.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/((E_(2)-E_(1)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{\\left(E_{2}-E_{1}\\right)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1316 preview-line 1316\" data_line_start=\"1316\" data_line_end=\"1316\" data_line=\"1316,1317\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad lambda=[(6.63 xx10^(-34)xx3xx10^(8))\/([-0.85-(-3.4)]xx1.6 xx10^(-19))]m<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\lambda=\\left[\\frac{6.63 \\times 10^{-34} \\times 3 \\times 10^{8}}{[-0.85-(-3.4)] \\times 1.6 \\times 10^{-19}}\\right] \\mathrm{m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.734ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 14468.3 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" 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629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"8590\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(9302, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13635.3, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1318 preview-line 1318\" data_line_start=\"1318\" data_line_end=\"1318\" data_line=\"1318,1319\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.875<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4875<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.875<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4875<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=4.875 xx10^(-7)m=4875″\u212b”<\/asciimath><latex style=\"display: none\">=4.875 \\times 10^{-7} \\mathrm{~m}=4875 \\AA<\/latex><mjx-container 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46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(7870.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(8926.5, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(10926.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>4.875<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>4875<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1320 preview-line 1320\" data_line_start=\"1320\" data_line_end=\"1320\" data_line=\"1320,1321\" count_line=\"1\">Balmer series<\/div>\n<ol start=\"41\" class=\"preview-paragraph-1322 preview-line 1322 1323\" data_line_start=\"1322\" data_line_end=\"1323\" data_line=\"1322,1324\" count_line=\"2\">\n<li>(i) The kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E_(k))<\/asciimath><latex style=\"display: none\">\\left(E_{k}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.376ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1934.4 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1545.4, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in an orbit is equal to negative of its total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1324 preview-line 1324\" data_line_start=\"1324\" data_line_end=\"1324\" data_line=\"1324,1325\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=-E=-(-1.5)=1.5eV<\/asciimath><latex style=\"display: none\">E_{k}=-E=-(-1.5)=1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.921ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12783.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1434.2, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2490, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3268, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4309.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5365.5, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6143.5, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 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214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11589.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1326 preview-line 1326\" data_line_start=\"1326\" data_line_end=\"1326\" data_line=\"1326,1327\" count_line=\"1\">(ii) The potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E_(p))<\/asciimath><latex style=\"display: none\">\\left(E_{p}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.348ex\" height=\"2.347ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1921.7 1037.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path 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336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1532.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in an orbit is equal to twice of its total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1328 preview-line 1328\" data_line_start=\"1328\" data_line_end=\"1328\" data_line=\"1328,1329\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>×<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.0<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u00d7<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.0<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=2E=-1.5 xx2=-3.0eV<\/asciimath><latex style=\"display: none\">E_{p}=2 E=-1.5 \\times 2=-3.0 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.4ex\" height=\"2.195ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 13436.8 970.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 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365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1421.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2477.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2977.2, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4019, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 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130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(12242.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>3.0<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1330 preview-line 1330\" data_line_start=\"1330\" data_line_end=\"1330\" data_line=\"1330,1331\" count_line=\"1\">(iii) Here, ground state energy of the H-atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-13.6eV<\/asciimath><latex style=\"display: none\">=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.873ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4805.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 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data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3611.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1332 preview-line 1332\" data_line_start=\"1332\" data_line_end=\"1332\" data_line=\"1332,1333\" count_line=\"1\">When the electron goes from the excited state to the ground state, energy emitted is given by<\/div>\n<div class=\"preview-paragraph-1334 preview-line 1334\" data_line_start=\"1334\" data_line_end=\"1334\" data_line=\"1334,1335\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=-1.5-(-13.6)=12.1eV=12.1 xx1.6 xx10^(-19)J<\/asciimath><latex style=\"display: none\">E=-1.5-(-13.6)=12.1 \\mathrm{eV}=12.1 \\times 1.6 \\times 10^{-19} \\mathrm{~J}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"51.858ex\" height=\"2.52ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 22921.2 1114\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 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244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(22157.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"4A\" d=\"M89 177Q115 177 133 160T152 112Q152 88 137 72T102 52Q99 51 101 49Q106 43 129 29Q159 15 190 15Q232 15 256 48T286 126Q286 127 286 142T286 183T286 238T287 306T287 378Q287 403 287 429T287 479T287 524T286 563T286 593T286 614V621Q281 630 263 633T182 637H154V683H166Q187 680 332 680Q439 680 457 683H465V637H449Q422 637 401 634Q393 631 389 623Q388 621 388 376T387 123Q377 61 322 20T194 -22Q188 -22 177 -21T160 -20Q96 -9 61 29T25 110Q25 144 44 160T89 177Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>12.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>12.1<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1336 preview-line 1336\" data_line_start=\"1336\" data_line_end=\"1336\" data_line=\"1336,1337\" count_line=\"1\">Now, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(hc)\/(lambda)<\/asciimath><latex style=\"display: none\">E=\\frac{h c}{\\lambda}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.8ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.355ex\" height=\"2.801ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3251 1238.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(370.6, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"913.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1338 preview-line 1338\" data_line_start=\"1338\" data_line_end=\"1338\" data_line=\"1338,1339\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/(E)=(6.62 xx10^(-34)xx3xx10^(8))\/(12.1 xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{E}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{12.1 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.273ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 10728.7 1476.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 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data_line_start=\"1340\" data_line_end=\"1340\" data_line=\"1340,1341\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.025<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.025<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1.025 xx10^(-7)<\/asciimath><latex style=\"display: none\">\\lambda=1.025 \\times 10^{-7}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.676ex\" height=\"2.156ex\" 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118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5417, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1.025<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1342 preview-line 1342\" data_line_start=\"1342\" data_line_end=\"1342\" data_line=\"1342,1343\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1025<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1025<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1025″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda=1025 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.218ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 4516.6 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3916.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1025<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"42\" class=\"preview-paragraph-1344 preview-line 1344 1345 1346 1347\" data_line_start=\"1344\" data_line_end=\"1347\" data_line=\"1344,1348\" count_line=\"4\">\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mrow>\n <mi>r<\/mi>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:'(mv^(2))\/(r_(n))=(1)\/(4piepsi_(0))(e^(2))\/(r_(n)^(2))<\/asciimath><latex style=\"display: none\">\\because \\frac{m v^{2}}{r_{n}}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.38ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.55ex\" height=\"3.605ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6873.2 1593.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 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381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -247) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"854.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2235<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msubsup><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1348 preview-line 1348\" data_line_start=\"1348\" data_line_end=\"1348\" data_line=\"1348,1349\" count_line=\"1\">and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr_(n)=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r_{n}=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.071ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4893.4 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2566, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1350 preview-line 1350\" data_line_start=\"1350\" data_line_end=\"1350\" data_line=\"1350,1351\" count_line=\"1\">From eqn. (i) and (ii)<\/div>\n<div class=\"preview-paragraph-1352 preview-line 1352 1353 1354\" data_line_start=\"1352\" data_line_end=\"1354\" data_line=\"1352,1355\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadr_(n)=(epsi_(0)h^(2)n^(2))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">\\therefore \\quad r_{n}=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.96ex\" height=\"5.237ex\" 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299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g 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629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1849.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 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31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3052.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1356 preview-line 1356\" data_line_start=\"1356\" data_line_end=\"1356\" data_line=\"1356,1357\" count_line=\"1\">Total energy<\/div>\n<div class=\"preview-paragraph-1358 preview-line 1358 1359 1360 1361 1362 1363 1364\" data_line_start=\"1358\" data_line_end=\"1364\" data_line=\"1358,1365\" count_line=\"7\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msubsup>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msubsup>\n <mrow>\n <mi>v<\/mi>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E_(n)=(1)\/(2)mv_(n)^(2)-(1)\/(4piepsi_(0))(e^(2))\/(r_(n))=(1)\/(8piepsi_(0))(e^(2))\/(r_(n))-(1)\/(4piepsi_(0))(e^(2))\/(r_(n))],[E_(n)=-(1)\/(8piepsi_(0))(e^(2))\/(r_(n))=-(1)\/(8epsi_(0)^(2))(me^(4))\/(h^(2)n^(2))],[E_(n)=(-Rhc)\/(n^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&E_{n}=\\frac{1}{2} m v_{n}^{2}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}=\\frac{1}{8 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}} \\\\\n&E_{n}=-\\frac{1}{8 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}=-\\frac{1}{8 \\varepsilon_{0}^{2}} \\frac{m e^{4}}{h^{2} n^{2}} \\\\\n&E_{n}=\\frac{-R h c}{n^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -8.203ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"46.009ex\" height=\"17.537ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -4125.8 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120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(991.2, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 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right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msubsup><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfrac><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1366 preview-line 1366\" data_line_start=\"1366\" data_line_end=\"1366\" data_line=\"1366,1367\" count_line=\"1\">where Rydberg constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <mi>c<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <mi>c<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=(me^(4))\/(8epsi_(0)^(2)h^(3)c)<\/asciimath><latex style=\"display: none\">R=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{3} c}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.181ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4499.8 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2092.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(585.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(2349.1, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><rect width=\"2167.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><mi>c<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1368 preview-line 1368\" data_line_start=\"1368\" data_line_end=\"1368\" data_line=\"1368,1369\" count_line=\"1\">Energy emitted <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">\\Delta E=E_{i}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.393ex\" height=\"2.287ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 6361.9 1011\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2930.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4184.7, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(5185, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1370 preview-line 1370 1371 1372\" data_line_start=\"1370\" data_line_end=\"1372\" data_line=\"1370,1373\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=Rhc[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))]<\/asciimath><latex style=\"display: none\">\\Delta E=R h c\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.646ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 10009.5 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 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424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -315.5) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><rect width=\"1238.9\" height=\"60\" 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73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4727.9, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1374 preview-line 1374\" data_line_start=\"1374\" data_line_end=\"1374\" data_line=\"1374,1375\" count_line=\"1\">But <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>h<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>h<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=hv<\/asciimath><latex style=\"display: none\">\\Delta E=h v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.031ex\" height=\"1.805ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 3991.6 798\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2930.6, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3506.6, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mi>h<\/mi><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1376 preview-line 1376 1377 1378\" data_line_start=\"1376\" data_line_end=\"1378\" data_line=\"1376,1379\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mtext> or <\/mtext>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=Rc[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))]” or “v=(me^(4))\/(8epsi_(0)^(2)h^(3))((1)\/(n_(f)^(2))-(1)\/(n_(i)^(2)))<\/asciimath><latex style=\"display: none\">v=R c\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right] \\text { or } v=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{3}}\\left(\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"45.362ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 20050 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 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113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4936.9, 0)\"><path data-c=\"29\" d=\"M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>v<\/mi><mo>=<\/mo><mi>R<\/mi><mi>c<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mtext>\u00a0or\u00a0<\/mtext><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1380 preview-line 1380\" data_line_start=\"1380\" data_line_end=\"1380\" data_line=\"1380,1381\" count_line=\"1\">When electron in hydrogen atom jumps from energy state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=4<\/asciimath><latex style=\"display: none\">n_{i}=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2727.5 834.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=3,2,1<\/asciimath><latex style=\"display: none\">n_{f}=3,2,1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.773ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 4761.8 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) 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56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2872.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3317.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3817.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4261.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, the Paschen, Balmer and Lyman spectral series are found.<\/div>\n<ol start=\"44\" class=\"preview-paragraph-1382 preview-line 1382 1383 1384 1385 1386 1387\" data_line_start=\"1382\" data_line_end=\"1387\" data_line=\"1382,1388\" count_line=\"6\">\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div>de-Broglie hypothesis : It states that a moving particle sometimes acts as a wave and sometimes as a particle or a wave is associated with moving particle which controls the particle in every respect. The wave associated with moving particle is called matter wave or de-Broglie wave whose wavelength is given by<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1388 preview-line 1388\" data_line_start=\"1388\" data_line_end=\"1388\" data_line=\"1388,1389\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv)<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.512ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3320.3 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(498.2, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1163.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1390 preview-line 1390\" data_line_start=\"1390\" data_line_end=\"1390\" data_line=\"1390,1391\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the mass and velocity of the particle and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h<\/asciimath><latex style=\"display: none\">h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.303ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 576 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is Planck’s constant.<\/div>\n<ol start=\"47\" class=\"preview-paragraph-1392 preview-line 1392 1393\" data_line_start=\"1392\" data_line_end=\"1393\" data_line=\"1392,1394\" count_line=\"2\">\n<li>Kinetic energy of the electron in the second state of hydrogen atom<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1394 preview-line 1394\" data_line_start=\"1394\" data_line_end=\"1394\" data_line=\"1394,1395\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(K)=(13.6eV)\/(n^(2))=(13.6eV)\/(4)=3.4 xx1.6 xx10^(-19)J<\/asciimath><latex style=\"display: none\">E_{K}=\\frac{13.6 \\mathrm{eV}}{n^{2}}=\\frac{13.6 \\mathrm{eV}}{4}=3.4 \\times 1.6 \\times 10^{-19} \\mathrm{~J}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"42.019ex\" height=\"2.974ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -877 18572.5 1314.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1694.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2750.2, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1778, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(916, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2301.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5569.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(6625.3, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 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397 257 397Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14501, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(15501.2, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17808.5, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"4A\" d=\"M89 177Q115 177 133 160T152 112Q152 88 137 72T102 52Q99 51 101 49Q106 43 129 29Q159 15 190 15Q232 15 256 48T286 126Q286 127 286 142T286 183T286 238T287 306T287 378Q287 403 287 429T287 479T287 524T286 563T286 593T286 614V621Q281 630 263 633T182 637H154V683H166Q187 680 332 680Q439 680 457 683H465V637H449Q422 637 401 634Q393 631 389 623Q388 621 388 376T387 123Q377 61 322 20T194 -22Q188 -22 177 -21T160 -20Q96 -9 61 29T25 110Q25 144 44 160T89 177Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mrow><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1396 preview-line 1396\" data_line_start=\"1396\" data_line_end=\"1396\" data_line=\"1396,1397\" count_line=\"1\">de Broglie wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(sqrt(2mE_(K)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{\\sqrt{2 m E_{K}}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" 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429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 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role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><msqrt><mn>2<\/mn><mi>m<\/mi><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><\/msqrt><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1398 preview-line 1398 1399 1400\" data_line_start=\"1398\" data_line_end=\"1400\" data_line=\"1398,1401\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(6.63 xx10^(-34))\/(sqrt(2xx9.1 xx10^(-31)xx3.4 xx1.6 xx10^(-19)))=0.67nm<\/asciimath><latex style=\"display: none\">=\\frac{6.63 \\times 10^{-34}}{\\sqrt{2 \\times 9.1 \\times 10^{-31} \\times 3.4 \\times 1.6 \\times 10^{-19}}}=0.67 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.76ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"50.514ex\" height=\"6.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1547.8 22327 2767.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><msqrt><mn>2<\/mn><mo>\u00d7<\/mo><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/msqrt><\/mfrac><mo>=<\/mo><mn>0.67<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"48\" class=\"preview-paragraph-1402 preview-line 1402 1403\" data_line_start=\"1402\" data_line_end=\"1403\" data_line=\"1402,1404\" count_line=\"2\">\n<li>According to Bohr’s postulates,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1404 preview-line 1404 1405 1406\" data_line_start=\"1404\" data_line_end=\"1406\" data_line=\"1404,1407\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.777ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 4763.6 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(273, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1376\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1408 preview-line 1408\" data_line_start=\"1408\" data_line_end=\"1408\" data_line=\"1408,1409\" count_line=\"1\">(where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=<\/asciimath><latex style=\"display: none\">m v r=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.493ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 2869.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> angular momentum of an electron and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is an integer).<\/div>\n<div class=\"preview-paragraph-1410 preview-line 1410\" data_line_start=\"1410\" data_line_end=\"1410\" data_line=\"1410,1411\" count_line=\"1\">Thus, the centripetal force, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.822ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 1689.1 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (experienced by the electron) is due to the electrostatic attraction, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(kZe^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{k Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.377ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 1934.5 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1244, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(665.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1694.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=<\/asciimath><latex style=\"display: none\">Z=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.024ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1778.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Atomic number<\/div>\n<div class=\"preview-paragraph-1412 preview-line 1412\" data_line_start=\"1412\" data_line_end=\"1412\" data_line=\"1412,1413\" count_line=\"1\">Therefore, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(kZe^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.215ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4957.2 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1244, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(665.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1694.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1414 preview-line 1414\" data_line_start=\"1414\" data_line_end=\"1414\" data_line=\"1414,1415\" count_line=\"1\">Substituting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v^(2)<\/asciimath><latex style=\"display: none\">v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.01ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 888.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from (i), we obtain:<\/div>\n<div class=\"preview-paragraph-1416 preview-line 1416 1417 1418\" data_line_start=\"1416\" data_line_end=\"1418\" data_line=\"1416,1419\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m)\/(r)(n^(2)h^(2))\/(4pi^(2)m^(2)r^(2))=(kZe^(2))\/(r^(2))quad:.quad r=(n^(2)h^(2))\/(4pi^(2)mkZe^(2))<\/asciimath><latex style=\"display: none\">\\frac{m}{r} \\frac{n^{2} h^{2}}{4 \\pi^{2} m^{2} r^{2}}=\\frac{k Z e^{2}}{r^{2}} \\quad \\therefore \\quad r=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"43.364ex\" height=\"5.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 19167 2314.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(220, 676)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(433.5, -686)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1078\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1318, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(1033.3, 676)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1003.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(570, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1473.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(878, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(2755.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3809.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5645.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(6701.2, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1244, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(849.5, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 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x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mi>m<\/mi><mi>r<\/mi><\/mfrac><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>m<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1420 preview-line 1420\" data_line_start=\"1420\" data_line_end=\"1420\" data_line=\"1420,1421\" count_line=\"1\">The relation for the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 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<mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(n^(2)h^(2))\/(4pi^(2)mkZe^(2))<\/asciimath><latex style=\"display: none\">=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" 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103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3357.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<ol start=\"49\" class=\"preview-paragraph-1422 preview-line 1422 1423\" data_line_start=\"1422\" data_line_end=\"1423\" data_line=\"1422,1424\" count_line=\"2\">\n<li>(i) Bohr’s quantization condition : The electron revolves around the nucleus only in those orbits for which the angular momentum is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h\/\/2pi<\/asciimath><latex style=\"display: none\">h \/ 2 \\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.855ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2146 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(576, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1076, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1576, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1424 preview-line 1424 1425 1426\" data_line_start=\"1424\" data_line_end=\"1426\" data_line=\"1424,1427\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext> i.e., <\/mtext>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext>\u00a0i.e.,\u00a0<\/mtext>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>.<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">” i.e., “L=mvr=n(h)\/(2pi);n=1,2,3,dots.<\/asciimath><latex style=\"display: none\">\\text { i.e., } L=m v r=n \\frac{h}{2 \\pi} ; n=1,2,3, \\ldots .<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.554ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 16157 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 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display=\"block\"><mtext>\u00a0i.e.,\u00a0<\/mtext><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>;<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1428 preview-line 1428\" data_line_start=\"1428\" data_line_end=\"1428\" data_line=\"1428,1429\" count_line=\"1\">de Broglie hypothesis may be used to derive Bohr’s formula by considering the electron to be a wave spread over the entire orbit, rather than as a particle which at any instant is located at a point in its orbit. The stable orbits in an atom are those which are standing waves. Formation of standing waves require that the circumference of the orbit is equal in length to an integral multiple of the wavelength. Thus, if <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the radius of the orbit<\/div>\n<div class=\"preview-paragraph-1430 preview-line 1430 1431 1432\" data_line_start=\"1430\" data_line_end=\"1432\" data_line=\"1430,1433\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mi>p<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>∵<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>p<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mi>p<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2235<\/mo> \n <mi>\u03bb<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mi>h<\/mi>\n <mi>p<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: 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-148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><rect width=\"776\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4613.3, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mn>2<\/mn><mi>\u03c0<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mi>p<\/mi><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo>\u2235<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mi>p<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1434 preview-line 1434\" data_line_start=\"1434\" data_line_end=\"1434\" data_line=\"1434,1435\" count_line=\"1\">which gives the angular momentum quantization<\/div>\n<div class=\"preview-paragraph-1436 preview-line 1436 1437 1438\" data_line_start=\"1436\" data_line_end=\"1438\" data_line=\"1436,1439\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>p<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>p<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=pr=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">L=p r=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.507ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 6412.1 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(958.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2014.6, 0)\"><path data-c=\"70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2517.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3246.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4302.1, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 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683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>L<\/mi><mo>=<\/mo><mi>p<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1441 preview-line 1441\" data_line_start=\"1441\" data_line_end=\"1441\" data_line=\"1441,1442\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=274&width=678&top_left_y=454&top_left_x=286\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1443 preview-line 1443\" data_line_start=\"1443\" data_line_end=\"1443\" data_line=\"1443,1444\" count_line=\"1\">(ii)<\/div>\n<div class=\"preview-paragraph-1445 preview-line 1445 1446\" data_line_start=\"1445\" data_line_end=\"1446\" data_line=\"1445,1447\" count_line=\"2\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=263&width=508&top_left_y=734&top_left_x=317\" alt=\"\"><br>\n<img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=542&width=648&top_left_y=454&top_left_x=316\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1448 preview-line 1448\" data_line_start=\"1448\" data_line_end=\"1448\" data_line=\"1448,1449\" count_line=\"1\">Clearly, from energy level diagram,<\/div>\n<div class=\"preview-paragraph-1450 preview-line 1450\" data_line_start=\"1450\" data_line_end=\"1450\" data_line=\"1450,1451\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>+<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <mo>+<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(C)-E_(A)=(E_(C)-E_(B))+(E_(B)-E_(A))<\/asciimath><latex style=\"display: none\">E_{C}-E_{A}=\\left(E_{C}-E_{B}\\right)+\\left(E_{B}-E_{A}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>C<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>B<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>+<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>B<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>A<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1452 preview-line 1452\" data_line_start=\"1452\" data_line_end=\"1452\" data_line=\"1452,1453\" count_line=\"1\">(On the basis of energy of emitted photon).<\/div>\n<div class=\"preview-paragraph-1454 preview-line 1454\" data_line_start=\"1454\" data_line_end=\"1454\" data_line=\"1454,1455\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n 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136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"913.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>+<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1456 preview-line 1456\" data_line_start=\"1456\" data_line_end=\"1456\" data_line=\"1456,1457\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>(1)\/(lambda_(3))=(1)\/(lambda_(1))+(1)\/(lambda_(2))=>lambda_(3)=(lambda_(1)lambda_(2))\/(lambda_(1)+lambda_(2))<\/asciimath><latex style=\"display: none\">\\Rightarrow \\frac{1}{\\lambda_{3}}=\\frac{1}{\\lambda_{1}}+\\frac{1}{\\lambda_{2}} \\Rightarrow \\lambda_{3}=\\frac{\\lambda_{1} \\lambda_{2}}{\\lambda_{1}+\\lambda_{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.56ex\" height=\"3.165ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -936.8 13507.6 1398.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 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308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2145.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mrow><mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1458 preview-line 1458\" data_line_start=\"1458\" data_line_end=\"1458\" data_line=\"1458,1459\" count_line=\"1\">which is the required relation between the three given wavelengths.<\/div>\n<ol start=\"50\" class=\"preview-paragraph-1460 preview-line 1460 1461\" data_line_start=\"1460\" data_line_end=\"1461\" data_line=\"1460,1462\" count_line=\"2\">\n<li>Kinetic energy in the first excited state of hydrogen atom<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1462 preview-line 1462\" data_line_start=\"1462\" data_line_end=\"1462\" data_line=\"1462,1463\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(K)=3.4eV=3.4 xx1.6 xx10^(-19)J<\/asciimath><latex style=\"display: none\">E_{K}=3.4 \\mathrm{eV}=3.4 \\times 1.6 \\times 10^{-19} \\mathrm{~J}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"33.095ex\" height=\"2.294ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 14627.9 1014\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 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112Q152 88 137 72T102 52Q99 51 101 49Q106 43 129 29Q159 15 190 15Q232 15 256 48T286 126Q286 127 286 142T286 183T286 238T287 306T287 378Q287 403 287 429T287 479T287 524T286 563T286 593T286 614V621Q281 630 263 633T182 637H154V683H166Q187 680 332 680Q439 680 457 683H465V637H449Q422 637 401 634Q393 631 389 623Q388 621 388 376T387 123Q377 61 322 20T194 -22Q188 -22 177 -21T160 -20Q96 -9 61 29T25 110Q25 144 44 160T89 177Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1464 preview-line 1464\" data_line_start=\"1464\" data_line_end=\"1464\" data_line=\"1464,1465\" count_line=\"1\">De Broglie wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(sqrt(2mE_(K)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{\\sqrt{2 m E_{K}}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.334ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.167ex\" height=\"3.335ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4935.8 1474.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 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width=\"2779.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><msqrt><mn>2<\/mn><mi>m<\/mi><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><\/msqrt><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1466 preview-line 1466\" data_line_start=\"1466\" data_line_end=\"1466\" data_line=\"1466,1467\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(6.63 xx10^(-34))\/(sqrt(2xx9.1 xx10^(-31)xx3.4 xx1.6 xx10^(-19)))=0.67nm<\/asciimath><latex style=\"display: none\">=\\frac{6.63 \\times 10^{-34}}{\\sqrt{2 \\times 9.1 \\times 10^{-31} \\times 3.4 \\times 1.6 \\times 10^{-19}}}=0.67 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.654ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.303ex\" height=\"3.94ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 16045.8 1741.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><msqrt><mn>2<\/mn><mo>\u00d7<\/mo><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/msqrt><\/mfrac><mo>=<\/mo><mn>0.67<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"51\" class=\"preview-paragraph-1468 preview-line 1468 1469\" data_line_start=\"1468\" data_line_end=\"1469\" data_line=\"1468,1470\" count_line=\"2\">\n<li><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=2.2 xx10^(8)m\/\/s<\/asciimath><latex style=\"display: none\">v=2.2 \\times 10^{8} \\mathrm{~m} \/ \\mathrm{s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" 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mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\/<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1470 preview-line 1470\" data_line_start=\"1470\" data_line_end=\"1470\" data_line=\"1470,1471\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mo>?<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mo>?<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=?<\/asciimath><latex style=\"display: none\">\\lambda=?<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.776ex\" height=\"1.781ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 2110.8 787\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1638.8, 0)\"><path data-c=\"3F\" d=\"M226 668Q190 668 162 656T124 632L114 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>P<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>P<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(P)quad:.quad P=mv<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{P} \\quad \\therefore \\quad P=m v<\/latex><mjx-container 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scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>P<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1474 preview-line 1474\" data_line_start=\"1474\" data_line_end=\"1474\" data_line=\"1474,1475\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv)=(6.63 xx10^(-34))\/(9.1 xx10^(-31)xx2.2 xx10^(8))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v}=\\frac{6.63 \\times 10^{-34}}{9.1 \\times 10^{-31} \\times 2.2 \\times 10^{8}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>2.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1476 preview-line 1476\" data_line_start=\"1476\" data_line_end=\"1476\" data_line=\"1476,1477\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.331<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>3.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>12<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.331<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>3.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>12<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=0.331 xx10^(-11)=3.3 xx10^(-12)m<\/asciimath><latex style=\"display: none\">=0.331 \\times 10^{-11}=3.3 \\times 10^{-12} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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data_line_end=\"1479\" data_line=\"1478,1480\" count_line=\"2\">\n<li>According to Bohr’s second postulate quantization of angular momentum<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1480 preview-line 1480\" data_line_start=\"1480\" data_line_end=\"1480\" data_line=\"1480,1481\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv_(n)r_(n)=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v_{n} r_{n}=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.332ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 5892.7 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 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666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1482 preview-line 1482\" data_line_start=\"1482\" data_line_end=\"1482\" data_line=\"1482,1483\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(nh)\/(2pi mv_(n))<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{n h}{2 \\pi m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.757ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4754.6 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 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339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1948, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2255.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h<\/asciimath><latex style=\"display: none\">h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.303ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 576 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the Planck’s constant<\/div>\n<div class=\"preview-paragraph-1484 preview-line 1484\" data_line_start=\"1484\" data_line_end=\"1484\" data_line=\"1484,1485\" count_line=\"1\">Circumference of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbital state in hydrogen atom,<\/div>\n<div class=\"preview-paragraph-1486 preview-line 1486\" data_line_start=\"1486\" data_line_end=\"1486\" data_line=\"1486,1487\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=2pi(nh)\/(2pi mv_(n))<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=2 \\pi \\frac{n h}{2 \\pi m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.599ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6894.6 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3328.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3828.8, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4398.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(832.1, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1948, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2255.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1488 preview-line 1488\" data_line_start=\"1488\" data_line_end=\"1488\" data_line=\"1488,1489\" count_line=\"1\">(Using (i))<\/div>\n<div class=\"preview-paragraph-1490 preview-line 1490\" data_line_start=\"1490\" data_line_end=\"1490\" data_line=\"1490,1491\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.823ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 5668 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3328.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3928.8, 0)\"><g data-mml-node=\"mi\" transform=\"translate(665.9, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1492 preview-line 1492\" data_line_start=\"1492\" data_line_end=\"1492\" data_line=\"1492,1493\" count_line=\"1\">But de Broglie wavelength of the electron<\/div>\n<div class=\"preview-paragraph-1494 preview-line 1494\" data_line_start=\"1494\" data_line_end=\"1494\" data_line=\"1494,1495\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.271ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3655.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(665.9, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1496 preview-line 1496\" data_line_start=\"1496\" data_line_end=\"1496\" data_line=\"1496,1497\" count_line=\"1\">From (ii) and (iii), we get<\/div>\n<div class=\"preview-paragraph-1498 preview-line 1498\" data_line_start=\"1498\" data_line_end=\"1498\" data_line=\"1498,1499\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n lambda<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.208ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4511.8 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3328.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3928.8, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"53\" class=\"preview-paragraph-1500 preview-line 1500 1501\" data_line_start=\"1500\" data_line_end=\"1501\" data_line=\"1500,1502\" count_line=\"2\">\n<li>(a) According to de-Broglie, a stationary orbit is that which contains an integral number of de-Broglie waves associated with the revolving electron.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1502 preview-line 1502\" data_line_start=\"1502\" data_line_end=\"1502\" data_line=\"1502,1503\" count_line=\"1\">For an electron revolving in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)<\/asciimath><latex style=\"display: none\">r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.093ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 925.3 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1504 preview-line 1504\" data_line_start=\"1504\" data_line_end=\"1504\" data_line=\"1504,1505\" count_line=\"1\">Total distance covered <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=<\/asciimath><latex style=\"display: none\">=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.76ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 778 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Circumference of the orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2pir_(n)<\/asciimath><latex style=\"display: none\">=2 \\pi r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.903ex\" height=\"1.864ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 3051 823.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1555.8, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2125.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1506 preview-line 1506\" data_line_start=\"1506\" data_line_end=\"1506\" data_line=\"1506,1507\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> For the permissible orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n lambda<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.208ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4511.8 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3328.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3928.8, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1508 preview-line 1508\" data_line_start=\"1508\" data_line_end=\"1508\" data_line=\"1508,1509\" count_line=\"1\">According to de-Broglie,<\/div>\n<div class=\"preview-paragraph-1510 preview-line 1510\" data_line_start=\"1510\" data_line_end=\"1510\" data_line=\"1510,1511\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.271ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3655.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(665.9, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1512 preview-line 1512\" data_line_start=\"1512\" data_line_end=\"1512\" data_line=\"1512,1513\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=445&width=442&top_left_y=1391&top_left_x=1184\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1514 preview-line 1514\" data_line_start=\"1514\" data_line_end=\"1514\" data_line=\"1514,1515\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v_(n)<\/asciimath><latex style=\"display: none\">v_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.17ex\" height=\"1.359ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 959.3 600.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is speed of electron revolving in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit.<\/div>\n<div class=\"preview-paragraph-1516 preview-line 1516\" data_line_start=\"1516\" data_line_end=\"1516\" data_line=\"1516,1517\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad2pir_(n)=(nh)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\therefore \\quad 2 \\pi r_{n}=\\frac{n h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.866ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 7012.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1944.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2444.8, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(3014.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4217.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5273.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(453.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1518 preview-line 1518\" data_line_start=\"1518\" data_line_end=\"1518\" data_line=\"1518,1519\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv_(n)r_(n)=(nh)\/(2pi)=n((h)\/(2pi))<\/asciimath><latex style=\"display: none\">m v_{n} r_{n}=\\frac{n h}{2 \\pi}=n\\left(\\frac{h}{2 \\pi}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.298ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 9413.8 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g 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405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3040.3, 0)\"><path 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0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 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315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1654.6, 0)\"><path data-c=\"29\" d=\"M305 251Q305 -145 69 -349H56Q43 -349 39 -347T35 -338Q37 -333 60 -307T108 -239T160 -136T204 27T221 250T204 473T160 636T108 740T60 807T35 839Q35 850 50 850H56H69Q197 743 256 566Q305 425 305 251Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>n<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1520 preview-line 1520\" data_line_start=\"1520\" data_line_end=\"1520\" data_line=\"1520,1521\" count_line=\"1\">(b) For ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1522 preview-line 1522\" data_line_start=\"1522\" data_line_end=\"1522\" data_line=\"1522,1523\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-13.6)\/(n^(2))=(-13.6)\/(1^(2))=-13.6eV<\/asciimath><latex style=\"display: none\">E=\\frac{-13.6}{n^{2}}=\\frac{-13.6}{1^{2}}=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"29.433ex\" height=\"2.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 13009.4 1306.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(768.9, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2007.4\" height=\"60\" 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652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(804.2, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2007.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(8203.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9259.4, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(10037.4, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11815.4, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1524 preview-line 1524\" data_line_start=\"1524\" data_line_end=\"1524\" data_line=\"1524,1525\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> K.E. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-E=-(-13.6)=13.6eV<\/asciimath><latex style=\"display: none\">=-E=-(-13.6)=13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.939ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12348.9 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1833.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2875.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3931.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4709.3, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5098.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5876.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7654.3, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8321.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9376.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11154.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1526 preview-line 1526\" data_line_start=\"1526\" data_line_end=\"1526\" data_line=\"1526,1527\" count_line=\"1\">…(i) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∵<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2235<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad:’<\/asciimath><latex style=\"display: none\">\\quad \\because<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1277.8, 0)\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2235<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> P.E. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2E<\/asciimath><latex style=\"display: none\">=2 E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.248ex\" height=\"1.724ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 2319.8 762\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1555.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1528 preview-line 1528\" data_line_start=\"1528\" data_line_end=\"1528\" data_line=\"1528,1529\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>.<\/mo>\n <mi>E<\/mi>\n <mo>.<\/mo>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>27.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>.<\/mo>\n <mi>E<\/mi>\n <mo>.<\/mo>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>27.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad P.E.=2(-13.6)=-27.2eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad P . E .=2(-13.6)=-27.2 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.404ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14322.4 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2695.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3140.4, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 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data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>P<\/mi><mo>.<\/mo><mi>E<\/mi><mo>.<\/mo><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>27.2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi 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more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260"}],"collection":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/comments?post=260"}],"version-history":[{"count":2,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260\/revisions"}],"predecessor-version":[{"id":262,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260\/revisions\/262"}],"wp:attachment":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/media?parent=260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/categories?post=260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/tags?post=260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":260,"date":"2022-11-04T15:12:51","date_gmt":"2022-11-04T15:12:51","guid":{"rendered":"https:\/\/successrouter.com\/articles\/?p=260"},"modified":"2022-11-04T15:13:06","modified_gmt":"2022-11-04T15:13:06","slug":"atoms","status":"publish","type":"post","link":"https:\/\/successrouter.com\/articles\/atoms\/","title":{"rendered":"Atoms"},"content":{"rendered":"\n\n\n\n \n Atoms<\/title>\n <meta name=\"viewport\" content=\"width=device-width, initial-scale=1\">\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.mathpix.com\/fonts\/cmu.css\"\/>\n <style>\n html,body {\n width: 100%;\n height: 100%;\n }\n *, *::before,*::after {\n box-sizing: border-box;\n }\n @-ms-viewport {\n width: device-width;\n }\n body {\n margin: 0;\n color: #1E2029;\n font-size: 14px;\n line-height: normal;\n }\n hr {\n box-sizing: content-box;\n height: 0;\n overflow: visible;\n }\n h1, h2, h3, h4, h5, h6 {\n margin-top: 0;\n margin-bottom: 0.5em;\n color: rgba(0, 0, 0, 0.85);\n font-weight: 500;\n }\n p {\n 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.mmd-context-menu-overlay{\n background: rgba(0, 0, 0, 0.56);\n }\n <\/style>\n<\/head>\n<body>\n <div id=\"preview\" class=\"preview scrollEditor\">\n <div id=\"container-ruller\" \/>\n <div id=\"preview-content\">\n <h1 type=\"title\" class=\"main-title preview-paragraph-0 preview-line 0 1 2\" id=\"atoms\" data_line_start=\"0\" data_line_end=\"2\" data_line=\"0,3\" count_line=\"3\">\nAtoms<\/h1>\n<div class=\"preview-paragraph-4 preview-line 4\" data_line_start=\"4\" data_line_end=\"4\" data_line=\"4,5\" count_line=\"1\">12.2 Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom<\/div>\n<div class=\"preview-paragraph-6 preview-line 6\" data_line_start=\"6\" data_line_end=\"6\" data_line=\"6,7\" count_line=\"1\">12.3 Atomic Spectra<\/div>\n<div class=\"preview-paragraph-8 preview-line 8\" data_line_start=\"8\" data_line_end=\"8\" data_line=\"8,9\" count_line=\"1\">12.4 Bohr Model of the Hydrogen Atom 12.5 The Line Spectra of the Hydrogen Atom<\/div>\n<div class=\"preview-paragraph-10 preview-line 10\" data_line_start=\"10\" data_line_end=\"10\" data_line=\"10,11\" count_line=\"1\">12.6 De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation<\/div>\n<div class=\"preview-paragraph-12 preview-line 12\" data_line_start=\"12\" data_line_end=\"12\" data_line=\"12,13\" count_line=\"1\">Topicwise Analysis of Last 10 Years’ CBSE Board Questions (2016-2007)<\/div>\n<div class=\"preview-paragraph-14 preview-line 14\" data_line_start=\"14\" data_line_end=\"14\" data_line=\"14,15\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-01.jpg?height=788&width=1448&top_left_y=1162&top_left_x=287\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-16 preview-line 16\" data_line_start=\"16\" data_line_end=\"16\" data_line=\"16,17\" count_line=\"1\">M Maximum weightage is of Bohr Model of Hydrogen <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad<\/asciimath><latex style=\"display: none\">\\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.262ex\" height=\"0\" role=\"img\" focusable=\"false\" viewBox=\"0 0 1000 0\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> No VBQ type questions were asked till now. Atom.<\/div>\n<ul class=\"preview-paragraph-18 preview-line 18 19\" data_line_start=\"18\" data_line_end=\"19\" data_line=\"18,20\" count_line=\"2\">\n<li>Maximum VSA, SAI, SAll and LA type questions were asked from Bohr Model of Hydrogen Atom.<\/li>\n<\/ul>\n<div class=\"preview-paragraph-20 preview-line 20\" data_line_start=\"20\" data_line_end=\"20\" data_line=\"20,21\" count_line=\"1\">QUICK RECAP<\/div>\n<div class=\"preview-paragraph-22 preview-line 22\" data_line_start=\"22\" data_line_end=\"22\" data_line=\"22,23\" count_line=\"1\">Thomson’s model of atom : It was proposed by J. J. Thomson in 1898. According to<\/div>\n<div class=\"preview-paragraph-24 preview-line 24\" data_line_start=\"24\" data_line_end=\"24\" data_line=\"24,25\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-01.jpg?height=189&width=343&top_left_y=2330&top_left_x=662\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-26 preview-line 26\" data_line_start=\"26\" data_line_end=\"26\" data_line=\"26,27\" count_line=\"1\">this model, the positive charge of the atom is uniformly distributed throughout the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon. (1) Rutherford’s <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-scattering experiment Rutherford and his two associates, Geiger and Marsden, studies the scattering of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles from a thin gold foil in order to investigate the structure of the atom.<\/div>\n<div class=\"preview-paragraph-28 preview-line 28\" data_line_start=\"28\" data_line_end=\"28\" data_line=\"28,29\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=465&width=737&top_left_y=687&top_left_x=288\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-30 preview-line 30\" data_line_start=\"30\" data_line_end=\"30\" data_line=\"30,31\" count_line=\"1\">Schematic arrangement of the Geiger-Marsden experiment<\/div>\n<div class=\"preview-paragraph-32 preview-line 32\" data_line_start=\"32\" data_line_end=\"32\" data_line=\"32,33\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=326&width=434&top_left_y=1202&top_left_x=454\" alt=\"\"><\/div>\n<ul class=\"preview-paragraph-34 preview-line 34 35 36 37 38 39 40 41\" data_line_start=\"34\" data_line_end=\"41\" data_line=\"34,42\" count_line=\"8\">\n<li>\n<div>Rutherford’s observations and results :<\/div>\n<\/li>\n<li>\n<div>Most of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles pass through the gold foil without any deflection. This shows that most of the space in an atom is empty.<\/div>\n<\/li>\n<li>\n<div>Few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles got scattered, deflecting at various angles from 0 to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">pi<\/asciimath><latex style=\"display: none\">\\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.29ex\" height=\"1ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -431 570 442\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. This shows that atom has a small positively charged core called ‘nucleus’ at centre of atom, which deflects the positively charged <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles at different angles depending on their distance from centre of nucleus.<\/div>\n<\/li>\n<li>\n<div>Very few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles (1 in 8000) suffers deflection of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>180<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>180<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">180^(@)<\/asciimath><latex style=\"display: none\">180^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.307ex\" height=\"1.649ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 1903.6 729\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1500, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>180<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. This shows that size of nucleus is very small, nearly <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/8000<\/asciimath><latex style=\"display: none\">1 \/ 8000<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.787ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3000 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1000, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>8000<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the size of atom.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-42 preview-line 42\" data_line_start=\"42\" data_line_end=\"42\" data_line=\"42,43\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-02.jpg?height=288&width=311&top_left_y=2169&top_left_x=564\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-44 preview-line 44\" data_line_start=\"44\" data_line_end=\"44\" data_line=\"44,45\" count_line=\"1\">This graph shows deflection of number of particles with angle of deflection <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. (A) Rutherford’s <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-scattering formulae Number of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particles scattered per unit area, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N(theta)<\/asciimath><latex style=\"display: none\">N(\\theta)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.83ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2135 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(888, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1277, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1746, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> at scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> varies inversely as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">sin^(4)(theta\/\/2)<\/asciimath><latex style=\"display: none\">\\sin ^{4}(\\theta \/ 2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.775ex\" height=\"2.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -874.8 3878.6 1124.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(394, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(672, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1228, 396.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1631.6, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2020.6, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2489.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2989.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3489.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>sin<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, i.e.,<\/div>\n<div class=\"preview-paragraph-46 preview-line 46 47 48\" data_line_start=\"46\" data_line_end=\"48\" data_line=\"46,49\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <msup>\n <mi>sin<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N(theta)prop(1)\/(sin^(4)(theta\/\/2))<\/asciimath><latex style=\"display: none\">N(\\theta) \\propto \\frac{1}{\\sin ^{4}(\\theta \/ 2)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.454ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.618ex\" height=\"5.49ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1342 7787.1 2426.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(888, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1277, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1746, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2412.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3468.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(1909.3, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -834.8)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(394, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(672, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1228, 396.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 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166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2489.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2989.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3489.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><rect width=\"4078.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u221d<\/mo><mfrac><mn>1<\/mn><mrow><msup><mi>sin<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-50 preview-line 50 51 52 53\" data_line_start=\"50\" data_line_end=\"53\" data_line=\"50,54\" count_line=\"4\">\n<li>\n<div>Impact parameter : It is defined as the perpendicular distance of the initial velocity vector of the alpha particle from the centre of the nucleus, when the particle is far away from the nucleus of the atom.<\/div>\n<\/li>\n<li>\n<div>The scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particle and impact parameter <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b<\/asciimath><latex style=\"display: none\">b<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.971ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 429 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are related as<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-54 preview-line 54 55 56\" data_line_start=\"54\" data_line_end=\"56\" data_line=\"54,57\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b=(Ze^(2)cot(theta\/\/2))\/(4piepsi_(0)K)<\/asciimath><latex style=\"display: none\">b=\\frac{Z e^{2} \\cot (\\theta \/ 2)}{4 \\pi \\varepsilon_{0} K}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.063ex\" height=\"5.42ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1543.9 7541.8 2395.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(706.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1762.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 710)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1759.2, 0)\"><path data-c=\"63\" d=\"M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(444, 0)\"><\/path><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\" transform=\"translate(944, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3481.2, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3950.2, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(4450.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4950.2, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1475.3, -686)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><rect width=\"5539.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>b<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>cot<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>K<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-58 preview-line 58\" data_line_start=\"58\" data_line_end=\"58\" data_line=\"58,59\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K<\/asciimath><latex style=\"display: none\">K<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.011ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 889 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the kinetic energy of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z<\/asciimath><latex style=\"display: none\">Z<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.636ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 723 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the atomic number of the nucleus.<\/div>\n<ul class=\"preview-paragraph-60 preview-line 60 61\" data_line_start=\"60\" data_line_end=\"61\" data_line=\"60,62\" count_line=\"2\">\n<li>Smaller the impact parameter, larger the angle of scattering <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ul>\n<div class=\"preview-paragraph-62 preview-line 62\" data_line_start=\"62\" data_line_end=\"62\" data_line=\"62,63\" count_line=\"1\">Distance of closest approach : At the distance of closest approach whole kinetic energy of the alpha particles is converted into potential energy.<\/div>\n<ul class=\"preview-paragraph-64 preview-line 64 65\" data_line_start=\"64\" data_line_end=\"65\" data_line=\"64,66\" count_line=\"2\">\n<li>Distance of closest approach<\/li>\n<\/ul>\n<div class=\"preview-paragraph-66 preview-line 66 67 68\" data_line_start=\"66\" data_line_end=\"68\" data_line=\"66,69\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>K<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(0)=(2Ze^(2))\/(4piepsi_(0)K)<\/asciimath><latex style=\"display: none\">r_{0}=\\frac{2 Z e^{2}}{4 \\pi \\varepsilon_{0} K}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.345ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 5456.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2188.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(588, 676)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1223, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><rect width=\"3028.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>r<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>K<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-70 preview-line 70\" data_line_start=\"70\" data_line_end=\"70\" data_line=\"70,71\" count_line=\"1\">(A) Rutherford’s nuclear model of the atom :<\/div>\n<div class=\"preview-paragraph-72 preview-line 72\" data_line_start=\"72\" data_line_end=\"72\" data_line=\"72,73\" count_line=\"1\">According to this the entire positive charge and most of the mass of the atom is concentrated in a small volume known as the nucleus with electrons revolving around it just as planets revolve around the sun.<\/div>\n<div class=\"preview-paragraph-74 preview-line 74\" data_line_start=\"74\" data_line_end=\"74\" data_line=\"74,75\" count_line=\"1\">(A) Bohr’s model : Bohr combined classical and early quantum concepts and gave his theory of hydrogen and hydrogen-like atoms which have only one orbital electron. His postulates are<\/div>\n<ul class=\"preview-paragraph-76 preview-line 76 77 78 79\" data_line_start=\"76\" data_line_end=\"79\" data_line=\"76,80\" count_line=\"4\">\n<li>\n<div>An electron can revolve around the nucleus only in certain allowed circular orbits of definite energy and in these orbits it does not radiate. These orbits are known as stationary orbits.<\/div>\n<\/li>\n<li>\n<div>Angular momentum of the electron in a stationary orbit is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h\/\/2pi<\/asciimath><latex style=\"display: none\">h \/ 2 \\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.855ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2146 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(576, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1076, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1576, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">L=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.435ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3286.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(958.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2014.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>L<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-80 preview-line 80\" data_line_start=\"80\" data_line_end=\"80\" data_line=\"80,81\" count_line=\"1\">This is known as Bohr’s quantisation condition. – The emission of radiation takes place when an electron makes a transition from a higher to a lower orbit. The frequency of the radiation is given by<\/div>\n<div class=\"preview-paragraph-82 preview-line 82\" data_line_start=\"82\" data_line_end=\"82\" data_line=\"82,83\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(E_(2)-E_(1))\/(h)<\/asciimath><latex style=\"display: none\">v=\\frac{E_{2}-E_{1}}{h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.007ex\" height=\"2.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -926.9 4423.1 1279.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 446.1) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1141.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1919.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1098.6, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"2364.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mrow><mi>h<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-84 preview-line 84\" data_line_start=\"84\" data_line_end=\"84\" data_line=\"84,85\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(2)<\/asciimath><latex style=\"display: none\">E_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.583ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1141.6 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)<\/asciimath><latex style=\"display: none\">E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.583ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1141.6 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies of the electron in the higher and lower orbits respectively.<\/div>\n<div class=\"preview-paragraph-86 preview-line 86\" data_line_start=\"86\" data_line_end=\"86\" data_line=\"86,87\" count_line=\"1\">(1) Bohr’s formulae<\/div>\n<div class=\"preview-paragraph-88 preview-line 88\" data_line_start=\"88\" data_line_end=\"88\" data_line=\"88,89\" count_line=\"1\">Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-90 preview-line 90\" data_line_start=\"90\" data_line_end=\"90\" data_line=\"90,91\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>0.53<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>Z<\/mi>\n <\/mfrac>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>0.53<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>Z<\/mi>\n <\/mfrac>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(4piepsi_(0)n^(2)h^(2))\/(4pi^(2)mZe^(2));r_(n)=(0.53n^(2))\/(Z)”\u212b”<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{4 \\pi \\varepsilon_{0} n^{2} h^{2}}{4 \\pi^{2} m Z e^{2}} ; r_{n}=\\frac{0.53 n^{2}}{Z} \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.335ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 11198.1 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1203, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2258.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(227.6, 457.1) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 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Ze^(2))\/(nh)=(2.2 xx10^(6)Z)\/(n)m\/\/s<\/asciimath><latex style=\"display: none\">v_{n}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{2 \\pi Z e^{2}}{n h}=\\frac{2.2 \\times 10^{6} \\mathrm{Z}}{n} \\mathrm{~m} \/ \\mathrm{s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"29.538ex\" height=\"3.319ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1004.9 13055.9 1467\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 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mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ul>\n<div class=\"preview-paragraph-94 preview-line 94\" data_line_start=\"94\" data_line_end=\"94\" data_line=\"94,95\" count_line=\"1\">The kinetic energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-96 preview-line 96 97 98 99 100 101\" data_line_start=\"96\" data_line_end=\"101\" data_line=\"96,102\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[K_(n)=(1)\/(4piepsi_(0))(Ze^(2))\/(2r_(n))=((1)\/(4piepsi_(0)))^(2)(2pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=(13.6Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nK_{n} &=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r_{n}}=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{2 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.6ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 17503.2 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 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data_line_start=\"103\" data_line_end=\"103\" data_line=\"103,104\" count_line=\"1\">The potential energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit<\/div>\n<div class=\"preview-paragraph-105 preview-line 105 106 107 108 109 110\" data_line_start=\"105\" data_line_end=\"110\" data_line=\"105,111\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>27.2<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>27.2<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[U_(n)=-(1)\/(4piepsi_(0))(Ze^(2))\/(r_(n))=-((1)\/(4piepsi_(0)))^(2)(4pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=(-27.2Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nU_{n} &=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r_{n}}=-\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{4 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=\\frac{-27.2 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"42.745ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 18893.2 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 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rowspacing=\"3pt\"><mtr><mtd><msub><mi>U<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>27.2<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-112 preview-line 112 113\" data_line_start=\"112\" data_line_end=\"113\" data_line=\"112,114\" count_line=\"2\">\n<li>Total energy of electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 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orbit<\/li>\n<\/ul>\n<div class=\"preview-paragraph-114 preview-line 114 115 116 117 118 119\" data_line_start=\"114\" data_line_end=\"119\" data_line=\"114,120\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E_(n)=U_(n)+K_(n)=-((1)\/(4piepsi_(0)))^(2)(2pi^(2)me^(4)Z^(2))\/(n^(2)h^(2))],[=-(13.6Z^(2))\/(n^(2))eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nE_{n} &=U_{n}+K_{n}=-\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{2 \\pi^{2} m e^{4} Z^{2}}{n^{2} h^{2}} \\\\\n&=-\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.33ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.505ex\" height=\"11.792ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2855.9 17461.1 5211.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 1208.4)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mn>13.6<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-121 preview-line 121\" data_line_start=\"121\" data_line_end=\"121\" data_line=\"121,122\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>U<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K_(n)=-E_(n),U_(n)=2E_(n)=-2K_(n)<\/asciimath><latex style=\"display: none\">K_{n}=-E_{n}, U_{n}=2 E_{n}=-2 K_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"29.931ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 13229.7 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 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transform=\"translate(849, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>K<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>,<\/mo><msub><mi>U<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>2<\/mn><msub><mi>K<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-123 preview-line 123 124\" data_line_start=\"123\" data_line_end=\"124\" data_line=\"123,125\" count_line=\"2\">\n<li>Frequency of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 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<mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v_(n)=((1)\/(4piepsi_(0)))^(2)(4pi^(2)Z^(2)e^(4)m)\/(n^(3)h^(3))=(6.62 xx10^(15)Z^(2))\/(n^(3))<\/asciimath><latex style=\"display: none\">v_{n}=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)^{2} \\frac{4 \\pi^{2} Z^{2} e^{4} m}{n^{3} h^{3}}=\\frac{6.62 \\times 10^{15} Z^{2}}{n^{3}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"43.234ex\" height=\"5.876ex\" role=\"img\" 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display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>15<\/mn><\/mrow><\/msup><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-129 preview-line 129 130\" data_line_start=\"129\" data_line_end=\"130\" data_line=\"129,131\" count_line=\"2\">\n<li>Wavelength of radiation in the transition from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">→<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">\u2192<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)rarrn_(1)<\/asciimath><latex style=\"display: none\">n_{2} \\rightarrow n_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.06ex\" height=\"1.495ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -511 3562.7 661\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"2192\" d=\"M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2559.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo stretchy=\"false\">\u2192<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=RZ^(2)[(1)\/(n_(1)^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R Z^{2}\\left[\\frac{1}{n_{1}^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.446ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 8595 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(249.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 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573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" 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26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3993.7, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R<\/asciimath><latex style=\"display: none\">R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.048ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 704\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called Rydberg’s constant. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=((1)\/(4piepsi_(0)))(2pi^(2)me^(4))\/(ch^(3))=1.097 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">R=\\left(\\frac{1}{4 \\pi \\varepsilon_{0}}\\right) \\frac{2 \\pi^{2} m e^{4}}{c h^{3}}=1.097 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.403ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 16089.9 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 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568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2408.5, 0)\"><path data-c=\"29\" d=\"M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z\"><\/path><\/g><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5098, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 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250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (A) Spectral series of hydrogen atom: When the electron in a <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom jumps from higher energy level to lower energy level, the difference of energies of the two energy levels is emitted as radiation of particular wavelength, known as spectral line. Spectral lines of different wavelengths are obtained for transition of electron between two different energy levels, which are found to fall in a number of spectral series given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-131 preview-line 131\" data_line_start=\"131\" data_line_end=\"131\" data_line=\"131,132\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-03.jpg?height=415&width=745&top_left_y=909&top_left_x=1041\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-133 preview-line 133\" data_line_start=\"133\" data_line_end=\"133\" data_line=\"133,134\" count_line=\"1\">Energy<\/div>\n<ul class=\"preview-paragraph-135 preview-line 135 136\" data_line_start=\"135\" data_line_end=\"136\" data_line=\"135,137\" count_line=\"2\">\n<li>Lyman series<\/li>\n<\/ul>\n<div class=\"preview-paragraph-137 preview-line 137\" data_line_start=\"137\" data_line_end=\"137\" data_line=\"137,138\" count_line=\"1\">Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>2<\/mn> \n <mo>,<\/mo> \n <mn>3<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=2,3,dots,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=2,3, \\ldots, \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.619ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7787.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 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278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4615.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5954.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(6398.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7398.8, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to first energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>1<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=1)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=1\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Lyman series.<\/div>\n<div class=\"preview-paragraph-139 preview-line 139\" data_line_start=\"139\" data_line_end=\"139\" data_line=\"139,140\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.606ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 7339.8 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(249.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"612.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1130, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2185.8, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2944.8, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M224 -649V1150H455V1099H275V-598H455V-649H224Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(472, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1773.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2773.4, 0)\"><g data-mml-node=\"mn\" transform=\"translate(398, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3923, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-141 preview-line 141\" data_line_start=\"141\" data_line_end=\"141\" data_line=\"141,142\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=2,3,4,dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=2,3,4, \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.025ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 9293.1 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g 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61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7848.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8293.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-143 preview-line 143 144\" data_line_start=\"143\" data_line_end=\"144\" data_line=\"143,145\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of Lyman series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-145 preview-line 145 146 147\" data_line_start=\"145\" data_line_end=\"147\" data_line=\"145,148\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext> or <\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(oo^(2))]=R quad” or “quad lambda=(1)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{\\infty^{2}}\\right]=R \\quad \\text { or } \\quad 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transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\" transform=\"translate(750, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1142, 0)\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(13065.7, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(14065.7, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 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data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mtext>\u00a0or\u00a0<\/mtext><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-149 preview-line 149 150\" data_line_start=\"149\" data_line_end=\"150\" data_line=\"149,151\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Lyman series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-151 preview-line 151 152 153\" data_line_start=\"151\" data_line_end=\"153\" data_line=\"151,154\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext> or <\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(2^(2))]=(3R)\/(4)quad” or “quad lambda=(4)\/(3R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right]=\\frac{3 R}{4} \\quad \\text { or } \\quad \\lambda=\\frac{4}{3 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"40.998ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 18121.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 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153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" 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21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1459\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><mn>4<\/mn><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mtext>\u00a0or\u00a0<\/mtext><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-155 preview-line 155 156 157 158 159 160 161 162\" data_line_start=\"155\" data_line_end=\"162\" data_line=\"155,163\" count_line=\"8\">\n<li>\n<div>Lyman series lie in the ultraviolet region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>Lyman series is obtained in emission as well<\/div>\n<\/li>\n<li>\n<div>Balmer series as in absorption spectrum.<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>3<\/mn> \n <mo>,<\/mo> \n <mn>4<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=3,4,dots oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=3,4, \\ldots \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.613ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7343.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4615.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5954.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6954.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to second energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>2<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=2)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=2\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Balmer series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-163 preview-line 163 164 165\" data_line_start=\"163\" data_line_end=\"165\" data_line=\"163,166\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-167 preview-line 167\" data_line_start=\"167\" data_line_end=\"167\" data_line=\"167,168\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=3,4,5<\/asciimath><latex style=\"display: none\">n_{2}=3,4,5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.693ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 4726.4 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-169 preview-line 169 170\" data_line_start=\"169\" data_line_end=\"170\" data_line=\"169,171\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of Balmer series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-171 preview-line 171 172 173\" data_line_start=\"171\" data_line_end=\"173\" data_line=\"171,174\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>4<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>4<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(oo^(2))]=(R)\/(4)” or “lambda=(4)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{4} \\text { or } \\lambda=\\frac{4}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.342ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 15621.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2093.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3094, 0)\"><g data-mml-node=\"mn\" transform=\"translate(671.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 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465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1603.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4937.6, 0)\"><path data-c=\"5D\" d=\"M11 1388V1450H280V-949H11V-887H218V1388H11Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8858.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9914.7, 0)\"><g data-mml-node=\"mi\" transform=\"translate(220, 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327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14422.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(349.5, 676)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>4<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-175 preview-line 175 176\" data_line_start=\"175\" data_line_end=\"176\" data_line=\"175,177\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Balmer series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-177 preview-line 177 178 179\" data_line_start=\"177\" data_line_end=\"179\" data_line=\"177,180\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>36<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>36<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5R)\/(36)” or “lambda=(36)\/(5R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5 R}{36} \\text { or } \\lambda=\\frac{36}{5 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.473ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16121.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13366.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14422.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(349.5, 676)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1459\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><mn>36<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-181 preview-line 181 182 183 184 185 186 187 188\" data_line_start=\"181\" data_line_end=\"188\" data_line=\"181,189\" count_line=\"8\">\n<li>\n<div>Balmer series lie in the visible region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Paschen series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>4<\/mn> \n <mo>,<\/mo> \n <mn>5<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>.<\/mo> \n <mo>.<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=4,5,dots..,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=4,5, \\ldots . ., \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.631ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 8677.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4615.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5954.1, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6398.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6843.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(7288.1, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8288.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to third energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>3<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=3)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=3\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Paschen series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-189 preview-line 189 190 191\" data_line_start=\"189\" data_line_end=\"191\" data_line=\"189,192\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-193 preview-line 193\" data_line_start=\"193\" data_line_end=\"193\" data_line=\"193,194\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=4,5,6dots dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=4,5,6 \\ldots \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.425ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 10353.8 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4893.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6231.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7570.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8909.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9353.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-195 preview-line 195 196\" data_line_start=\"195\" data_line_end=\"196\" data_line=\"195,197\" count_line=\"2\">\n<li>Series limit line (shortest wavelength) of the Paschen series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-197 preview-line 197 198 199\" data_line_start=\"197\" data_line_end=\"199\" data_line=\"197,200\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>9<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>9<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(oo^(2))]=(R)\/(9)” or “lambda=(9)\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{9} \\text { or } \\lambda=\\frac{9}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.342ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 15621.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 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313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(349.5, -686)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(11113.7, 0)\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\" transform=\"translate(750, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1142, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(12505.7, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13366.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14422.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(349.5, 676)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>9<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>9<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-201 preview-line 201\" data_line_start=\"201\" data_line_end=\"201\" data_line=\"201,202\" count_line=\"1\">The first line (longest wavelength) of the Paschen series is given by<\/div>\n<div class=\"preview-paragraph-203 preview-line 203 204 205\" data_line_start=\"203\" data_line_end=\"205\" data_line=\"203,206\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>144<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>144<\/mn>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>144<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>144<\/mn>\n <mrow>\n <mn>7<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(3^(2))-(1)\/(4^(2))]=(7R)\/(144)” or “lambda=(144)\/(7R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{3^{2}}-\\frac{1}{4^{2}}\\right]=\\frac{7 R}{144} \\text { or } \\lambda=\\frac{144}{7 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.564ex\" height=\"5.428ex\" 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458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1700\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>7<\/mn><mi>R<\/mi><\/mrow><mn>144<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>144<\/mn><mrow><mn>7<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-207 preview-line 207 208 209 210 211 212 213 214\" data_line_start=\"207\" data_line_end=\"214\" data_line=\"207,215\" count_line=\"8\">\n<li>\n<div>Paschen series lie in the infrared region of the electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Brackett Series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>5<\/mn> \n <mo>,<\/mo> \n <mn>6<\/mn> \n <mo>,<\/mo> \n <mn>7<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>.<\/mo> \n <mo>.<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=5,6,7,dots..,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=5,6,7, \\ldots . ., \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.769ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 9621.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 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60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4615.4, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5115.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5560.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6898.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7343.4, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7788.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8232.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9232.8, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to fourth energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>4<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=4)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=4\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Brackett series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-215 preview-line 215 216 217\" data_line_start=\"215\" data_line_end=\"217\" data_line=\"215,218\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 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50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-219 preview-line 219\" data_line_start=\"219\" data_line_end=\"219\" data_line=\"219,220\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>.<\/mo>\n <mo>.<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=5,6,7dots dots dots..oo<\/asciimath><latex style=\"display: none\">n_{2}=5,6,7 \\ldots \\ldots \\ldots . . \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.431ex\" height=\"1.968ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 10798.4 870\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4226.4, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4893.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6231.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7570.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8909.1, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9353.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9798.4, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo>,<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>.<\/mo><mo>.<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Series limit line (shortest wavelength) of Brackett series is given by<\/div>\n<div class=\"preview-paragraph-221 preview-line 221 222 223\" data_line_start=\"221\" data_line_end=\"223\" data_line=\"221,224\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>16<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>16<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>16<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>16<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(oo^(2))]=(R)\/( 16)” or “lambda=(16 )\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{16} \\text { or } \\lambda=\\frac{16}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.433ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16103.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2093.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3094, 0)\"><g data-mml-node=\"mn\" transform=\"translate(671.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1603.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4937.6, 0)\"><path data-c=\"5D\" d=\"M11 1388V1450H280V-949H11V-887H218V1388H11Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8858.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9914.7, 0)\"><g data-mml-node=\"mi\" transform=\"translate(340.5, 676)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 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414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(11354.7, 0)\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 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75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(340.5, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>16<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>16<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-225 preview-line 225 226\" data_line_start=\"225\" data_line_end=\"226\" data_line=\"225,227\" count_line=\"2\">\n<li>The first line (longest wavelength) of Brackett series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-227 preview-line 227 228 229\" data_line_start=\"227\" data_line_end=\"229\" data_line=\"227,230\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>400<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>400<\/mn>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>4<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>400<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>400<\/mn>\n <mrow>\n <mn>9<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(4^(2))-(1)\/(5^(2))]=(9R)\/(400)” or “lambda=(400)\/(9R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{4^{2}}-\\frac{1}{5^{2}}\\right]=\\frac{9 R}{400} \\text { or } \\lambda=\\frac{400}{9 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.564ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16603.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" 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80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1700\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>4<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>9<\/mn><mi>R<\/mi><\/mrow><mn>400<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>400<\/mn><mrow><mn>9<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-231 preview-line 231 232 233 234 235 236 237 238\" data_line_start=\"231\" data_line_end=\"238\" data_line=\"231,239\" count_line=\"8\">\n<li>\n<div>Brackett series lie in the infrared region of the electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Pfund series<\/div>\n<\/li>\n<li>\n<div>Emission spectral lines corresponding to the transition of electron from higher energy levels <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mn>8<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>6<\/mn> \n <mo>,<\/mo> \n <mn>7<\/mn> \n <mo>,<\/mo> \n <mn>8<\/mn> \n <mo>,<\/mo> \n <mo>\u2026<\/mo> \n <mo>\u2026<\/mo> \n <mo>.<\/mo> \n <mo>,<\/mo> \n <mi mathvariant=\"normal\">\u221e<\/mi> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(2)=6,7,8,dots dots.,oo)<\/asciimath><latex style=\"display: none\">\\left(n_{2}=6,7,8, \\ldots \\ldots ., \\infty\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.791ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 10515.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" 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380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3670.8, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4170.8, 0)\"><path 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36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8237.4, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8682.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(9126.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to fifth energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5<\/mn>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <mo>=<\/mo> \n <mn>5<\/mn> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(1)=5)<\/asciimath><latex style=\"display: none\">\\left(n_{1}=5\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.179ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3615.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1670.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2726.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3226.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> constitute Pfund series.<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-239 preview-line 239 240 241\" data_line_start=\"239\" data_line_end=\"241\" data_line=\"239,242\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(n_(2)^(2))]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{n_{2}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.758ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8291.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M269 -1249V1750H577V1677H342V-1176H577V-1249H269Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(583, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2148.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3149, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.6, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-243 preview-line 243\" data_line_start=\"243\" data_line_end=\"243\" data_line=\"243,244\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>6<\/mn>\n <mo>,<\/mo>\n <mn>7<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=6,7,dots dots dots dots,oo<\/asciimath><latex style=\"display: none\">n_{2}=6,7, \\ldots \\ldots \\ldots \\ldots, \\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.945ex\" height=\"1.968ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 11025.8 870\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2837.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3281.8, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3781.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4226.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5565.1, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6903.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8242.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9581.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(10025.8, 0)\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>6<\/mn><mo>,<\/mo><mn>7<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-245 preview-line 245\" data_line_start=\"245\" data_line_end=\"245\" data_line=\"245,246\" count_line=\"1\">Series limit line (shortest wavelength) of Pfund series is given by<\/div>\n<div class=\"preview-paragraph-247 preview-line 247 248 249\" data_line_start=\"247\" data_line_end=\"249\" data_line=\"247,250\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">∞<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>25<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>25<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mi>R<\/mi>\n <mn>25<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>25<\/mn>\n <mi>R<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(oo^(2))]=(R)\/( 25)” or “lambda=(25 )\/(R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{\\infty^{2}}\\right]=\\frac{R}{25} \\text { or } \\lambda=\\frac{25}{R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.433ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 16103.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M247 -949V1450H516V1388H309V-887H516V-949H247Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(528, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2093.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3094, 0)\"><g data-mml-node=\"mn\" transform=\"translate(671.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 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85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -686)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mtext\" transform=\"translate(11354.7, 0)\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(250, 0)\"><\/path><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\" transform=\"translate(750, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1142, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(12746.7, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13607.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(14663.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 676)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(340.5, -686)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><rect width=\"1200\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">\u221e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mi>R<\/mi><mn>25<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>25<\/mn><mi>R<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-251 preview-line 251 252\" data_line_start=\"251\" data_line_end=\"252\" data_line=\"251,253\" count_line=\"2\">\n<li>The first line (longest wavelength) of the Pfund series is given by<\/li>\n<\/ul>\n<div class=\"preview-paragraph-253 preview-line 253 254 255\" data_line_start=\"253\" data_line_end=\"255\" data_line=\"253,256\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>6<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>900<\/mn>\n <\/mfrac>\n <mtext> or <\/mtext>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>900<\/mn>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>5<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>6<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>900<\/mn>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>900<\/mn>\n <mrow>\n <mn>11<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(5^(2))-(1)\/(6^(2))]=(11 R)\/(900)” or “lambda=(900)\/(11 R)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{5^{2}}-\\frac{1}{6^{2}}\\right]=\\frac{11 R}{900} \\text { or } \\lambda=\\frac{900}{11 R}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" 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16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1000, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><rect width=\"1959\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>5<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>6<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>11<\/mn><mi>R<\/mi><\/mrow><mn>900<\/mn><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>900<\/mn><mrow><mn>11<\/mn><mi>R<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-257 preview-line 257 258 259 260 261 262\" data_line_start=\"257\" data_line_end=\"262\" data_line=\"257,263\" count_line=\"6\">\n<li>\n<div>Pfund series also lie in the infrared region of electromagnetic spectrum.<\/div>\n<\/li>\n<li>\n<div>This series is obtained only in the emission spectrum.<\/div>\n<\/li>\n<li>\n<div>Number of spectral lines due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 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0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit to lower orbit is<\/div>\n<\/li>\n<\/ul>\n<div class=\"preview-paragraph-263 preview-line 263 264 265\" data_line_start=\"263\" data_line_end=\"265\" data_line=\"263,266\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>N<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">N=(n(n-1))\/(2)<\/asciimath><latex style=\"display: none\">N=\\frac{n(n-1)}{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.552ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.394ex\" height=\"4.855ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1460 6362 2146\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4E\" d=\"M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1165.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2221.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 710)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 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52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1811.2, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2811.4, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3311.4, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1820.2, -686)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><rect width=\"3900.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>N<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mn>2<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-267 preview-line 267\" data_line_start=\"267\" data_line_end=\"267\" data_line=\"267,268\" count_line=\"1\">(B) Ionization energy and ionization potential Ionisation : The process of knocking an electron out of the atom is called ionisation. ionisation<\/div>\n<div class=\"preview-paragraph-269 preview-line 269 270 271\" data_line_start=\"269\" data_line_end=\"271\" data_line=\"269,272\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext> energy <\/mtext>\n <mo>=<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext>\u00a0energy\u00a0<\/mtext>\n <mo>=<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">” energy “=(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">\\text { energy }=\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.347ex\" height=\"4.857ex\" role=\"img\" focusable=\"false\" viewBox=\"0 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216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(607.2, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1978\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6915.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtext>\u00a0energy\u00a0<\/mtext><mo>=<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ul class=\"preview-paragraph-273 preview-line 273 274 275 276\" data_line_start=\"273\" data_line_end=\"276\" data_line=\"273,277\" count_line=\"4\">\n<li>\n<div>Ionisation energy : The energy required, to knock an electron completely out of the atom.<\/div>\n<\/li>\n<li>\n<div>Ionisation potential <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(13.6Z^(2))\/(n^(2))V<\/asciimath><latex style=\"display: none\">=\\frac{13.6 Z^{2}}{n^{2}} \\mathrm{~V}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.386ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4590.6 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1055.8, 0)\"><g 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429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(912.6, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2294.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3590.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><mn>13.6<\/mn><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ul>\n<h2 type=\"section\" class=\"section-title preview-paragraph-277 preview-line 277\" id=\"previous-years'-cbse-board-questions\" data_line_start=\"277\" data_line_end=\"277\" data_line=\"277,278\" count_line=\"1\">\n<span class=\"section-number\">1. <\/span>Previous Years’ CBSE Board Questions<\/h2>\n<div class=\"preview-paragraph-279 preview-line 279\" data_line_start=\"279\" data_line_end=\"279\" data_line=\"279,280\" count_line=\"1\">12.2 Alpha Particle scattering and Rutherford’s Nuclear Model of Atom<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-281 preview-line 281\" id=\"vsa-(1-mark)\" data_line_start=\"281\" data_line_end=\"281\" data_line=\"281,282\" count_line=\"1\">\n<span class=\"section-number\">2. <\/span>VSA (1 mark)<\/h2>\n<ol class=\"preview-paragraph-283 preview-line 283 284\" data_line_start=\"283\" data_line_end=\"284\" data_line=\"283,285\" count_line=\"2\">\n<li>Why is the classical (Rutherford) model for an atom of electron orbiting around the nucleus not able to explain the atomic structure?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-285 preview-line 285\" data_line_start=\"285\" data_line_end=\"285\" data_line=\"285,286\" count_line=\"1\">(Delhi 2012C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-287 preview-line 287\" id=\"sa-i-(-2-marks)\" data_line_start=\"287\" data_line_end=\"287\" data_line=\"287,288\" count_line=\"1\">\n<span class=\"section-number\">3. <\/span>SA I ( 2 marks)<\/h2>\n<ol start=\"2\" class=\"preview-paragraph-289 preview-line 289 290\" data_line_start=\"289\" data_line_end=\"290\" data_line=\"289,291\" count_line=\"2\">\n<li>Using Rutherford’s model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-291 preview-line 291\" data_line_start=\"291\" data_line_end=\"291\" data_line=\"291,292\" count_line=\"1\">(AI 2014)<\/div>\n<ol start=\"3\" class=\"preview-paragraph-293 preview-line 293 294\" data_line_start=\"293\" data_line_end=\"294\" data_line=\"293,295\" count_line=\"2\">\n<li>In an experiment on <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle scattering by a thin foil of gold, draw a plot showing the number of particles scattered versus the scattering angle <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta<\/asciimath><latex style=\"display: none\">\\theta<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.023ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.061ex\" height=\"1.618ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 469 715\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Why is it that a very small fraction of the particles are scattered at <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta > 90^(@)<\/asciimath><latex style=\"display: none\">\\theta>90^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.09ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.254ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 3206.1 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>><\/mo><msup><mn>90<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-295 preview-line 295\" data_line_start=\"295\" data_line_end=\"295\" data_line=\"295,296\" count_line=\"1\">Write two important conclusions that can be drawn regarding the structure of the atom from the study of this experiment.<\/div>\n<div class=\"preview-paragraph-297 preview-line 297\" data_line_start=\"297\" data_line_end=\"297\" data_line=\"297,298\" count_line=\"1\">(Foreign 2013)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-299 preview-line 299\" id=\"sa-ii-(3-marks)\" data_line_start=\"299\" data_line_end=\"299\" data_line=\"299,300\" count_line=\"1\">\n<span class=\"section-number\">4. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"4\" class=\"preview-paragraph-301 preview-line 301 302\" data_line_start=\"301\" data_line_end=\"302\" data_line=\"301,303\" count_line=\"2\">\n<li>Draw a schematic arrangement of the Geiger – Marsden experiment for studying <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle scattering by a thin foil of gold. Describe briefly, by drawing trajectories of the scattered <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles, how this study can be used to estimate the size of the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-303 preview-line 303\" data_line_start=\"303\" data_line_end=\"303\" data_line=\"303,304\" count_line=\"1\">(Foreign 2010, AI 2009)<\/div>\n<ol start=\"5\" class=\"preview-paragraph-305 preview-line 305 306\" data_line_start=\"305\" data_line_end=\"306\" data_line=\"305,307\" count_line=\"2\">\n<li>State the basic assumption of the Rutherford model of the atom. Explain, in brief, why this model cannot account for the stability of an atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-307 preview-line 307\" data_line_start=\"307\" data_line_end=\"307\" data_line=\"307,308\" count_line=\"1\">(Delhi 2010C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-309 preview-line 309\" id=\"la-%24%5Cquad(5%24-marks)\" data_line_start=\"309\" data_line_end=\"309\" data_line=\"309,310\" count_line=\"1\">\n<span class=\"section-number\">5. <\/span>LA <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(5<\/asciimath><latex style=\"display: none\">\\quad(5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.274ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> marks)<\/h2>\n<ol start=\"6\" class=\"preview-paragraph-311 preview-line 311 312\" data_line_start=\"311\" data_line_end=\"312\" data_line=\"311,313\" count_line=\"2\">\n<li>In Rutherford scattering experiment, draw the trajectory traced by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles in the coulomb field of target nucleus and explain how this led to estimate the size of the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-313 preview-line 313\" data_line_start=\"313\" data_line_end=\"313\" data_line=\"313,314\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(3\/\/5<\/asciimath><latex style=\"display: none\">(3 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.274ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(389, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, AI 2015C <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">)<\/asciimath><latex style=\"display: none\">)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<h3 type=\"subsection\" class=\"sub_section-title preview-paragraph-315 preview-line 315\" id=\"atomic-spectra\" data_line_start=\"315\" data_line_end=\"315\" data_line=\"315,316\" count_line=\"1\">\n<span class=\"section-number\">5.<\/span><span class=\"sub_section-number\">1.<\/span> Atomic Spectra<\/h3>\n<h2 type=\"section\" class=\"section-title preview-paragraph-317 preview-line 317\" id=\"sa-i-(2-marks)\" data_line_start=\"317\" data_line_end=\"317\" data_line=\"317,318\" count_line=\"1\">\n<span class=\"section-number\">6. <\/span>SA I (2 marks)<\/h2>\n<ol start=\"7\" class=\"preview-paragraph-319 preview-line 319 320\" data_line_start=\"319\" data_line_end=\"320\" data_line=\"319,321\" count_line=\"2\">\n<li>Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infrared, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-321 preview-line 321\" data_line_start=\"321\" data_line_end=\"321\" data_line=\"321,322\" count_line=\"1\">(AI 2015)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-323 preview-line 323\" id=\"sa-ii-(3-marks)-2\" data_line_start=\"323\" data_line_end=\"323\" data_line=\"323,324\" count_line=\"1\">\n<span class=\"section-number\">7. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"8\" class=\"preview-paragraph-325 preview-line 325 326\" data_line_start=\"325\" data_line_end=\"326\" data_line=\"325,327\" count_line=\"2\">\n<li>The second member of Lyman series in hydrogen spectrum has wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5400<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5400<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5400″\u212b”<\/asciimath><latex style=\"display: none\">5400 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.882ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2600 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2000, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5400<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> A. Find the wavelength of the first member.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-327 preview-line 327\" data_line_start=\"327\" data_line_end=\"327\" data_line=\"327,328\" count_line=\"1\">(Delhi 2008)<\/div>\n<h3 type=\"subsection\" class=\"sub_section-title preview-paragraph-329 preview-line 329\" id=\"bohr-model-of-hydrogen-atom\" data_line_start=\"329\" data_line_end=\"329\" data_line=\"329,330\" count_line=\"1\">\n<span class=\"section-number\">7.<\/span><span class=\"sub_section-number\">1.<\/span> Bohr Model of Hydrogen Atom<\/h3>\n<h2 type=\"section\" class=\"section-title preview-paragraph-331 preview-line 331\" id=\"vsa-(1-mark)-2\" data_line_start=\"331\" data_line_end=\"331\" data_line=\"331,332\" count_line=\"1\">\n<span class=\"section-number\">8. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"9\" class=\"preview-paragraph-333 preview-line 333 334\" data_line_start=\"333\" data_line_end=\"334\" data_line=\"333,335\" count_line=\"2\">\n<li>What is the ratio of radii of the orbits corresponding to first excited state and ground state in a hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-335 preview-line 335\" data_line_start=\"335\" data_line_end=\"335\" data_line=\"335,336\" count_line=\"1\">(Delhi 2010)<\/div>\n<ol start=\"10\" class=\"preview-paragraph-337 preview-line 337 338\" data_line_start=\"337\" data_line_end=\"338\" data_line=\"337,339\" count_line=\"2\">\n<li>Define ionisation energy. What is its value for a hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-339 preview-line 339\" data_line_start=\"339\" data_line_end=\"339\" data_line=\"339,340\" count_line=\"1\">(AI 2010)<\/div>\n<ol start=\"11\" class=\"preview-paragraph-341 preview-line 341 342\" data_line_start=\"341\" data_line_end=\"342\" data_line=\"341,343\" count_line=\"2\">\n<li>State Bohr’s quantisation condition for defining stationary orbits.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-343 preview-line 343\" data_line_start=\"343\" data_line_end=\"343\" data_line=\"343,344\" count_line=\"1\">(Foreign 2010)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-345 preview-line 345\" id=\"sa-i-(2-marks)-2\" data_line_start=\"345\" data_line_end=\"345\" data_line=\"345,346\" count_line=\"1\">\n<span class=\"section-number\">9. <\/span>SA I (2 marks)<\/h2>\n<ol start=\"12\" class=\"preview-paragraph-347 preview-line 347 348\" data_line_start=\"347\" data_line_end=\"348\" data_line=\"347,349\" count_line=\"2\">\n<li>State Bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-349 preview-line 349\" data_line_start=\"349\" data_line_end=\"349\" data_line=\"349,350\" count_line=\"1\">(Foreign 2016)<\/div>\n<ol start=\"13\" class=\"preview-paragraph-351 preview-line 351 352\" data_line_start=\"351\" data_line_end=\"352\" data_line=\"351,353\" count_line=\"2\">\n<li>Show that the radius of the orbit in hydrogen atom varies as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the principal quantum number of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-353 preview-line 353\" data_line_start=\"353\" data_line_end=\"353\" data_line=\"353,354\" count_line=\"1\">(Delhi 2015)<\/div>\n<ol start=\"14\" class=\"preview-paragraph-355 preview-line 355 356\" data_line_start=\"355\" data_line_end=\"356\" data_line=\"355,357\" count_line=\"2\">\n<li>Using Bohr’s postulates of the atomic model, derive the expression for the radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> electron orbit. Hence obtain the expression for Bohr’s radius.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-357 preview-line 357\" data_line_start=\"357\" data_line_end=\"357\" data_line=\"357,358\" count_line=\"1\">(AI 2014)<\/div>\n<ol start=\"15\" class=\"preview-paragraph-359 preview-line 359 360\" data_line_start=\"359\" data_line_end=\"360\" data_line=\"359,361\" count_line=\"2\">\n<li>In the ground state of hydrogen atom, its Bohr radius is given as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5.3 xx10^(-11)m<\/asciimath><latex style=\"display: none\">5.3 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.327ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5890.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4807.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The atom is excited such that the radius becomes <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>21.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>21.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">21.2 xx10^(-11)m<\/asciimath><latex style=\"display: none\">21.2 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.459ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 6390.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2000.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3000.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5307.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>21.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find (i) the value of the principal quantum number and (ii) the total energy of the atom in this excited state.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-361 preview-line 361\" data_line_start=\"361\" data_line_end=\"361\" data_line=\"361,362\" count_line=\"1\">(Delhi 2013C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-363 preview-line 363\" id=\"sa-ii-(3-marks)-3\" data_line_start=\"363\" data_line_end=\"363\" data_line=\"363,364\" count_line=\"1\">\n<span class=\"section-number\">10. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"16\" class=\"preview-paragraph-365 preview-line 365 366\" data_line_start=\"365\" data_line_end=\"366\" data_line=\"365,367\" count_line=\"2\">\n<li>(a) The radius of the innermost electron orbit of a hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">5.3 xx10^(-11)m<\/asciimath><latex style=\"display: none\">5.3 \\times 10^{-11} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.327ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5890.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4807.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Calculate its radius in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-367 preview-line 367\" data_line_start=\"367\" data_line_end=\"367\" data_line=\"367,368\" count_line=\"1\">(b) The total energy of an electron in the first excited state of the hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">3.4eV<\/asciimath><latex style=\"display: none\">3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.593ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2472 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1278, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find out its (i) kinetic energy and (ii) potential energy in this state.<\/div>\n<div class=\"preview-paragraph-369 preview-line 369\" data_line_start=\"369\" data_line_end=\"369\" data_line=\"369,370\" count_line=\"1\">(Delhi 2014C)<\/div>\n<ol start=\"17\" class=\"preview-paragraph-371 preview-line 371 372\" data_line_start=\"371\" data_line_end=\"372\" data_line=\"371,373\" count_line=\"2\">\n<li>Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-373 preview-line 373\" data_line_start=\"373\" data_line_end=\"373\" data_line=\"373,374\" count_line=\"1\">(Delhi 2013)<\/div>\n<ol start=\"18\" class=\"preview-paragraph-375 preview-line 375 376\" data_line_start=\"375\" data_line_end=\"376\" data_line=\"375,377\" count_line=\"2\">\n<li>Using Bohr’s postulates for hydrogen atom, show that the total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in the stationary states can be expressed as the sum of kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(K)<\/asciimath><latex style=\"display: none\">(K)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.771ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1667 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1278, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>K<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(U)<\/asciimath><latex style=\"display: none\">(U)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.495ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1545 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1156, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>U<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mi>U<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <mi>U<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=-2U<\/asciimath><latex style=\"display: none\">K=-2 U<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.655ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4267.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1166.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2222.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3000.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3500.6, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mi>U<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Hence deduce the expression for the total energy in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> energy level of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-377 preview-line 377\" data_line_start=\"377\" data_line_end=\"377\" data_line=\"377,378\" count_line=\"1\">(Foreign 2012)<\/div>\n<ol start=\"19\" class=\"preview-paragraph-379 preview-line 379 380\" data_line_start=\"379\" data_line_end=\"380\" data_line=\"379,381\" count_line=\"2\">\n<li>The energy levels of a hypothetical atom are shown below. Which of the shown transitions will result in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-381 preview-line 381\" data_line_start=\"381\" data_line_end=\"381\" data_line=\"381,382\" count_line=\"1\">Which of these transitions correspond to emission of radiation of (i) maximum and (ii) minimum wavelength?<\/div>\n<div class=\"preview-paragraph-383 preview-line 383\" data_line_start=\"383\" data_line_end=\"383\" data_line=\"383,384\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-06.jpg?height=228&width=465&top_left_y=1856&top_left_x=424\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-385 preview-line 385\" data_line_start=\"385\" data_line_end=\"385\" data_line=\"385,386\" count_line=\"1\">(Delhi 2011)<\/div>\n<ol start=\"20\" class=\"preview-paragraph-387 preview-line 387 388\" data_line_start=\"387\" data_line_end=\"388\" data_line=\"387,389\" count_line=\"2\">\n<li>Using the postulates of Bohr’s model of hydrogen atom, obtain an expression for the frequency of radiation emitted when atom make a transition from the higher energy state with quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to the lower energy state with quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo><<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub> \n <mo><<\/mo> \n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)(n_(f) < n_(i))<\/asciimath><latex style=\"display: none\">n_{f}\\left(n_{f}<n_{i}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.501ex\" height=\"2.364ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 5083.3 1045\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(1038.9, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1705.7, 0)\"><path data-c=\"3C\" d=\"M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2761.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3655.4, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo><<\/mo><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-389 preview-line 389\" data_line_start=\"389\" data_line_end=\"389\" data_line=\"389,390\" count_line=\"1\">(Foreign 2011)<\/div>\n<ol start=\"21\" class=\"preview-paragraph-391 preview-line 391 392\" data_line_start=\"391\" data_line_end=\"392\" data_line=\"391,393\" count_line=\"2\">\n<li>Using the relevant Bohr’s postulates, derive the expressions for the (a) speed of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-393 preview-line 393\" data_line_start=\"393\" data_line_end=\"393\" data_line=\"393,394\" count_line=\"1\">(b) radius of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of the electron, in hydrogen atom.<\/div>\n<div class=\"preview-paragraph-395 preview-line 395\" data_line_start=\"395\" data_line_end=\"395\" data_line=\"395,396\" count_line=\"1\">(Delhi 2010C)<\/div>\n<ol start=\"22\" class=\"preview-paragraph-397 preview-line 397 398\" data_line_start=\"397\" data_line_end=\"398\" data_line=\"397,399\" count_line=\"2\">\n<li>State any two postulates of Bohr’s theory of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-399 preview-line 399\" data_line_start=\"399\" data_line_end=\"399\" data_line=\"399,400\" count_line=\"1\">What is the maximum possible number of spectral lines observed when the hydrogen atom is in its second excited state? Justify your answer. Calculate the ratio of the maximum and minimum wavelengths of the radiations emitted in this process.<\/div>\n<ol start=\"23\" class=\"preview-paragraph-401 preview-line 401 402\" data_line_start=\"401\" data_line_end=\"402\" data_line=\"401,403\" count_line=\"2\">\n<li>(a) The energy levels of an atom are as shown below. Which of them will result in the transition of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-403 preview-line 403\" data_line_start=\"403\" data_line_end=\"403\" data_line=\"403,404\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-06.jpg?height=248&width=597&top_left_y=1064&top_left_x=1135\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-405 preview-line 405\" data_line_start=\"405\" data_line_end=\"405\" data_line=\"405,406\" count_line=\"1\">(b) Which transition corresponds to emission of radiation of maximum wavelength?<\/div>\n<div class=\"preview-paragraph-407 preview-line 407\" data_line_start=\"407\" data_line_end=\"407\" data_line=\"407,408\" count_line=\"1\">(Delhi 2009)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-409 preview-line 409\" id=\"la-(5-marks)\" data_line_start=\"409\" data_line_end=\"409\" data_line=\"409,410\" count_line=\"1\">\n<span class=\"section-number\">11. <\/span>LA (5 marks)<\/h2>\n<ol start=\"24\" class=\"preview-paragraph-411 preview-line 411 412\" data_line_start=\"411\" data_line_end=\"412\" data_line=\"411,413\" count_line=\"2\">\n<li>(a) Write two important limitations of Rutherford model which could not explain the observed features of atomic spectra. How were these explained in Bohr’s model of hydrogen atom?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-413 preview-line 413\" data_line_start=\"413\" data_line_end=\"413\" data_line=\"413,414\" count_line=\"1\">(b) Using Bohr’s postulates, obtain the expression for the radius of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit in hydrogen atom. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>4<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>4<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(4\/\/5<\/asciimath><latex style=\"display: none\">\\quad(4 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.536ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, Delhi <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2015<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2015<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2015 C)<\/asciimath><latex style=\"display: none\">2015 C)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.124ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3149 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2000, 0)\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2760, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2015<\/mn><mi>C<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"25\" class=\"preview-paragraph-415 preview-line 415 416 417 418\" data_line_start=\"415\" data_line_end=\"418\" data_line=\"415,419\" count_line=\"4\">\n<li>\n<div>Using Bohr’s postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom. (3\/5, Foreign 2014)<\/div>\n<\/li>\n<li>\n<div>(a) Using Bohr’s theory of hydrogen atom, derive the expression for the total energy of the electron in the stationary states of the atom.<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-419 preview-line 419\" data_line_start=\"419\" data_line_end=\"419\" data_line=\"419,420\" count_line=\"1\">(b) If electron in the atom is replaced by a particle (muon) having the same charge but mass about 200 times as that of the electron to form a muonic atom, how would (i) the radius and (ii) the ground state energy of this be affected?<\/div>\n<div class=\"preview-paragraph-421 preview-line 421\" data_line_start=\"421\" data_line_end=\"421\" data_line=\"421,422\" count_line=\"1\">(3\/5, Delhi <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2012<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">C<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2012<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">C<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2012C)<\/asciimath><latex style=\"display: none\">2012 \\mathrm{C})<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.038ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3111 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2000, 0)\"><g data-mml-node=\"mi\"><path data-c=\"43\" d=\"M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q322 658 252 588Q173 509 173 342Q173 221 211 151Q232 111 263 84T328 45T384 29T428 24Q517 24 571 93T626 244Q626 251 632 257H660L666 251V236Q661 133 590 56T403 -21Q262 -21 159 83T56 342Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2722, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2012<\/mn><mrow><mi mathvariant=\"normal\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"27\" class=\"preview-paragraph-423 preview-line 423 424\" data_line_start=\"423\" data_line_end=\"424\" data_line=\"423,425\" count_line=\"2\">\n<li>(a) Using postulates of Bohr’s theory of hydrogen atom, show that<\/li>\n<\/ol>\n<div class=\"preview-paragraph-425 preview-line 425\" data_line_start=\"425\" data_line_end=\"425\" data_line=\"425,426\" count_line=\"1\">(i) the radii of orbits increase as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, and (ii) the total energy of the electron increase as <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/n^(2)<\/asciimath><latex style=\"display: none\">1 \/ n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.533ex\" height=\"2.452ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 2003.6 1083.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1000, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the principal quantum number of the atom. (3\/5, AI 2011C)<\/div>\n<ol start=\"28\" class=\"preview-paragraph-427 preview-line 427 428\" data_line_start=\"427\" data_line_end=\"428\" data_line=\"427,429\" count_line=\"2\">\n<li>The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">102.7nm<\/asciimath><latex style=\"display: none\">102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.862ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3917 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2278, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-429 preview-line 429\" data_line_start=\"429\" data_line_end=\"429\" data_line=\"429,430\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=285&width=602&top_left_y=757&top_left_x=333\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-431 preview-line 431\" data_line_start=\"431\" data_line_end=\"431\" data_line=\"431,432\" count_line=\"1\">(Delhi 2008)<\/div>\n<div class=\"preview-paragraph-433 preview-line 433\" data_line_start=\"433\" data_line_end=\"433\" data_line=\"433,434\" count_line=\"1\">12.5 The Line Spectra of the Hydrogen Atom<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-435 preview-line 435\" id=\"vsa-(1-mark)-3\" data_line_start=\"435\" data_line_end=\"435\" data_line=\"435,436\" count_line=\"1\">\n<span class=\"section-number\">12. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"29\" class=\"preview-paragraph-437 preview-line 437 438\" data_line_start=\"437\" data_line_end=\"438\" data_line=\"437,439\" count_line=\"2\">\n<li>When is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line of the Balmer series in the emission spectrum of hydrogen atom obtained?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-439 preview-line 439\" data_line_start=\"439\" data_line_end=\"439\" data_line=\"439,440\" count_line=\"1\">(Delhi 2013C)<\/div>\n<ol start=\"30\" class=\"preview-paragraph-441 preview-line 441 442\" data_line_start=\"441\" data_line_end=\"442\" data_line=\"441,443\" count_line=\"2\">\n<li>What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state?<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-443 preview-line 443\" id=\"sai-(2-marks)\" data_line_start=\"443\" data_line_end=\"443\" data_line=\"443,444\" count_line=\"1\">\n<span class=\"section-number\">13. <\/span>SAI (2 marks)<\/h2>\n<ol start=\"31\" class=\"preview-paragraph-445 preview-line 445 446\" data_line_start=\"445\" data_line_end=\"446\" data_line=\"445,447\" count_line=\"2\">\n<li>Define ionization energy.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-447 preview-line 447\" data_line_start=\"447\" data_line_end=\"447\" data_line=\"447,448\" count_line=\"1\">How would the ionization energy change when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge?<\/div>\n<div class=\"preview-paragraph-449 preview-line 449\" data_line_start=\"449\" data_line_end=\"449\" data_line=\"449,450\" count_line=\"1\">(AI 2016)<\/div>\n<ol start=\"32\" class=\"preview-paragraph-451 preview-line 451 452\" data_line_start=\"451\" data_line_end=\"452\" data_line=\"451,453\" count_line=\"2\">\n<li>An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-453 preview-line 453\" data_line_start=\"453\" data_line_end=\"453\" data_line=\"453,454\" count_line=\"1\">(Foreign 2016)<\/div>\n<ol start=\"33\" class=\"preview-paragraph-455 preview-line 455 456\" data_line_start=\"455\" data_line_end=\"456\" data_line=\"455,457\" count_line=\"2\">\n<li>The figure shows energy level diagram of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-457 preview-line 457\" data_line_start=\"457\" data_line_end=\"457\" data_line=\"457,458\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=277&width=494&top_left_y=2169&top_left_x=381\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-459 preview-line 459\" data_line_start=\"459\" data_line_end=\"459\" data_line=\"459,460\" count_line=\"1\">(a) Find out the transition which results in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>496<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>496<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">496nm<\/asciimath><latex style=\"display: none\">496 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.581ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 3139 699\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>496<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. (b) Which transition corresponds to the emission of radiation of maximum wavelength? Justify your answer.<\/div>\n<div class=\"preview-paragraph-461 preview-line 461\" data_line_start=\"461\" data_line_end=\"461\" data_line=\"461,462\" count_line=\"1\">(AI 2015C)<\/div>\n<ol start=\"34\" class=\"preview-paragraph-463 preview-line 463 464\" data_line_start=\"463\" data_line_end=\"464\" data_line=\"463,465\" count_line=\"2\">\n<li>(i) In hydrogen atom, an electron undergoes transition from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2^(“nd “)<\/asciimath><latex style=\"display: none\">2^{\\text {nd }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.423ex\" height=\"1.932ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1513.1 853.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(556, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1112, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>2<\/mn><mrow><mtext>nd\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> excited state to the first excited state and then to the ground state. Identify the spectral series to which these transitions belong. (ii) Find out the ratio of the wavelengths of the emitted radiations in the two cases. (AI 2012C)<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-465 preview-line 465\" id=\"sa-ii-(3-marks)-4\" data_line_start=\"465\" data_line_end=\"465\" data_line=\"465,466\" count_line=\"1\">\n<span class=\"section-number\">14. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"35\" class=\"preview-paragraph-467 preview-line 467 468 469 470\" data_line_start=\"467\" data_line_end=\"470\" data_line=\"467,471\" count_line=\"4\">\n<li>\n<div>Using Rydberg formula, calculate the longest wavelength belonging to Lyman and Balmer series of hydrogen spectrum. In which region these transitions lie? <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">(<\/mo>\n <mn>3<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad(3\/\/5<\/asciimath><latex style=\"display: none\">\\quad(3 \/ 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.536ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2889 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(2389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, Foreign 2015)<\/div>\n<\/li>\n<li>\n<div>A <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">12.5eV<\/asciimath><latex style=\"display: none\">12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.724ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2972 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1778, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the hydrogen atoms would be excited?<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-471 preview-line 471\" data_line_start=\"471\" data_line_end=\"471\" data_line=\"471,472\" count_line=\"1\">Calculate the wavelengths of the first member of Lyman and first member of Balmer series.<\/div>\n<div class=\"preview-paragraph-473 preview-line 473\" data_line_start=\"473\" data_line_end=\"473\" data_line=\"473,474\" count_line=\"1\">(Delhi 2014)<\/div>\n<ol start=\"37\" class=\"preview-paragraph-475 preview-line 475 476\" data_line_start=\"475\" data_line_end=\"476\" data_line=\"475,477\" count_line=\"2\">\n<li>The value of ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-477 preview-line 477\" data_line_start=\"477\" data_line_end=\"477\" data_line=\"477,478\" count_line=\"1\">(i) Find the energy required to move an electron from the ground state to the first excited state of the atom.<\/div>\n<div class=\"preview-paragraph-479 preview-line 479\" data_line_start=\"479\" data_line_end=\"479\" data_line=\"479,480\" count_line=\"1\">(ii) Determine (a) the kinetic energy and (b) orbital radius in the first excited state of the atom.<\/div>\n<div class=\"preview-paragraph-481 preview-line 481\" data_line_start=\"481\" data_line_end=\"481\" data_line=\"481,482\" count_line=\"1\">(Given the value of Bohr radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.53<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.53<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=0.53″\u212b”<\/asciimath><latex style=\"display: none\">=0.53 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.769ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3433.8 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2833.8, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>0.53<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-483 preview-line 483\" data_line_start=\"483\" data_line_end=\"483\" data_line=\"483,484\" count_line=\"1\">(AI 2014C)<\/div>\n<ol start=\"38\" class=\"preview-paragraph-485 preview-line 485 486\" data_line_start=\"485\" data_line_end=\"486\" data_line=\"485,487\" count_line=\"2\">\n<li>(a) The energy levels of a hypothetical hydrogen-like atom are shown in the figure. Find out the transition, from the ones shown in the figure, which will result in the emission of a photon of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">275nm<\/asciimath><latex style=\"display: none\">275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.102ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3139 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1500, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-487 preview-line 487\" data_line_start=\"487\" data_line_end=\"487\" data_line=\"487,488\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-07.jpg?height=306&width=599&top_left_y=2080&top_left_x=1111\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-489 preview-line 489\" data_line_start=\"489\" data_line_end=\"489\" data_line=\"489,490\" count_line=\"1\">(b) Which of these transitions corresponds to the emission of radiation of (i) maximum and (ii) minimum wavelength? (Foreign 2013) 39. The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?<\/div>\n<div class=\"preview-paragraph-491 preview-line 491\" data_line_start=\"491\" data_line_end=\"491\" data_line=\"491,492\" count_line=\"1\">(1\/3, Delhi 2012)<\/div>\n<ol start=\"40\" class=\"preview-paragraph-493 preview-line 493 494\" data_line_start=\"493\" data_line_end=\"494\" data_line=\"493,495\" count_line=\"2\">\n<li>The ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. If an electron makes a transition from an energy level <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-0.85eV<\/asciimath><latex style=\"display: none\">-0.85 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-3.4eV<\/asciimath><latex style=\"display: none\">-3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.353ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3250 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2056, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-495 preview-line 495\" data_line_start=\"495\" data_line_end=\"495\" data_line=\"495,496\" count_line=\"1\">(AI 2012)<\/div>\n<ol start=\"41\" class=\"preview-paragraph-497 preview-line 497 498\" data_line_start=\"497\" data_line_end=\"498\" data_line=\"497,499\" count_line=\"2\">\n<li>The electron in a given Bohr orbit has a total energy of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-1.5eV<\/asciimath><latex style=\"display: none\">-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.353ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3250 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2056, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Calculate its<\/li>\n<\/ol>\n<div class=\"preview-paragraph-499 preview-line 499\" data_line_start=\"499\" data_line_end=\"499\" data_line=\"499,500\" count_line=\"1\">(i) kinetic energy.<\/div>\n<div class=\"preview-paragraph-501 preview-line 501\" data_line_start=\"501\" data_line_end=\"501\" data_line=\"501,502\" count_line=\"1\">(ii) potential energy.<\/div>\n<div class=\"preview-paragraph-503 preview-line 503\" data_line_start=\"503\" data_line_end=\"503\" data_line=\"503,504\" count_line=\"1\">(iii) wavelength of radiation emitted, when this electron makes a transition to the ground state. [Given : Energy in the ground state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-13.6eV<\/asciimath><latex style=\"display: none\">=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.873ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4805.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3611.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and Rybderg’s constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=1.09 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">=1.09 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.96ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 7496.5 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3056, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(4056.2, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(5459.8, 0)\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ]<\/div>\n<div class=\"preview-paragraph-505 preview-line 505\" data_line_start=\"505\" data_line_end=\"505\" data_line=\"505,506\" count_line=\"1\">(Delhi 2011C)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-507 preview-line 507\" id=\"la-(5-marks)-2\" data_line_start=\"507\" data_line_end=\"507\" data_line=\"507,508\" count_line=\"1\">\n<span class=\"section-number\">15. <\/span>LA (5 marks)<\/h2>\n<ol start=\"42\" class=\"preview-paragraph-509 preview-line 509 510\" data_line_start=\"509\" data_line_end=\"510\" data_line=\"509,511\" count_line=\"2\">\n<li>Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-511 preview-line 511\" data_line_start=\"511\" data_line_end=\"511\" data_line=\"511,512\" count_line=\"1\">(2\/5, Foreign 2014)<\/div>\n<ol start=\"43\" class=\"preview-paragraph-513 preview-line 513 514\" data_line_start=\"513\" data_line_end=\"514\" data_line=\"513,515\" count_line=\"2\">\n<li>Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ) to the lower state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n_(f))<\/asciimath><latex style=\"display: none\">\\left(n_{f}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.111ex\" height=\"2.364ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1816.9 1045\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1427.9, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. When electron in hydrogen atom jumps from energy state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=4<\/asciimath><latex style=\"display: none\">n_{i}=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2727.5 834.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=3,2,1<\/asciimath><latex style=\"display: none\">n_{f}=3,2,1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.773ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 4761.8 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2872.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3317.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3817.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4261.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Identify the spectral series to which the emission lines belong.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-515 preview-line 515\" data_line_start=\"515\" data_line_end=\"515\" data_line=\"515,516\" count_line=\"1\">(AI 2013)<\/div>\n<ol start=\"44\" class=\"preview-paragraph-517 preview-line 517 518\" data_line_start=\"517\" data_line_end=\"518\" data_line=\"517,519\" count_line=\"2\">\n<li>Calculate the wavelength of the first spectral line in the corresponding Lyman series of this atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-519 preview-line 519\" data_line_start=\"519\" data_line_end=\"519\" data_line=\"519,520\" count_line=\"1\">(2\/5, Delhi 2012C)<\/div>\n<ol start=\"45\" class=\"preview-paragraph-521 preview-line 521 522\" data_line_start=\"521\" data_line_end=\"522\" data_line=\"521,523\" count_line=\"2\">\n<li>Calculate the wavlength of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line in Balmer series of hydrogen atom, given Rydberg constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=1.097 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">R=1.097 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.437ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 9033.2 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2092.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4592.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5593, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(6996.6, 0)\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-523 preview-line 523\" data_line_start=\"523\" data_line_end=\"523\" data_line=\"523,524\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mi>A<\/mi>\n <mi>I<\/mi>\n <mn>2011<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mi>A<\/mi>\n <mi>I<\/mi>\n <mn>2011<\/mn>\n <mi>C<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(2\/\/5,AI 2011 C)<\/asciimath><latex style=\"display: none\">(2 \/ 5, A I 2011 C)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.241ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 6736.7 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(389, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(889, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1389, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1889, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2333.7, 0)\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3083.7, 0)\"><path data-c=\"49\" d=\"M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3587.7, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5587.7, 0)\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6347.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>5<\/mn><mo>,<\/mo><mi>A<\/mi><mi>I<\/mi><mn>2011<\/mn><mi>C<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-525 preview-line 525\" data_line_start=\"525\" data_line_end=\"525\" data_line=\"525,526\" count_line=\"1\">12.6 de Broglie’s Explanation of Bohr’s Second Postulate of Quantisation<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-527 preview-line 527\" id=\"vsa-(1-mark)-4\" data_line_start=\"527\" data_line_end=\"527\" data_line=\"527,528\" count_line=\"1\">\n<span class=\"section-number\">16. <\/span>VSA (1 mark)<\/h2>\n<ol start=\"46\" class=\"preview-paragraph-529 preview-line 529 530\" data_line_start=\"529\" data_line_end=\"530\" data_line=\"529,531\" count_line=\"2\">\n<li>State de-Broglie hypothesis.<\/li>\n<\/ol>\n<h2 type=\"section\" class=\"section-title preview-paragraph-531 preview-line 531\" id=\"sai-(2-marks)-2\" data_line_start=\"531\" data_line_end=\"531\" data_line=\"531,532\" count_line=\"1\">\n<span class=\"section-number\">17. <\/span>SAI (2 marks)<\/h2>\n<ol start=\"47\" class=\"preview-paragraph-533 preview-line 533 534\" data_line_start=\"533\" data_line_end=\"534\" data_line=\"533,535\" count_line=\"2\">\n<li>Calculate the de-Broglie wavelength of the electron orbiting in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state of hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-535 preview-line 535\" data_line_start=\"535\" data_line_end=\"535\" data_line=\"535,536\" count_line=\"1\">(AI 2016)<\/div>\n<ol start=\"48\" class=\"preview-paragraph-537 preview-line 537 538\" data_line_start=\"537\" data_line_end=\"538\" data_line=\"537,539\" count_line=\"2\">\n<li>Use de-Broglie’s hypothesis to write the relation for the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> radius of Bohr orbit in terms of Bohr’s quantization condition of orbital angular momentum.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-539 preview-line 539\" data_line_start=\"539\" data_line_end=\"539\" data_line=\"539,540\" count_line=\"1\">(Foreign 2016)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-541 preview-line 541\" id=\"sa-ii-(3-marks)-5\" data_line_start=\"541\" data_line_end=\"541\" data_line=\"541,542\" count_line=\"1\">\n<span class=\"section-number\">18. <\/span>SA II (3 marks)<\/h2>\n<ol start=\"49\" class=\"preview-paragraph-543 preview-line 543 544\" data_line_start=\"543\" data_line_end=\"544\" data_line=\"543,545\" count_line=\"2\">\n<li>(i) State Bohr’s quantization condition for defining stationary orbits. How does de Broglie hypothesis explain the stationary orbits ?<\/li>\n<\/ol>\n<div class=\"preview-paragraph-545 preview-line 545\" data_line_start=\"545\" data_line_end=\"545\" data_line=\"545,546\" count_line=\"1\">(ii) Find the relation between the three wavelengths <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>,<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1),lambda_(2)<\/asciimath><latex style=\"display: none\">\\lambda_{1}, \\lambda_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.47ex\" height=\"2.009ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 2417.8 888\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(986.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1431.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(3)<\/asciimath><latex style=\"display: none\">\\lambda_{3}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.945ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 859.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from the energy level diagram shown below.<\/div>\n<div class=\"preview-paragraph-547 preview-line 547\" data_line_start=\"547\" data_line_end=\"547\" data_line=\"547,548\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-08.jpg?height=317&width=534&top_left_y=1195&top_left_x=1161\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-549 preview-line 549\" data_line_start=\"549\" data_line_end=\"549\" data_line=\"549,550\" count_line=\"1\">(Delhi 2016)<\/div>\n<ol start=\"50\" class=\"preview-paragraph-551 preview-line 551 552\" data_line_start=\"551\" data_line_end=\"552\" data_line=\"551,553\" count_line=\"2\">\n<li>The kinetic energy of the electron orbiting in the first excited state of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">3.4eV<\/asciimath><latex style=\"display: none\">3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.593ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2472 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1278, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Determine the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-553 preview-line 553\" data_line_start=\"553\" data_line_end=\"553\" data_line=\"553,554\" count_line=\"1\">(Foreign 2015)<\/div>\n<ol start=\"51\" class=\"preview-paragraph-555 preview-line 555 556\" data_line_start=\"555\" data_line_end=\"556\" data_line=\"555,557\" count_line=\"2\">\n<li>An electron is revolving around the nucleus with a constant speed of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2.2 xx10^(8)m\/\/s<\/asciimath><latex style=\"display: none\">2.2 \\times 10^{8} \\mathrm{~m} \/ \\mathrm{s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.305ex\" height=\"2.52ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 5881 1114\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1500.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2500.4, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3904, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4987, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5487, 0)\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\/<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Find the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-557 preview-line 557\" data_line_start=\"557\" data_line_end=\"557\" data_line=\"557,558\" count_line=\"1\">(AI 2014C)<\/div>\n<ol start=\"52\" class=\"preview-paragraph-559 preview-line 559 560\" data_line_start=\"559\" data_line_end=\"560\" data_line=\"559,561\" count_line=\"2\">\n<li>Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbital state in hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the de Broglie wavelength associated with it.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-561 preview-line 561\" data_line_start=\"561\" data_line_end=\"561\" data_line=\"561,562\" count_line=\"1\">(2\/3, Delhi 2012)<\/div>\n<ol start=\"53\" class=\"preview-paragraph-563 preview-line 563 564\" data_line_start=\"563\" data_line_end=\"564\" data_line=\"563,565\" count_line=\"2\">\n<li>(a) Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-565 preview-line 565\" data_line_start=\"565\" data_line_end=\"565\" data_line=\"565,566\" count_line=\"1\">(b) The ground state energy of hydrogen atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-13.6eV<\/asciimath><latex style=\"display: none\">-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.484ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2556, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. What are the kinetic and potential energies of the electron in this state? (AI 2011)<\/div>\n<h2 type=\"section\" class=\"section-title preview-paragraph-567 preview-line 567\" id=\"detailed-solutions\" data_line_start=\"567\" data_line_end=\"567\" data_line=\"567,568\" count_line=\"1\">\n<span class=\"section-number\">19. <\/span>Detailed Solutions<\/h2>\n<ol class=\"preview-paragraph-569 preview-line 569 570 571 572\" data_line_start=\"569\" data_line_end=\"572\" data_line=\"569,573\" count_line=\"4\">\n<li>\n<div>According to electromagnetic theory, electron revolving around the nucleus are continuously accelerated. Since an accelerated charge emits energy, the radius of the circular path of a revolving electron should go on decreasing and ultimately it should fall into the nucleus. So, it could not explain the structure of the atom. As matter is stable, we cannot expect the atoms to collapse.<\/div>\n<\/li>\n<li>\n<div>An electron revolving in an orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, has both kinetic energy and electrostatic potential energy. Kinetic energy of the electron revolving in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(K)=(1)\/(2)mv^(2)<\/asciimath><latex style=\"display: none\">E_{K}=\\frac{1}{2} m v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.781ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.014ex\" height=\"2.737ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 5310.3 1209.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 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70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2750.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 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422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-573 preview-line 573\" data_line_start=\"573\" data_line_end=\"573\" data_line=\"573,574\" count_line=\"1\">Since, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))(e^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.324ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5889 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 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363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"814.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-575 preview-line 575 576 577\" data_line_start=\"575\" data_line_end=\"577\" data_line=\"575,578\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext> or <\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadE_(K)=(1)\/(2)xx(1)\/(4piepsi_(0))(e^(2))\/(r)” or “E_(K)=(1)\/(4piepsi_(0))(e^(2))\/(2r)<\/asciimath><latex style=\"display: none\">\\therefore \\quad E_{K}=\\frac{1}{2} \\times \\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r} \\text { or } E_{K}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.763ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 18459.2 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 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width=\"1em\"><\/mspace><\/mstyle><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-579 preview-line 579\" data_line_start=\"579\" data_line_end=\"579\" data_line=\"579,580\" count_line=\"1\">Electrostatic potential energy of electron of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> revolving around the nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in an orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-581 preview-line 581 582 583\" data_line_start=\"581\" data_line_end=\"583\" data_line=\"581,584\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo>+<\/mo>\n <mi>e<\/mi>\n <mo>×<\/mo>\n <mo>−<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext> or <\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo>+<\/mo>\n <mi>e<\/mi>\n <mo>\u00d7<\/mo>\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mtext>\u00a0or\u00a0<\/mtext>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(P)=(1)\/(4piepsi_(0))(+e xx-e)\/(r)” or “E_(P)=(-1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">E_{P}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{+e \\times-e}{r} \\text { or } E_{P}=\\frac{-1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.272ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 16916.3 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 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290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1069.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>E<\/mi><mrow><mi>P<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mo>+<\/mo><mi>e<\/mi><mo>\u00d7<\/mo><mo>\u2212<\/mo><mi>e<\/mi><\/mrow><mi>r<\/mi><\/mfrac><mtext>\u00a0or\u00a0<\/mtext><msub><mi>E<\/mi><mrow><mi>P<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-585 preview-line 585\" data_line_start=\"585\" data_line_end=\"585\" data_line=\"585,586\" count_line=\"1\">So, total energy of electron in orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-587 preview-line 587 588 589\" data_line_start=\"587\" data_line_end=\"589\" data_line=\"587,590\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mtext> or <\/mtext>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>P<\/mi>\n <\/mrow>\n <\/msub>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(K)+E_(P)” or “E=(1)\/(4piepsi_(0))(e^(2))\/(2r)-(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">E=E_{K}+E_{P} \\text { or } E=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.238ex\" 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447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(429.3, -686)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1069.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>E<\/mi><mrow><mi>P<\/mi><\/mrow><\/msub><mtext>\u00a0or\u00a0<\/mtext><mi>E<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-591 preview-line 591\" data_line_start=\"591\" data_line_end=\"591\" data_line=\"591,592\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-1)\/(4piepsi_(0))(e^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E=\\frac{-1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.361ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5021.5 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 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405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"872.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-593 preview-line 593\" data_line_start=\"593\" data_line_end=\"593\" data_line=\"593,594\" count_line=\"1\">The -ve sign of the energy of electron indicates that the electron and nucleus together form a bound system i.e., electron is bound to the nucleus.<\/div>\n<div class=\"preview-paragraph-595 preview-line 595\" data_line_start=\"595\" data_line_end=\"595\" data_line=\"595,596\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-09.jpg?height=456&width=528&top_left_y=1985&top_left_x=250\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-597 preview-line 597\" data_line_start=\"597\" data_line_end=\"597\" data_line=\"597,598\" count_line=\"1\">A very small fraction of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles are scattered at <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>∘<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>><\/mo>\n <msup>\n <mn>90<\/mn>\n <mrow>\n <mo>\u2218<\/mo>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta > 90^(@)<\/asciimath><latex style=\"display: none\">\\theta>90^{\\circ}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.09ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.254ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -707 3206.1 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2218\" d=\"M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251ZM245 403Q188 403 142 361T96 250Q96 183 141 140T250 96Q284 96 313 109T354 135T375 160Q403 197 403 250Q403 313 360 358T245 403Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>><\/mo><msup><mn>90<\/mn><mrow><mo>\u2218<\/mo><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> because the size of nucleus is very small nearly <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>1<\/mn>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>8000<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1\/\/8000<\/asciimath><latex style=\"display: none\">1 \/ 8000<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.787ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3000 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(500, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1000, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mrow><mo>\/<\/mo><\/mrow><mn>8000<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> times the size of atom. So, a few <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles experience a strong repulsive force and turn back. Conclusions :<\/div>\n<div class=\"preview-paragraph-599 preview-line 599\" data_line_start=\"599\" data_line_end=\"599\" data_line=\"599,600\" count_line=\"1\">(i) Entire positive charge and most of the mass of the atom is concentrated in the nucleus with the electrons some distance away.<\/div>\n<div class=\"preview-paragraph-601 preview-line 601\" data_line_start=\"601\" data_line_end=\"601\" data_line=\"601,602\" count_line=\"1\">(ii) Size of the nucleus is about <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-15)m<\/asciimath><latex style=\"display: none\">10^{-15} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>14<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>14<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-14)m<\/asciimath><latex style=\"display: none\">10^{-14} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.022ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.8 3390.2 893.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>14<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, while size of the atom is <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-10)m<\/asciimath><latex style=\"display: none\">10^{-10} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so the electrons are at distance <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(4)m<\/asciimath><latex style=\"display: none\">10^{4} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.626ex\" height=\"2.022ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.8 2486.6 893.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1403.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mn>4<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>5<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>5<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(5)m<\/asciimath><latex style=\"display: none\">10^{5} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.626ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 2486.6 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1403.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mn>5<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from the nucleus, and being large empty space in the atom, most <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> particles go through the empty space.<\/div>\n<ol start=\"4\" class=\"preview-paragraph-603 preview-line 603 604\" data_line_start=\"603\" data_line_end=\"604\" data_line=\"603,605\" count_line=\"2\">\n<li><\/li>\n<\/ol>\n<div class=\"preview-paragraph-605 preview-line 605\" data_line_start=\"605\" data_line_end=\"605\" data_line=\"605,606\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-09.jpg?height=462&width=741&top_left_y=1134&top_left_x=1040\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-607 preview-line 607\" data_line_start=\"607\" data_line_end=\"607\" data_line=\"607,608\" count_line=\"1\">Only a small fraction of the number of incident <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles (1 in 8000) rebound back. This shows that the number of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particles undergoing head on collision is small. This implies that the entire positive charge of the atom is concentrated in a small volume.<\/div>\n<div class=\"preview-paragraph-609 preview-line 609\" data_line_start=\"609\" data_line_end=\"609\" data_line=\"609,610\" count_line=\"1\">So, this experiment is an important way to determine an upper limit on the size of nucleus.<\/div>\n<ol start=\"5\" class=\"preview-paragraph-611 preview-line 611 612\" data_line_start=\"611\" data_line_end=\"612\" data_line=\"611,613\" count_line=\"2\">\n<li>Assumptions of Rutherford’s atomic model :<\/li>\n<\/ol>\n<div class=\"preview-paragraph-613 preview-line 613\" data_line_start=\"613\" data_line_end=\"613\" data_line=\"613,614\" count_line=\"1\">(i) Every atom consists of a tiny central core called the atomic nucleus, in which the entire positive charge and atmost entire mass of the atom are concentrated.<\/div>\n<div class=\"preview-paragraph-615 preview-line 615\" data_line_start=\"615\" data_line_end=\"615\" data_line=\"615,616\" count_line=\"1\">(ii) The size of nucleus is of the order of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>15<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-15)m<\/asciimath><latex style=\"display: none\">10^{-15} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, which is very small as compared to the size of the atom which is of the order of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-10)m<\/asciimath><latex style=\"display: none\">10^{-10} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.67ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 3390.2 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2307.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-617 preview-line 617\" data_line_start=\"617\" data_line_end=\"617\" data_line=\"617,618\" count_line=\"1\">(iii) The atomic nucleus is surrounded by certain number of electrons. As atom on the whole is electrically neutral, the total negative charge of electrons surrounding the nucleus is equal to total positive charge on the nucleus. (iv) The electrons revolve around the nucleus in various circular orbits.<\/div>\n<div class=\"preview-paragraph-619 preview-line 619\" data_line_start=\"619\" data_line_end=\"619\" data_line=\"619,620\" count_line=\"1\">Refer to answer 1.<\/div>\n<ol start=\"6\" class=\"preview-paragraph-621 preview-line 621 622\" data_line_start=\"621\" data_line_end=\"622\" data_line=\"621,623\" count_line=\"2\">\n<li><\/li>\n<\/ol>\n<div class=\"preview-paragraph-623 preview-line 623\" data_line_start=\"623\" data_line_end=\"623\" data_line=\"623,624\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-10.jpg?height=349&width=554&top_left_y=605&top_left_x=340\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-625 preview-line 625\" data_line_start=\"625\" data_line_end=\"625\" data_line=\"625,626\" count_line=\"1\">The size of the nucleus can be obtained by finding impact parameter <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b<\/asciimath><latex style=\"display: none\">b<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.971ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 429 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> using trajectories of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle. The impact parameter is the perpendicular distance of the initial velocity vector of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle from the central line of nucleus, when it is far away from the atom. Rutherford calculated impact parameter as<\/div>\n<div class=\"preview-paragraph-627 preview-line 627\" data_line_start=\"627\" data_line_end=\"627\" data_line=\"627,628\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">⁡<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>θ<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>b<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>cot<\/mi>\n <mo data-mjx-texclass=\"NONE\">\u2061<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03b8<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">b=(1)\/(4piepsi_(0))*(Ze^(2)cot(theta\/\/2))\/(E)<\/asciimath><latex style=\"display: none\">b=\\frac{1}{4 \\pi \\varepsilon_{0}} \\cdot \\frac{Z e^{2} \\cot (\\theta \/ 2)}{E}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.258ex\" height=\"3.549ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1106.5 8511.9 1568.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(706.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1762.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3796.2, 0)\"><path data-c=\"22C5\" d=\"M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4296.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 516.8) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1759.2, 0)\"><path data-c=\"63\" d=\"M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z\"><\/path><path data-c=\"6F\" d=\"M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z\" transform=\"translate(444, 0)\"><\/path><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\" transform=\"translate(944, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"2061\" d=\"\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3092.2, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3481.2, 0)\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3950.2, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(4450.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4950.2, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1837.6, -345) scale(0.707)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><rect width=\"3975.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo>\u22c5<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>cot<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b8<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mi>E<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-629 preview-line 629\" data_line_start=\"629\" data_line_end=\"629\" data_line=\"629,630\" count_line=\"1\">where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=KE<\/asciimath><latex style=\"display: none\">E=K E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.485ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 3750.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2986.6, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>α<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b1<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">alpha<\/asciimath><latex style=\"display: none\">\\alpha<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.448ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 640 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-particle<\/div>\n<div class=\"preview-paragraph-631 preview-line 631\" data_line_start=\"631\" data_line_end=\"631\" data_line=\"631,632\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>θ<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03b8<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">theta=<\/asciimath><latex style=\"display: none\">\\theta=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.45ex\" height=\"1.781ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 1524.8 787\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3B8\" d=\"M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(746.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b8<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> scattering angle<\/div>\n<div class=\"preview-paragraph-633 preview-line 633\" data_line_start=\"633\" data_line_end=\"633\" data_line=\"633,634\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=<\/asciimath><latex style=\"display: none\">Z=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.024ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1778.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> atomic number of atom<\/div>\n<div class=\"preview-paragraph-635 preview-line 635\" data_line_start=\"635\" data_line_end=\"635\" data_line=\"635,636\" count_line=\"1\">The size of the nucleus is smaller than the impact parameter.<\/div>\n<ol start=\"7\" class=\"preview-paragraph-637 preview-line 637 638\" data_line_start=\"637\" data_line_end=\"638\" data_line=\"637,639\" count_line=\"2\">\n<li>Wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>λ<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>\u03bb<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda)<\/asciimath><latex style=\"display: none\">(\\lambda)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.079ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1361 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(972, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>\u03bb<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of Balmer series is given by<\/li>\n<\/ol>\n<div class=\"preview-paragraph-639 preview-line 639 640 641\" data_line_start=\"639\" data_line_end=\"641\" data_line=\"639,642\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mtext> where <\/mtext>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mtext>\u00a0where\u00a0<\/mtext>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R_(H)[(1)\/(2^(2))-(1)\/(n_(i)^(2))]” where “n_(i)=3,4,5,dots<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R_{H}\\left[\\frac{1}{2^{2}}-\\frac{1}{n_{i}^{2}}\\right] \\text { where } n_{i}=3,4,5, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.313ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 18260.5 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2356.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 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442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 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442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(13198.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(14254.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 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data-mml-node=\"mo\" transform=\"translate(16643.9, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(17088.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><msub><mi>R<\/mi><mrow><mi>H<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mtext>\u00a0where\u00a0<\/mtext><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-643 preview-line 643\" data_line_start=\"643\" data_line_end=\"643\" data_line=\"643,644\" count_line=\"1\">For shortest wavelength, when transition of electrons take place from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi mathvariant=\"normal\">∞<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=oo<\/asciimath><latex style=\"display: none\">n_{i}=\\infty<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.302ex\" height=\"1.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 3227.5 740.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 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214Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=2<\/asciimath><latex style=\"display: none\">n_{f}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.499ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2872.5 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, wavelength of emitted photon is shortest.<\/div>\n<div class=\"preview-paragraph-645 preview-line 645 646 647 648 649 650\" data_line_start=\"645\" data_line_end=\"650\" data_line=\"645,651\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi mathvariant=\"normal\">∞<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.646<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3646<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <msub>\n <mi>R<\/mi>\n <mrow>\n <mi>H<\/mi>\n <\/mrow>\n <\/msub>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.646<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3646<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[(1)\/(lambda_(min))=R_(H)[(1)\/(2^(2))-(1)\/(oo)]=(1.097 xx10^(7))\/(4)],[:.quadlambda_(min)=3.646 xx10^(-7)m=3646″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\frac{1}{\\lambda_{\\min }}=R_{H}\\left[\\frac{1}{2^{2}}-\\frac{1}{\\infty}\\right]=\\frac{1.097 \\times 10^{7}}{4} \\\\\n&\\therefore \\quad \\lambda_{\\min }=3.646 \\times 10^{-7} \\mathrm{~m}=3646 \\AA\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.889ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"37.923ex\" height=\"8.909ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2218.8 16761.8 3937.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 671.7)\"><g data-mml-node=\"mtd\"><\/g><g data-mml-node=\"mtd\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(875.9, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 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0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(15238.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><msub><mi>R<\/mi><mrow><mi>H<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mi mathvariant=\"normal\">\u221e<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>4<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>3.646<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>3646<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-652 preview-line 652\" data_line_start=\"652\" data_line_end=\"652\" data_line=\"652,653\" count_line=\"1\">This wavelength lies in visible region of electromagnetic spectrum.<\/div>\n<ol start=\"8\" class=\"preview-paragraph-654 preview-line 654 655\" data_line_start=\"654\" data_line_end=\"655\" data_line=\"654,656\" count_line=\"2\">\n<li>For Lyman series,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-656 preview-line 656 657 658\" data_line_start=\"656\" data_line_end=\"658\" data_line=\"656,659\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">[<\/mo>\n <mo>∴<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2234<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R((1)\/(1^(2))-(1)\/(n^(2)))quad[:.n=2,3,4,dots]<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{n^{2}}\\right) \\quad[\\therefore n=2,3,4, \\ldots]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.546ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 17037.4 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 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52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2301.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3302, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4745.6, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 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388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11697.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(12753.4, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13253.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(13698.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14198.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(14642.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(15142.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(15587.4, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(16759.4, 0)\"><path data-c=\"5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo stretchy=\"false\">[<\/mo><mo>\u2234<\/mo><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo stretchy=\"false\">]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-660 preview-line 660\" data_line_start=\"660\" data_line_end=\"660\" data_line=\"660,661\" count_line=\"1\">Let <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1)<\/asciimath><latex style=\"display: none\">\\lambda_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)<\/asciimath><latex style=\"display: none\">\\lambda_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.232ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 986.6 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be the wavelength of the first and second line respectively, then<\/div>\n<div class=\"preview-paragraph-662 preview-line 662 663 664\" data_line_start=\"662\" data_line_end=\"664\" data_line=\"662,665\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1<\/mn>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1<\/mn> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mn>4<\/mn>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(1))=R((1)\/(1^(2))-(1)\/(2^(2)))=R(1-(1)\/(4))=(3)\/(4)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{1}}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right)=R\\left(1-\\frac{1}{4}\\right)=\\frac{3}{4} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.086ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 18160.2 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-666 preview-line 666\" data_line_start=\"666\" data_line_end=\"666\" data_line=\"666,667\" count_line=\"1\">and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1<\/mn>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1<\/mn> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mn>9<\/mn>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(2))=R((1)\/(1^(2))-(1)\/(3^(2)))=R(1-(1)\/(9))=(8)\/(9)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{2}}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right)=R\\left(1-\\frac{1}{9}\\right)=\\frac{8}{9} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.686ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 16215.1 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(392, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 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682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>9<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>8<\/mn><mn>9<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-668 preview-line 668\" data_line_start=\"668\" data_line_end=\"668\" data_line=\"668,669\" count_line=\"1\">Dividing (ii) by (i), we get<\/div>\n<div class=\"preview-paragraph-670 preview-line 670\" data_line_start=\"670\" data_line_end=\"670\" data_line=\"670,671\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <mrow>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mn>3<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <mrow>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>8<\/mn>\n <mn>9<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mn>3<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">((1)\/(lambda_(2)))\/((1)\/(lambda_(1)))=((8)\/(9)R)\/((3)\/(4)R)=>(1)\/(lambda_(2))xx(lambda_(1))\/(1)=(8)\/(9)xx(4)\/(3)<\/asciimath><latex style=\"display: none\">\\frac{\\frac{1}{\\lambda_{2}}}{\\frac{1}{\\lambda_{1}}}=\\frac{\\frac{8}{9} R}{\\frac{3}{4} R} \\Rightarrow \\frac{1}{\\lambda_{2}} \\times \\frac{\\lambda_{1}}{1}=\\frac{8}{9} \\times \\frac{4}{3}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.284ex\" height=\"4.985ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1351.8 13385.3 2203.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mfrac\" transform=\"translate(220, 740.2) scale(0.707)\"><g 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(1))\/(lambda_(2))=(32)\/(27)<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{1}}{\\lambda_{2}}=\\frac{32}{27}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"897.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1415.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2471.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 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data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-674 preview-line 674\" data_line_start=\"674\" data_line_end=\"674\" data_line=\"674,675\" count_line=\"1\">As <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5400<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>5400<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=5400<\/asciimath><latex style=\"display: none\">\\lambda_{2}=5400<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.774ex\" height=\"1.91ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4320.1 844\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1264.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2320.1, 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198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5400<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-676 preview-line 676\" data_line_start=\"676\" data_line_end=\"676\" data_line=\"676,677\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>×<\/mo>\n <mn>5400<\/mn>\n <mo>=<\/mo>\n <mn>6400<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>27<\/mn>\n <\/mfrac>\n <mo>\u00d7<\/mo>\n <mn>5400<\/mn>\n <mo>=<\/mo>\n <mn>6400<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadlambda_(1)=(32)\/(27)xxlambda_(2)=(32)\/(27)xx5400=6400″\u212b”<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\lambda_{1}=\\frac{32}{27} \\times \\lambda_{2}=\\frac{32}{27} \\times 5400=6400 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.044ex\" height=\"2.773ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 17257.7 1225.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(1944.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" 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-10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(10323.9, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(11324.1, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13601.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(14657.7, 0)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(16657.7, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><mo>\u00d7<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>32<\/mn><mn>27<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>5400<\/mn><mo>=<\/mo><mn>6400<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"9\" class=\"preview-paragraph-678 preview-line 678 679\" data_line_start=\"678\" data_line_end=\"679\" data_line=\"678,680\" count_line=\"2\">\n<li>Since <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r propn^(2)<\/asciimath><latex style=\"display: none\">r \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.308ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 2788.1 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-680 preview-line 680\" data_line_start=\"680\" data_line_end=\"680\" data_line=\"680,681\" count_line=\"1\">For ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(1)=1<\/asciimath><latex style=\"display: none\">n_{1}=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.419ex\" height=\"1.846ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2837.1 816\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-682 preview-line 682\" data_line_start=\"682\" data_line_end=\"682\" data_line=\"682,683\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mtext>st <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mtext>st\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">1^(“st “)<\/asciimath><latex style=\"display: none\">1^{\\text {st }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.897ex\" height=\"1.805ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -797.9 1280.4 797.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\" transform=\"translate(394, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(783, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>1<\/mn><mrow><mtext>st\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> excited state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)=2<\/asciimath><latex style=\"display: none\">n_{2}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.419ex\" height=\"1.846ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2837.1 816\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2337.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-684 preview-line 684\" data_line_start=\"684\" data_line_end=\"684\" data_line=\"684,685\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Required ratio of radii of the orbits<\/div>\n<div class=\"preview-paragraph-686 preview-line 686 687 688\" data_line_start=\"686\" data_line_end=\"688\" data_line=\"686,689\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>:<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo>:<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(r_(2))\/(r_(1))=(n_(2)^(2))\/(n_(1)^(2))=(2^(2))\/(1)=4:1<\/asciimath><latex style=\"display: none\">\\frac{r_{2}}{r_{1}}=\\frac{n_{2}^{2}}{n_{1}^{2}}=\\frac{2^{2}}{1}=4: 1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.448ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.434ex\" height=\"6.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1581.9 9915.9 2663.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"msub\" 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666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><rect width=\"1054.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1572.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2628.1, 0)\"><g data-mml-node=\"msubsup\" transform=\"translate(220, 747.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 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404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4349.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5405.2, 0)\"><g data-mml-node=\"msup\" transform=\"translate(220, 676)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(421.8, -686)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(7026.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(8082.3, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8860.1, 0)\"><path data-c=\"3A\" d=\"M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9415.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><msub><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msubsup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msubsup><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>=<\/mo><mfrac><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><mn>1<\/mn><\/mfrac><mo>=<\/mo><mn>4<\/mn><mo>:<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"10\" class=\"preview-paragraph-690 preview-line 690 691\" data_line_start=\"690\" data_line_end=\"691\" data_line=\"690,692\" count_line=\"2\">\n<li>Ionisation energy for an atom is defined as the energy required to remove an electron completely from the outermost shell of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-692 preview-line 692\" data_line_start=\"692\" data_line_end=\"692\" data_line=\"692,693\" count_line=\"1\">For hydrogen atom,<\/div>\n<div class=\"preview-paragraph-694 preview-line 694 695 696\" data_line_start=\"694\" data_line_end=\"696\" data_line=\"694,697\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi mathvariant=\"normal\">∞<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi mathvariant=\"normal\">\u221e<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(oo)-E_(1)=0-(-13.6)eV=13.6eV<\/asciimath><latex style=\"display: none\">E=E_{\\infty}-E_{1}=0-(-13.6) \\mathrm{eV}=13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"40.376ex\" height=\"2.262ex\" role=\"img\" 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data-mjx-texclass=\"ORD\" transform=\"translate(16652.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi mathvariant=\"normal\">\u221e<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"11\" class=\"preview-paragraph-698 preview-line 698 699\" data_line_start=\"698\" data_line_end=\"699\" data_line=\"698,700\" count_line=\"2\">\n<li>Quantum condition : The stationary orbits are those in which angular momentum of electron is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi)<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.707ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 1196.6 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e.,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-700 preview-line 700 701 702\" data_line_start=\"700\" data_line_end=\"702\" data_line=\"700,703\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=n(h)\/(2pi),n=1,2,3,dots<\/asciimath><latex style=\"display: none\">m v r=n \\frac{h}{2 \\pi}, n=1,2,3, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.339ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 11641.8 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 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225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3147.6, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3747.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(467, 676)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5257.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5702.2, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6580, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(7635.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8135.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(8580.4, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9080.4, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9525.1, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10025.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10469.8, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-704 preview-line 704\" data_line_start=\"704\" data_line_end=\"704\" data_line=\"704,705\" count_line=\"1\">Integer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called the principal quantum number. This equation is called Bohr’s quantum condition.<\/div>\n<ol start=\"12\" class=\"preview-paragraph-706 preview-line 706 707\" data_line_start=\"706\" data_line_end=\"707\" data_line=\"706,708\" count_line=\"2\">\n<li>Frequency condition : An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-708 preview-line 708 709 710\" data_line_start=\"708\" data_line_end=\"710\" data_line=\"708,711\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">h v=E_{i}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.181ex\" height=\"2.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 5825.9 989\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1338.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2394.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3648.7, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4649, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-712 preview-line 712\" data_line_start=\"712\" data_line_end=\"712\" data_line=\"712,713\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is frequency of radiation emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies associated with stationary orbits of principal quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> respectively <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(:}<\/asciimath><latex style=\"display: none\">\\left(\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(389, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i) > n_(f)<\/asciimath><latex style=\"display: none\">n_{i}>n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.39ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -540 3266.4 835\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2227.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>><\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-714 preview-line 714\" data_line_start=\"714\" data_line_end=\"714\" data_line=\"714,715\" count_line=\"1\">13 According to Bohr’s theory, a hydrogen atom consists of a nucleus with a positive charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Ze<\/asciimath><latex style=\"display: none\">Z e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.69ex\" height=\"1.57ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1189 694\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(723, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, and a single electron of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, which revolves around it in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-716 preview-line 716\" data_line_start=\"716\" data_line_end=\"716\" data_line=\"716,717\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-11.jpg?height=217&width=285&top_left_y=557&top_left_x=491\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-718 preview-line 718\" data_line_start=\"718\" data_line_end=\"718\" data_line=\"718,719\" count_line=\"1\">Here <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z<\/asciimath><latex style=\"display: none\">Z<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.636ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 723 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the atomic number and for hydrogen <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The electrostatic force of attraction between the hydrogen nucleus and the electron is<\/div>\n<div class=\"preview-paragraph-720 preview-line 720\" data_line_start=\"720\" data_line_end=\"720\" data_line=\"720,721\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>e<\/mi>\n <mo>⋅<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>e<\/mi>\n <mo>\u22c5<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"[\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">F=(ke*e)\/(r^(2))=(ke^(2))\/(r^(2))quad[:}<\/asciimath><latex style=\"display: none\">F=\\frac{k e \\cdot e}{r^{2}}=\\frac{k e^{2}}{r^{2}} \\quad\\left[\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" 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212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1026.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2082.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 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250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1265, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(529.9, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 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367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5080.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(6503.4, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(7503.4, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(278, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>F<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>e<\/mi><mo>\u22c5<\/mo><mi>e<\/mi><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <mi>k<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"\" close=\"]\" separators=\"|\">\n <mrow>\n <mi>k<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:k=(1)\/(4piepsi_(0))]<\/asciimath><latex style=\"display: none\">\\left.k=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.362ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 4138 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><\/g><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1854.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3666, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><mi>k<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-722 preview-line 722\" data_line_start=\"722\" data_line_end=\"722\" data_line=\"722,723\" count_line=\"1\">To keep the electron in its orbit, the centripetal force on the electron must be equal to the electrostatic attraction. Therefore,<\/div>\n<div class=\"preview-paragraph-724 preview-line 724\" data_line_start=\"724\" data_line_end=\"724\" data_line=\"724,725\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(ke^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.059ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4446 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-726 preview-line 726\" data_line_start=\"726\" data_line_end=\"726\" data_line=\"726,727\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.234ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4523.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2044.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3100.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-728 preview-line 728\" data_line_start=\"728\" data_line_end=\"728\" data_line=\"728,729\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(ke^(2))\/(mv^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{k e^{2}}{m v^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.859ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 3473.7 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(352.9, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-730 preview-line 730\" data_line_start=\"730\" data_line_end=\"730\" data_line=\"730,731\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the mass of the electron, and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, its speed in an orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-732 preview-line 732\" data_line_start=\"732\" data_line_end=\"732\" data_line=\"732,733\" count_line=\"1\">Bohr’s quantisation condition for angular momentum is<\/div>\n<div class=\"preview-paragraph-734 preview-line 734\" data_line_start=\"734\" data_line_end=\"734\" data_line=\"734,735\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">L=m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.556ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6433.7 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(958.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2014.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2892.6, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3377.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4106.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5162.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi mv)<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.925ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3944.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-736 preview-line 736\" data_line_start=\"736\" data_line_end=\"736\" data_line=\"736,737\" count_line=\"1\">From equation (ii) and (iii), we get<\/div>\n<div class=\"preview-paragraph-738 preview-line 738\" data_line_start=\"738\" data_line_end=\"738\" data_line=\"738,739\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(ke^(2))\/(mv^(2))=(nh)\/(2pi mv)quad<\/asciimath><latex style=\"display: none\">\\frac{k e^{2}}{m v^{2}}=\\frac{n h}{2 \\pi m v} \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.989ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6183.1 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(352.9, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(5183.1, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad v=(2pi ke^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\quad v=\\frac{2 \\pi k e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.309ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4998.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1000, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1591, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(674.2, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"1939.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-740 preview-line 740\" data_line_start=\"740\" data_line_end=\"740\" data_line=\"740,741\" count_line=\"1\">Substituting this value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (iii), we get<\/div>\n<div class=\"preview-paragraph-742 preview-line 742\" data_line_start=\"742\" data_line_end=\"742\" data_line=\"742,743\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi m)*(nh)\/(2pi ke^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m} \\cdot \\frac{n h}{2 \\pi k e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.716ex\" height=\"2.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6504.3 1322.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g 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153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 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393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1591, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1939.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><\/mrow><\/mfrac><mo>\u22c5<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-744 preview-line 744\" data_line_start=\"744\" data_line_end=\"744\" data_line=\"744,745\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>r=(n^(2)h^(2))\/(4pi^(2)mke^(2))quad:.r propn^(2)<\/asciimath><latex style=\"display: none\">\\Rightarrow r=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k e^{2}} \\quad \\therefore r \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.247ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 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496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2872.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 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0)\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8371, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9099.7, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(10155.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"14\" class=\"preview-paragraph-746 preview-line 746 747\" data_line_start=\"746\" data_line_end=\"747\" data_line=\"746,748\" count_line=\"2\">\n<li>Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of hydrogen atom : In <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, an electron having charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>−<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">-e<\/asciimath><latex style=\"display: none\">-e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2212<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> revolves around the nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in a circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, such that necessary centripetal force is provided by the electrostatic force of attraction between the electron and nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-748 preview-line 748\" data_line_start=\"748\" data_line_end=\"748\" data_line=\"748,749\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-11.jpg?height=242&width=374&top_left_y=453&top_left_x=1224\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-750 preview-line 750\" data_line_start=\"750\" data_line_end=\"750\" data_line=\"750,751\" count_line=\"1\">i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>e<\/mi>\n <mo>.<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>e<\/mi>\n <mo>.<\/mo>\n <mi>e<\/mi>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))(e.e)\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e . e}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.868ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6129.8 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 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61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(744, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(345.7, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1055.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>e<\/mi><mo>.<\/mo><mi>e<\/mi><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.499ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5966.4 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" 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81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(368, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"814.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-752 preview-line 752\" data_line_start=\"752\" data_line_end=\"752\" data_line=\"752,753\" count_line=\"1\">From Bohr’s quantization condition<\/div>\n<div class=\"preview-paragraph-754 preview-line 754\" data_line_start=\"754\" data_line_end=\"754\" data_line=\"754,755\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.948ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3954.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(652.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-756 preview-line 756\" data_line_start=\"756\" data_line_end=\"756\" data_line=\"756,757\" count_line=\"1\">Using equation (ii) in (i), we get<\/div>\n<div class=\"preview-paragraph-758 preview-line 758\" data_line_start=\"758\" data_line_end=\"758\" data_line=\"758,759\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>⋅<\/mo>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>\u22c5<\/mo>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m*((nh)\/(2pi mr))^(2)=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">m \\cdot\\left(\\frac{n h}{2 \\pi m r}\\right)^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.942ex\" height=\"3.495ex\" role=\"img\" focusable=\"false\" 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <mo>⋅<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <mo>\u22c5<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m*n^(2)h^(2))\/(4pi^(2)m^(2)r^(2))=(1)\/(4piepsi_(0))(e^(2))\/(r)<\/asciimath><latex style=\"display: none\">\\frac{m \\cdot n^{2} h^{2}}{4 \\pi^{2} m^{2} r^{2}}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.272ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 7192.3 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(386.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 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<mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(n^(2)h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n^{2} h^{2} 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333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(409.2, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2217.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-762 preview-line 762\" data_line_start=\"762\" data_line_end=\"762\" data_line=\"762,763\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,2,3,dots<\/asciimath><latex style=\"display: none\">n=1,2,3, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.438ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 5939.6 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2878.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3378.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3822.9, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4322.9, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4767.6, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is principal quantum number. Equation (iii), gives the radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom. So the radii of the orbits increase proportionally with <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(2)<\/asciimath><latex style=\"display: none\">n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.27ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 1003.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mi>r<\/mi> \n <mo>\u221d<\/mo> \n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">[r propn^(2)]<\/asciimath><latex style=\"display: none\">\\left[r \\propto n^{2}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.195ex\" height=\"2.713ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -849.5 3622.1 1199\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M202 -349V850H394V810H242V-309H394V-349H202Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(417, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1145.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2201.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3205.1, 0)\"><path data-c=\"5D\" d=\"M22 810V850H214V-349H22V-309H174V810H22Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. Radius of first orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom is called Bohr radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)<\/asciimath><latex style=\"display: none\">a_{0}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.11ex\" height=\"1.372ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -441 932.6 606.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and is given by<\/div>\n<div class=\"preview-paragraph-764 preview-line 764\" data_line_start=\"764\" data_line_end=\"764\" data_line=\"764,765\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)=(h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">a_{0}=\\frac{h^{2} \\varepsilon_{0}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.83ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4344.9 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1210.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2266.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(385.6, 457.1) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(979.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1838.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> for <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>a<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">a_(0)=0.529″\u212b”<\/asciimath><latex style=\"display: none\">a_{0}=0.529 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.638ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 5144.1 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(529, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1210.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2266.1, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4544.1, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>0.529<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-766 preview-line 766\" data_line_start=\"766\" data_line_end=\"766\" data_line=\"766,767\" count_line=\"1\">So, radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom then becomes<\/div>\n<div class=\"preview-paragraph-768 preview-line 768\" data_line_start=\"768\" data_line_end=\"768\" data_line=\"768,769\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>0.529<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=n^(2)xx0.529″\u212b”<\/asciimath><latex style=\"display: none\">r=n^{2} \\times 0.529 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.585ex\" height=\"2.339ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 6888.6 1033.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3010.3, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4010.6, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6288.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>0.529<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"15\" class=\"preview-paragraph-770 preview-line 770 771\" data_line_start=\"770\" data_line_end=\"771\" data_line=\"770,772\" count_line=\"2\">\n<li>(i) Since, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>;<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>g<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>;<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>g<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r propn^(2);(r_(n))\/(r_(g))=(n^(2))\/(1^(2))<\/asciimath><latex style=\"display: none\">r \\propto n^{2} ; \\frac{r_{n}}{r_{g}}=\\frac{n^{2}}{1^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.252ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.408ex\" height=\"3.478ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6810.2 1537.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 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0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>;<\/mo><mfrac><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mi>g<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-772 preview-line 772\" data_line_start=\"772\" data_line_end=\"772\" data_line=\"772,773\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mn>21.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mn>21.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mn>1<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(21.2 xx10^(-11))\/(5.3 xx10^(-11))=(n^(2))\/(1)<\/asciimath><latex style=\"display: none\">\\frac{21.2 \\times 10^{-11}}{5.3 \\times 10^{-11}}=\\frac{n^{2}}{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.394ex\" height=\"3.329ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1004.9 6362 1471.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 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421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1278, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2056, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3638.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4156.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 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387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(398, -345) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><rect width=\"909.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mn>21.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mn>1<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-774 preview-line 774\" data_line_start=\"774\" data_line_end=\"774\" data_line=\"774,775\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>212<\/mn>\n <mn>53<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">⇒<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>212<\/mn>\n <mn>53<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(212)\/(53)=n^(2)=>n^(2)=4quad<\/asciimath><latex style=\"display: none\">\\frac{212}{53}=n^{2} \\Rightarrow n^{2}=4 \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.883ex\" height=\"2.773ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 9230.4 1225.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(396.8, -345) scale(0.707)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"1260.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1778.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2834.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4115.5, 0)\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5393.3, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(6674.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(7730.4, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(8230.4, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>212<\/mn><mn>53<\/mn><\/mfrac><mo>=<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">\u21d2<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mn>4<\/mn><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <msqrt>\n <mn>4<\/mn>\n <\/msqrt>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <msqrt>\n <mn>4<\/mn>\n <\/msqrt>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad n=sqrt4=2<\/asciimath><latex style=\"display: none\">\\quad n=\\sqrt{4}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.213ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.846ex\" height=\"2.398ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -966 6120.1 1060\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1000, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msqrt\" transform=\"translate(2933.6, 0)\"><g transform=\"translate(853, 0)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(0, 106)\"><path data-c=\"221A\" d=\"M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z\"><\/path><\/g><rect width=\"500\" height=\"60\" x=\"853\" y=\"846\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4564.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5620.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>n<\/mi><mo>=<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-776 preview-line 776\" data_line_start=\"776\" data_line_end=\"776\" data_line=\"776,777\" count_line=\"1\">(ii) We know that <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-13.6)\/(n^(2))=(-13.6)\/(4)=-3.4eV<\/asciimath><latex style=\"display: none\">E=\\frac{-13.6}{n^{2}}=\\frac{-13.6}{4}=-3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.302ex\" height=\"2.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 12509.4 1306.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" 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329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11315.4, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><mn>4<\/mn><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"16\" class=\"preview-paragraph-778 preview-line 778 779\" data_line_start=\"778\" data_line_end=\"779\" data_line=\"778,780\" count_line=\"2\">\n<li>(a) Radius of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)propn^(2)<\/asciimath><latex style=\"display: none\">r_{n} \\propto n^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.381ex\" height=\"2.244ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 3262.4 991.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 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429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>\u221d<\/mo><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-780 preview-line 780\" data_line_start=\"780\" data_line_end=\"780\" data_line=\"780,781\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>9<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>9<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>(r_(3))\/(r_(1))=(3^(2))\/(1^(2))=9<\/asciimath><latex style=\"display: none\">\\Rightarrow \\frac{r_{3}}{r_{1}}=\\frac{3^{2}}{1^{2}}=9<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.86ex\" height=\"3.246ex\" role=\"img\" focusable=\"false\" viewBox=\"0 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248Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><msub><mi>r<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mn>9<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-782 preview-line 782\" data_line_start=\"782\" data_line_end=\"782\" data_line=\"782,783\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <mo>×<\/mo>\n <mn>5.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>5.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(3)=9r_(1)=9xx5.3 xx10^(-11)<\/asciimath><latex style=\"display: none\">r_{3}=9 r_{1}=9 \\times 5.3 \\times 10^{-11}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.806ex\" height=\"2.329ex\" role=\"img\" 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0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>9<\/mn><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>9<\/mn><mo>\u00d7<\/mo><mn>5.3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-784 preview-line 784\" data_line_start=\"784\" data_line_end=\"784\" data_line=\"784,785\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>47.7<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4.77<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>47.7<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4.77<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=47.7 xx10^(-11)m=4.77 xx10^(-10)m<\/asciimath><latex style=\"display: none\">=47.7 \\times 10^{-11} \\mathrm{~m}=4.77 \\times 10^{-10} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.323ex\" height=\"2.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 15170.7 946\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" 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364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>47.7<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>4.77<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-786 preview-line 786\" data_line_start=\"786\" data_line_end=\"786\" data_line=\"786,787\" count_line=\"1\">(b) (i) Kinetic Energy,<\/div>\n<div class=\"preview-paragraph-788 preview-line 788\" data_line_start=\"788\" data_line_end=\"788\" data_line=\"788,789\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>×<\/mo>\n <mn>1<\/mn>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1<\/mn>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=-E=-(-3.4)xx1=3.4eV<\/asciimath><latex style=\"display: none\">E_{k}=-E=-(-3.4) \\times 1=3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.818ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14505.5 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 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count_line=\"1\">(ii) Potential Energy,<\/div>\n<div class=\"preview-paragraph-792 preview-line 792\" data_line_start=\"792\" data_line_end=\"792\" data_line=\"792,793\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>6.8<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>6.8<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=2E=-3.4 xx2=-6.8eV<\/asciimath><latex style=\"display: none\">E_{p}=2 E=-3.4 \\times 2=-6.8 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.4ex\" height=\"2.195ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 13436.8 970.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 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21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7353, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(8353.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9131, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 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417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(12242.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>6.8<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> 17. (i) According to Bohr’s postulates, in a hydrogen atom, as single electron revolves around a nucleus of charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>+<\/mo>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">+e<\/asciimath><latex style=\"display: none\">+e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.814ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1244 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>+<\/mo><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. For an electron moving with a uniform speed in a circular orbit of a given radius, the centripetal force is provided by coulomb force of attraction between the electron and the nucleus. The gravitational attraction may be neglected as the mass of electron and proton is very small.<\/div>\n<div class=\"preview-paragraph-794 preview-line 794\" data_line_start=\"794\" data_line_end=\"794\" data_line=\"794,795\" count_line=\"1\">So, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(ke^(2))\/(r^(2))quad(:}<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}} \\quad\\left(\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.201ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 5835 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(409.5, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mstyle\" transform=\"translate(4446, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(5446, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(389, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <mi>k<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"\" close=\")\" separators=\"|\">\n <mrow>\n <mi>k<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:k=(1)\/(4piepsi_(0)))<\/asciimath><latex style=\"display: none\">\\left.k=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.645ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 4263 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><\/g><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1854.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3666, 0)\"><path data-c=\"29\" d=\"M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><mi>k<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-796 preview-line 796\" data_line_start=\"796\" data_line_end=\"796\" data_line=\"796,797\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.234ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4523.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2044.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3100.1, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(521, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-798 preview-line 798\" data_line_start=\"798\" data_line_end=\"798\" data_line=\"798,799\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m=<\/asciimath><latex style=\"display: none\">m=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.375ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1933.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1155.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> mass of electron<\/div>\n<div class=\"preview-paragraph-800 preview-line 800\" data_line_start=\"800\" data_line_end=\"800\" data_line=\"800,801\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=<\/asciimath><latex style=\"display: none\">r=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.409ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1506.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> radius of electronic orbit<\/div>\n<div class=\"preview-paragraph-802 preview-line 802\" data_line_start=\"802\" data_line_end=\"802\" data_line=\"802,803\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=<\/asciimath><latex style=\"display: none\">v=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.486ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1540.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> velocity of electron<\/div>\n<div class=\"preview-paragraph-804 preview-line 804\" data_line_start=\"804\" data_line_end=\"804\" data_line=\"804,805\" count_line=\"1\">Again, by Bohr’s second postulates<\/div>\n<div class=\"preview-paragraph-806 preview-line 806\" data_line_start=\"806\" data_line_end=\"806\" data_line=\"806,807\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-808 preview-line 808\" data_line_start=\"808\" data_line_end=\"808\" data_line=\"808,809\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,2,3dots dots<\/asciimath><latex style=\"display: none\">n=1,2,3 \\ldots \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.838ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 7000.2 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2878.2, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3378.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3822.9, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4489.6, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5828.2, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-810 preview-line 810\" data_line_start=\"810\" data_line_end=\"810\" data_line=\"810,811\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.948ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3954.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(652.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-812 preview-line 812\" data_line_start=\"812\" data_line_end=\"812\" data_line=\"812,813\" count_line=\"1\">Putting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in eq. (i)<\/div>\n<div class=\"preview-paragraph-814 preview-line 814\" data_line_start=\"814\" data_line_end=\"814\" data_line=\"814,815\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m((nh)\/(2pi mr))^(2)=(ke^(2))\/(r)=>r=(n^(2)h^(2))\/(4pi^(2)kme^(2))<\/asciimath><latex style=\"display: none\">m\\left(\\frac{n h}{2 \\pi m r}\\right)^{2}=\\frac{k e^{2}}{r} \\Rightarrow r=\\frac{n^{2} h^{2}}{4 \\pi^{2} k m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.581ex\" height=\"3.439ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1082.7 13516.9 1520.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>k<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-816 preview-line 816\" data_line_start=\"816\" data_line_end=\"816\" data_line=\"816,817\" count_line=\"1\">Kinetic energy of electron,<\/div>\n<div class=\"preview-paragraph-818 preview-line 818\" data_line_start=\"818\" data_line_end=\"818\" data_line=\"818,819\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>∵<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2235<\/mo> \n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac> \n <mo>=<\/mo> \n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=(1)\/(2)mv^(2)=(ke^(2))\/(2r)quad(:'(mv^(2))\/(r)=(ke^(2))\/(r^(2)))<\/asciimath><latex style=\"display: none\">E_{k}=\\frac{1}{2} m v^{2}=\\frac{k e^{2}}{2 r} \\quad\\left(\\because \\frac{m v^{2}}{r}=\\frac{k e^{2}}{r^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.823ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" 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1138Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo>\u2235<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-820 preview-line 820\" data_line_start=\"820\" data_line_end=\"820\" data_line=\"820,821\" count_line=\"1\">Using eq. (ii) we get<\/div>\n<div class=\"preview-paragraph-822 preview-line 822\" data_line_start=\"822\" data_line_end=\"822\" data_line=\"822,823\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>2<\/mn>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=(ke^(2))\/(2)(4pi^(2)kme^(2))\/(n^(2)h^(2))=(2pi^(2)k^(2)me^(4))\/(n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{k}=\\frac{k e^{2}}{2} \\frac{4 \\pi^{2} k m e^{2}}{n^{2} h^{2}}=\\frac{2 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.48ex\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mn>2<\/mn><\/mfrac><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>k<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-824 preview-line 824\" data_line_start=\"824\" data_line_end=\"824\" data_line=\"824,825\" count_line=\"1\">Potential energy of electron,<\/div>\n<div class=\"preview-paragraph-826 preview-line 826\" data_line_start=\"826\" data_line_end=\"826\" data_line=\"826,827\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>×<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo>\u00d7<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=-(k(e)xx(e))\/(r)=-(ke^(2))\/(r)<\/asciimath><latex style=\"display: none\">E_{p}=-\\frac{k(e) \\times(e)}{r}=-\\frac{k e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.416ex\" height=\"3.167ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1047.1 9907.9 1399.9\" aria-hidden=\"true\"><g 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409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(552.2, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1183.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>k<\/mi><mo stretchy=\"false\">(<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-828 preview-line 828\" data_line_start=\"828\" data_line_end=\"828\" data_line=\"828,829\" count_line=\"1\">Using eq. (ii), we get<\/div>\n<div class=\"preview-paragraph-830 preview-line 830\" data_line_start=\"830\" data_line_end=\"830\" data_line=\"830,831\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>k<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>k<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=-ke^(2)xx(4pi^(2)kme^(2))\/(n^(2)h^(2))=-(4pik^(2)me^(4))\/(n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{p}=-k e^{2} \\times \\frac{4 \\pi^{2} k m e^{2}}{n^{2} h^{2}}=-\\frac{4 \\pi k^{2} m e^{4}}{n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.018ex\" height=\"3.228ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 14151.9 1426.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mi>k<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>k<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-832 preview-line 832\" data_line_start=\"832\" data_line_end=\"832\" data_line=\"832,833\" count_line=\"1\">Hence, total energy of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(p)+E_(k)<\/asciimath><latex style=\"display: none\">E=E_{p}+E_{k}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg 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26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>+<\/mo><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-834 preview-line 834\" data_line_start=\"834\" data_line_end=\"834\" data_line=\"834,835\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-836 preview-line 836\" data_line_start=\"836\" data_line_end=\"836\" data_line=\"836,837\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>k<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-(2pi^(2)k^(2)me^(4))\/(n^(2)h^(2))=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">=-\\frac{2 \\pi^{2} k^{2} m e^{4}}{n^{2} h^{2}}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.095ex\" 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transform=\"translate(3276.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(984.6, -429.7) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1003.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 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250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(7316.8, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(493.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1457.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(9014, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mn>2<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>k<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> When the electron in a hydrogen atom jumps from higher energy level to the lower energy level, the difference of energies of the two energy levels is emitted as a radiation of particular wavelength. It is called a spectral line.<\/div>\n<div class=\"preview-paragraph-838 preview-line 838\" data_line_start=\"838\" data_line_end=\"838\" data_line=\"838,839\" count_line=\"1\">(ii) In <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom, when an electron jumps form the orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, the wavelength of the emitted radiation is given by<\/div>\n<div class=\"preview-paragraph-840 preview-line 840 841 842\" data_line_start=\"840\" data_line_end=\"842\" data_line=\"840,843\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>;<\/mo>\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>;<\/mo>\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))];R=1.09 xx10^(7)m^(-1)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right] ; R=1.09 \\times 10^{7} \\mathrm{~m}^{-1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"39.376ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 17404.4 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1083, 413) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>;<\/mo><mi>R<\/mi><mo>=<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-844 preview-line 844\" data_line_start=\"844\" data_line_end=\"844\" data_line=\"844,845\" count_line=\"1\">For Balmar series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=2<\/asciimath><latex style=\"display: none\">n_{f}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.499ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2872.5 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3,4,5,dots dots<\/asciimath><latex style=\"display: none\">n_{i}=3,4,5, \\ldots \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.132ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 7572.2 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2727.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3172.2, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3672.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4116.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4616.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5061.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6400.2, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-846 preview-line 846 847 848\" data_line_start=\"846\" data_line_end=\"848\" data_line=\"846,849\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R((1)\/(2^(2))-(1)\/(n_(i)^(2)))<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left(\\frac{1}{2^{2}}-\\frac{1}{n_{i}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.827ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.704ex\" height=\"6.785ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 8709.1 2999\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(261.5, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -686)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"783\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1300.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2356.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3115.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(792, 0)\"><g data-mml-node=\"mn\" transform=\"translate(421.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1103.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2357.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3358, 0)\"><g data-mml-node=\"mn\" transform=\"translate(471.8, 676)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4801.6, 0)\"><path data-c=\"29\" d=\"M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mn>1<\/mn><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-850 preview-line 850\" data_line_start=\"850\" data_line_end=\"850\" data_line=\"850,851\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>4<\/mn>\n <mo>,<\/mo>\n <mn>5<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3,4,5,dots<\/asciimath><latex style=\"display: none\">n_{i}=3,4,5, \\ldots<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.103ex\" height=\"1.971ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 6233.5 871\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2727.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3172.2, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3672.2, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4116.8, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4616.8, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5061.5, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>4<\/mn><mo>,<\/mo><mn>5<\/mn><mo>,<\/mo><mo>\u2026<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-852 preview-line 852\" data_line_start=\"852\" data_line_end=\"852\" data_line=\"852,853\" count_line=\"1\">These spectral lines lie on the visible region.<\/div>\n<div class=\"preview-paragraph-854 preview-line 854\" data_line_start=\"854\" data_line_end=\"854\" data_line=\"854,855\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-12.jpg?height=498&width=611&top_left_y=1213&top_left_x=1131\" alt=\"\"><\/div>\n<ol start=\"18\" class=\"preview-paragraph-856 preview-line 856 857\" data_line_start=\"856\" data_line_end=\"857\" data_line=\"856,858\" count_line=\"2\">\n<li>According to Bohr’s postulates for hydrogen atom, electron revolves in a circular orbit around the heavy positively charged nucleus. These are the stationary (orbits) states of the atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-858 preview-line 858\" data_line_start=\"858\" data_line_end=\"858\" data_line=\"858,859\" count_line=\"1\">For a particular orbit, electron moves there, so it has kinetic energy.<\/div>\n<div class=\"preview-paragraph-860 preview-line 860\" data_line_start=\"860\" data_line_end=\"860\" data_line=\"860,861\" count_line=\"1\">Also, there is potential energy due to charge on electron and heavy positively charged nucleus.<\/div>\n<div class=\"preview-paragraph-862 preview-line 862\" data_line_start=\"862\" data_line_end=\"862\" data_line=\"862,863\" count_line=\"1\">Hence, total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of atom is sum of kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>K<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(K)<\/asciimath><latex style=\"display: none\">(K)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.771ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1667 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1278, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>K<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>U<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(U)<\/asciimath><latex style=\"display: none\">(U)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.495ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1545 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1156, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>U<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-864 preview-line 864\" data_line_start=\"864\" data_line_end=\"864\" data_line=\"864,865\" count_line=\"1\">i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mo>+<\/mo>\n <mi>U<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mo>+<\/mo>\n <mi>U<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=K+U<\/asciimath><latex style=\"display: none\">E=K+U<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.258ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4976 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3208.8, 0)\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4209, 0)\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 680Q696 680 723 681T752 682Q767 682 767 672Q767 650 759 642Q756 637 737 637Q666 633 648 597Q646 592 598 404Q557 235 548 205Q515 105 433 42T263 -22Q171 -22 116 34T60 167V183Q60 201 115 421Q164 622 164 628Q164 635 107 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mo>+<\/mo><mi>U<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-866 preview-line 866\" data_line_start=\"866\" data_line_end=\"866\" data_line=\"866,867\" count_line=\"1\">Let us assume that the nucleus has positive charge <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mi>e<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Ze<\/asciimath><latex style=\"display: none\">Z e<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.69ex\" height=\"1.57ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1189 694\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(723, 0)\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mi>e<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. An electron moving with a constant speed <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> along a circle of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> with centre at the nucleus.<\/div>\n<div class=\"preview-paragraph-868 preview-line 868 869 870\" data_line_start=\"868\" data_line_end=\"870\" data_line=\"868,871\" count_line=\"3\">Force acting on electron due to nucleus is given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">F=(Ze^(2))\/(4piepsi_(0)r^(2))<\/asciimath><latex style=\"display: none\">F=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.237ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.177ex\" height=\"3.463ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4498.3 1530.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"46\" d=\"M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1026.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2082.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(644.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1939.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2175.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>F<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><br>\nThe acceleration of electron <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(v^(2))\/(r)<\/asciimath><latex style=\"display: none\">=\\frac{v^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.806ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 2124.1 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1055.8, 0)\"><g data-mml-node=\"msup\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(374.7, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"828.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (towards the<br>\ncentre).<\/div>\n<div class=\"preview-paragraph-872 preview-line 872\" data_line_start=\"872\" data_line_end=\"872\" data_line=\"872,873\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m=<\/asciimath><latex style=\"display: none\">m=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.375ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 1933.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1155.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> mass of an electron, then from Newton’s second law<\/div>\n<div class=\"preview-paragraph-874 preview-line 874 875 876 877 878 879\" data_line_start=\"874\" data_line_end=\"879\" data_line=\"874,880\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>F<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[F=m((v^(2))\/(r))],[=>(Ze^(2))\/(4piepsi_(0)r^(2))=m((v^(2))\/(r))=>r=(Ze^(2))\/(4piepsi_(0)mv^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&F=m\\left(\\frac{v^{2}}{r}\\right) \\\\\n&\\Rightarrow \\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r^{2}}=m\\left(\\frac{v^{2}}{r}\\right) \\Rightarrow r=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} m v^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.349ex\" 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315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3906.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>F<\/mi><mo>=<\/mo><mi>m<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mi>m<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>r<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-881 preview-line 881\" data_line_start=\"881\" data_line_end=\"881\" data_line=\"881,882\" count_line=\"1\">From Bohr’s quantisation rules,<\/div>\n<div class=\"preview-paragraph-883 preview-line 883 884 885\" data_line_start=\"883\" data_line_end=\"885\" data_line=\"883,886\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.895ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 5257.6 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3147.6, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3747.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(467, 676)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-887 preview-line 887\" data_line_start=\"887\" data_line_end=\"887\" data_line=\"887,888\" count_line=\"1\">Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is a positive integer<\/div>\n<div class=\"preview-paragraph-889 preview-line 889\" data_line_start=\"889\" data_line_end=\"889\" data_line=\"889,890\" count_line=\"1\">Substituting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from eq. (i), we get<\/div>\n<div class=\"preview-paragraph-891 preview-line 891 892 893\" data_line_start=\"891\" data_line_end=\"893\" data_line=\"891,894\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mo>⋅<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mo>\u22c5<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>m<\/mi> \n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv*(Ze^(2))\/(4piepsi_(0)(mv^(2)))=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v \\cdot \\frac{Z e^{2}}{4 \\pi \\varepsilon_{0}\\left(m v^{2}\\right)}=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.622ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"23.962ex\" height=\"6.038ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 10591.1 2668.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1585.2, 0)\"><path data-c=\"22C5\" d=\"M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2085.4, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(1734.8, 676)\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -809.5)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 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d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mo>\u22c5<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-895 preview-line 895 896 897 898 899\" data_line_start=\"895\" data_line_end=\"899\" data_line=\"895,900\" count_line=\"5\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:v=(Ze^(2))\/(2epsi_(0)hn):}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n& v=\\frac{Z e^{2}}{2 \\varepsilon_{0} h n}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.106ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.869ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1430.7 4804.1 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, -79.2)\"><g data-mml-node=\"mtd\"><\/g><g data-mml-node=\"mtd\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 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130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"2745.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>h<\/mi><mi>n<\/mi><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-901 preview-line 901\" data_line_start=\"901\" data_line_end=\"901\" data_line=\"901,902\" count_line=\"1\">So, kinetic energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(2)mv^(2)=(Z^(2)e^(4))\/(8epsi_(0)^(2)h^(2)n^(2))<\/asciimath><latex style=\"display: none\">K=\\frac{1}{2} m v^{2}=\\frac{Z^{2} e^{4}}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.197ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 8926.9 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 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345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2570.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-903 preview-line 903\" data_line_start=\"903\" data_line_end=\"903\" data_line=\"903,904\" count_line=\"1\">Potential energy of the atom,<\/div>\n<div class=\"preview-paragraph-905 preview-line 905 906 907\" data_line_start=\"905\" data_line_end=\"907\" data_line=\"905,908\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">U=-(Ze^(2))\/(4piepsi_(0)r)<\/asciimath><latex style=\"display: none\">U=-\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.917ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 5709.1 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"55\" d=\"M107 637Q73 637 71 641Q70 643 70 649Q70 673 81 682Q83 683 98 683Q139 681 234 681Q268 681 297 681T342 682T362 682Q378 682 378 672Q378 670 376 658Q371 641 366 638H364Q362 638 359 638T352 638T343 637T334 637Q295 636 284 634T266 623Q265 621 238 518T184 302T154 169Q152 155 152 140Q152 86 183 55T269 24Q336 24 403 69T501 205L552 406Q599 598 599 606Q599 633 535 637Q511 637 511 648Q511 650 513 660Q517 676 519 679T529 683Q532 683 561 682T645 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448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(723, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 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318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1939.6, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"2590.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>U<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-909 preview-line 909\" data_line_start=\"909\" data_line_end=\"909\" data_line=\"909,910\" count_line=\"1\">Using eq. (iii) in eq. (i), we get<\/div>\n<div class=\"preview-paragraph-911 preview-line 911 912 913 914 915 916\" data_line_start=\"911\" data_line_end=\"916\" data_line=\"911,917\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <mfrac>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>2<\/mn>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>h<\/mi>\n <mi>n<\/mi>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mi>m<\/mi>\n <mfrac>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>Z<\/mi> \n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>2<\/mn> \n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub> \n <mi>h<\/mi> \n <mi>n<\/mi> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>4<\/mn> \n <mi>\u03c0<\/mi> \n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[r=(Ze^(2))\/(4piepsi_(0)m((Ze^(2))^(2))\/((2epsi_(0)hn)^(2)))=(4epsi_(0)^(2)h^(2)n^(2))\/((4piepsi_(0))mZe^(2))],[r=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&r=\\frac{Z e^{2}}{4 \\pi \\varepsilon_{0} m \\frac{\\left(Z e^{2}\\right)^{2}}{\\left(2 \\varepsilon_{0} h n\\right)^{2}}}=\\frac{4 \\varepsilon_{0}^{2} h^{2} n^{2}}{\\left(4 \\pi \\varepsilon_{0}\\right) m Z e^{2}} \\\\\n&r=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -6.434ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.116ex\" height=\"13.998ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -3343.6 15079.2 6187.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(313.9, 676)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(869.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1849.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1448, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2171, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3240.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>m<\/mi><mfrac><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>2<\/mn><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mi>h<\/mi><mi>n<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-918 preview-line 918\" data_line_start=\"918\" data_line_end=\"918\" data_line=\"918,919\" count_line=\"1\">Using value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in eq. ( <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">v<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">v<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v)<\/asciimath><latex style=\"display: none\">\\mathrm{v})<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.075ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 917 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M338 431Q344 429 422 429Q479 429 503 431H508V385H497Q439 381 423 345Q421 341 356 172T288 -2Q283 -11 263 -11Q244 -11 239 -2Q99 359 98 364Q93 378 82 381T43 385H19V431H25L33 430Q41 430 53 430T79 430T104 429T122 428Q217 428 232 431H240V385H226Q187 384 184 370Q184 366 235 234L286 102L377 341V349Q377 363 367 372T349 383T335 385H331V431H338Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(528, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">v<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, we get<\/div>\n<div class=\"preview-paragraph-920 preview-line 920 921 922\" data_line_start=\"920\" data_line_end=\"922\" data_line=\"920,923\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>U<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">U=(-Ze^(2))\/(4piepsi_(0)((epsi_(0)h^(2)n^(2))\/(pi mZe^(2))))=(-Z^(2)e^(4)m)\/(4epsi_(0)^(2)h^(2)n^(2))<\/asciimath><latex style=\"display: none\">U=\\frac{-Z e^{2}}{4 \\pi \\varepsilon_{0}\\left(\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\\right)}=\\frac{-Z^{2} e^{4} m}{4 \\varepsilon_{0}^{2} h^{2} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.98ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"31.104ex\" height=\"7.413ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1517.7 13747.8 3276.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path 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transform=\"translate(2100.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(1896.5, 676)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1501, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-924 preview-line 924\" data_line_start=\"924\" data_line_end=\"924\" data_line=\"924,925\" count_line=\"1\">So, the total energy,<\/div>\n<div class=\"preview-paragraph-926 preview-line 926 927 928 929 930 931\" data_line_start=\"926\" data_line_end=\"931\" data_line=\"926,932\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" 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<\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>K<\/mi>\n <mo>+<\/mo>\n <mi>U<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E=K+U],[=+(mZ^(2)e^(4))\/(8epsi_(0)^(2)h^(2)n^(2))-(mZ^(2)e^(4))\/(4epsi_(0)^(2)h^(2)n^(2))=-(Z^(2)e^(4)m)\/(8epsi_(0)^(2)h^(2)n^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&E=K+U \\\\\n&=+\\frac{m Z^{2} e^{4}}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}-\\frac{m Z^{2} e^{4}}{4 \\varepsilon_{0}^{2} h^{2} n^{2}}=-\\frac{Z^{2} e^{4} m}{8 \\varepsilon_{0}^{2} h^{2} n^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.863ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.062ex\" height=\"8.858ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -2207.6 16823.5 3915.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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-10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(2349.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3552.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>E<\/mi><mo>=<\/mo><mi>K<\/mi><mo>+<\/mo><mi>U<\/mi><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mo>+<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>\u2212<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mi>m<\/mi><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-933 preview-line 933\" data_line_start=\"933\" data_line_end=\"933\" data_line=\"933,934\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so the total energy of the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> energy level of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom.<\/div>\n<div class=\"preview-paragraph-935 preview-line 935 936 937\" data_line_start=\"935\" data_line_end=\"937\" data_line=\"935,938\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(me^(4))\/(8n^(2)epsi_(0)^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{m e^{4}}{8 n^{2} \\varepsilon_{0}^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.483ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.101ex\" height=\"5.917ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1517.7 7116.5 2615.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 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429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3552.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-939 preview-line 939\" data_line_start=\"939\" data_line_end=\"939\" data_line=\"939,940\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-13.jpg?height=240&width=583&top_left_y=451&top_left_x=1042\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-941 preview-line 941\" data_line_start=\"941\" data_line_end=\"941\" data_line=\"941,942\" count_line=\"1\">The wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=4)<\/asciimath><latex style=\"display: none\">(n=4)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2822.6, 0)\"><path data-c=\"29\" d=\"M60 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stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=2)<\/asciimath><latex style=\"display: none\">(n=2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 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is<\/div>\n<div class=\"preview-paragraph-943 preview-line 943 944 945 946 947 948\" data_line_start=\"943\" data_line_end=\"948\" data_line=\"943,949\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>4.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>2.75<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>4.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>2.75<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda=(hc)\/((E_(4)-E_(2)))=(6.6 xx10^(-34)xx3xx10^(8))\/([0-(-4.5)]xx1.6 xx10^(-19))],[=2.75 xx10^(-7)m=275 xx10^(-9)m=275nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\lambda=\\frac{h c}{\\left(E_{4}-E_{2}\\right)}=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{[0-(-4.5)] \\times 1.6 \\times 10^{-19}} \\\\\n&=2.75 \\times 10^{-7} \\mathrm{~m}=275 \\times 10^{-9} \\mathrm{~m}=275 \\mathrm{~nm}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" 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transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>4<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4.5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>2.75<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>275<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-950 preview-line 950\" data_line_start=\"950\" data_line_end=\"950\" data_line=\"950,951\" count_line=\"1\">…(ii) Hence, transition shown by arrow <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">B<\/asciimath><latex style=\"display: none\">B<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>B<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to emission of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>275<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=275nm<\/asciimath><latex style=\"display: none\">=275 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.49ex\" height=\"1.715ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 4194.8 758\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2555.8, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>275<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-952 preview-line 952\" data_line_start=\"952\" data_line_end=\"952\" data_line=\"952,953\" count_line=\"1\">(i) The maximum wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4<\/asciimath><latex style=\"display: none\">n=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.717ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2433.6 759\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-954 preview-line 954 955 956 957 958 959\" data_line_start=\"954\" data_line_end=\"959\" data_line=\"954,960\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mn>0<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.18<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mo>×<\/mo>\n 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<mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>618<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda=(hc)\/([0-(-2)]eV)=>lambda=(6.6 xx10^(-34)xx3xx10^(8))\/(2xx1.6 xx10^(-19))],[=6.18 xx10^(-7)m=618 xx10^(-9)m=618nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\lambda=\\frac{h c}{[0-(-2)] \\mathrm{eV}} \\Rightarrow \\lambda=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{2 \\times 1.6 \\times 10^{-19}} \\\\\n&=6.18 \\times 10^{-7} \\mathrm{~m}=618 \\times 10^{-9} \\mathrm{~m}=618 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494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17296.9, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 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335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mrow><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6.18<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>618<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>618<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-961 preview-line 961\" data_line_start=\"961\" data_line_end=\"961\" data_line=\"961,962\" count_line=\"1\">Hence transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to maximum wavelength.<\/div>\n<div class=\"preview-paragraph-963 preview-line 963\" data_line_start=\"963\" data_line_end=\"963\" data_line=\"963,964\" count_line=\"1\">(ii) The minimum wavelength of emitted radiation from state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is<\/div>\n<div class=\"preview-paragraph-965 preview-line 965\" data_line_start=\"965\" data_line_end=\"965\" data_line=\"965,966\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>−<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>10<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2212<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>10<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(6.6 xx10^(-34)xx3xx10^(8))\/([-2eV-(-10eV)])=(6.6 xx10^(-34)xx3xx10^(8))\/(8xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{[-2 \\mathrm{eV}-(-10 \\mathrm{eV})]}=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{8 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"34.374ex\" height=\"3.524ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 15193.2 1557.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2556, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3334, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 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666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"5731.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mo stretchy=\"false\">[<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>10<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-967 preview-line 967\" data_line_start=\"967\" data_line_end=\"967\" data_line=\"967,968\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.55<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>155<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.55<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>155<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1.55 xx10^(-7)m=155nm<\/asciimath><latex style=\"display: none\">\\lambda=1.55 \\times 10^{-7} \\mathrm{~m}=155 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.114ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 12426.2 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3916.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(4917, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6870.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8231.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9287.2, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(10787.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1.55<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>155<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-969 preview-line 969\" data_line_start=\"969\" data_line_end=\"969\" data_line=\"969,970\" count_line=\"1\">Hence transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to minimum wavelength.<\/div>\n<ol start=\"20\" class=\"preview-paragraph-971 preview-line 971 972\" data_line_start=\"971\" data_line_end=\"972\" data_line=\"971,973\" count_line=\"2\">\n<li>Suppose <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be the mass of an electron and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> be its speed in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. The centripetal force for revolution is produced by electrostatic attraction between electron and nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-973 preview-line 973 974 975\" data_line_start=\"973\" data_line_end=\"975\" data_line=\"973,976\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(1)\/(4piepsi_(0))((Ze)(e))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{(Z e)(e)}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.653ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 9570.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 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stretchy=\"false\">)<\/mo><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-977 preview-line 977\" data_line_start=\"977\" data_line_end=\"977\" data_line=\"977,978\" count_line=\"1\">or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv^(2)=(1)\/(4piepsi_(0))(Ze^(2))\/(r)<\/asciimath><latex style=\"display: none\">m v^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.655ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6477.7 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" 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280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(623.6, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-979 preview-line 979\" data_line_start=\"979\" data_line_end=\"979\" data_line=\"979,980\" count_line=\"1\">So, kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(2)mv^(2)<\/asciimath><latex style=\"display: none\">K=\\frac{1}{2} m v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.781ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.821ex\" height=\"2.737ex\" role=\"img\" focusable=\"false\" viewBox=\"0 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301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1166.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2222.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path 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40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-981 preview-line 981 982 983\" data_line_start=\"981\" data_line_end=\"983\" data_line=\"981,984\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K=(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">K=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.927ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.011ex\" height=\"5.343ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 6634.7 2361.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g 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display=\"block\"><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-985 preview-line 985\" data_line_start=\"985\" data_line_end=\"985\" data_line=\"985,986\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-13.jpg?height=274&width=259&top_left_y=2025&top_left_x=1521\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-987 preview-line 987\" data_line_start=\"987\" data_line_end=\"987\" data_line=\"987,988\" count_line=\"1\">Potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mi>Z<\/mi>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mi>e<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(1)\/(4piepsi_(0))((Ze)(-e))\/(r)=-(1)\/(4piepsi_(0))(Ze^(2))\/(r)<\/asciimath><latex style=\"display: none\">=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{(Z e)(-e)}{r}=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" 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239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>Z<\/mi><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Total energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=<\/asciimath><latex style=\"display: none\">E=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.117ex\" height=\"1.724ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1819.8 762\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> K.E. + P.E.<\/div>\n<div class=\"preview-paragraph-989 preview-line 989\" data_line_start=\"989\" data_line_end=\"989\" data_line=\"989,990\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>+<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(1)\/(4piepsi_(0))(Ze^(2))\/(2r)+(-(1)\/(4piepsi_(0))(Ze^(2))\/(r))<\/asciimath><latex style=\"display: none\">=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}+\\left(-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.899ex\" 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data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=-(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.147ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6253.1 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 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285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-991 preview-line 991\" data_line_start=\"991\" data_line_end=\"991\" data_line=\"991,992\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E<\/asciimath><latex style=\"display: none\">E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.729ex\" height=\"1.538ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 764 680\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> can be written as<\/div>\n<div class=\"preview-paragraph-993 preview-line 993\" data_line_start=\"993\" data_line_end=\"993\" data_line=\"993,994\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(1)\/(4piepsi_(0))(Ze^(2))\/(2r)<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{2 r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.162ex\" height=\"3.271ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6701.4 1445.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2545.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3323.8, 0)\"><g data-mml-node=\"mn\" transform=\"translate(729, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1571.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5135.3, 0)\"><g data-mml-node=\"mrow\" 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280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(446.8, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1326.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-995 preview-line 995\" data_line_start=\"995\" data_line_end=\"995\" data_line=\"995,996\" count_line=\"1\">Again from Bohr’s postulate for quantization of angular momentum.<\/div>\n<div class=\"preview-paragraph-997 preview-line 997\" data_line_start=\"997\" data_line_end=\"997\" data_line=\"997,998\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3147.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-999 preview-line 999\" data_line_start=\"999\" data_line_end=\"999\" data_line=\"999,1000\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(nh)\/(2pi mr)<\/asciimath><latex style=\"display: none\">v=\\frac{n h}{2 \\pi m r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.948ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3954.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(652.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><rect width=\"1896.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1001 preview-line 1001\" data_line_start=\"1001\" data_line_end=\"1001\" data_line=\"1001,1002\" count_line=\"1\">Substituting this value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (i), we get<\/div>\n<div class=\"preview-paragraph-1003 preview-line 1003\" data_line_start=\"1003\" data_line_end=\"1003\" data_line=\"1003,1004\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <msup>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <msup>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m)\/(r)[(nh)\/(2pi mr)]^(2)=(1)\/(4piepsi_(0))(Ze^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m}{r}\\left[\\frac{n h}{2 \\pi m r}\\right]^{2}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.692ex\" height=\"3.495ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1082.7 9145.9 1544.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(371, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"820.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"msup\" transform=\"translate(1060.8, 0)\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M202 -349V850H394V810H242V-309H394V-349H202Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(417, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(652.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 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138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 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<mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.897ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4374.6 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 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675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2171, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2350\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(epsi_(0)h^(2)n^(2))\/(pi mZe^(2))<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.97ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4848.8 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1203, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2258.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(286.4, 457.1) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(869.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1849.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1448, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(2171, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2350\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1007 preview-line 1007\" data_line_start=\"1007\" data_line_end=\"1007\" data_line=\"1007,1008\" count_line=\"1\">Substituting value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)<\/asciimath><latex style=\"display: none\">r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.093ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 925.3 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> in equation (ii), we get<\/div>\n<div class=\"preview-paragraph-1009 preview-line 1009\" data_line_start=\"1009\" data_line_end=\"1009\" data_line=\"1009,1010\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(1)\/(2xx4piepsi_(0))(Ze^(2))\/(((epsi_(0)h^(2)n^(2))\/(pi mZe^(2))))=(mZ^(2)e^(4)xx ch)\/(8epsi_(0)^(2)ch^(3)n^(2))<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{1}{2 \\times 4 \\pi \\varepsilon_{0}} \\frac{Z e^{2}}{\\left(\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m Z e^{2}}\\right)}=\\frac{m Z^{2} e^{4} \\times c h}{8 \\varepsilon_{0}^{2} c h^{3} n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.476ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"33.003ex\" height=\"5.714ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 14587.4 2525.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 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y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><mrow><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mi>c<\/mi><mi>h<\/mi><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1011 preview-line 1011\" data_line_start=\"1011\" data_line_end=\"1011\" data_line=\"1011,1012\" count_line=\"1\">or, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>,<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>Z<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>,<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(Z^(2)Rhc)\/(n^(2)),quad<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{Z^{2} R h c}{n^{2}}, \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: 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38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1943.6, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2519.6, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(909.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2287.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(5851.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(6296.3, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><msup><mi>Z<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>,<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mi>c<\/mi>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=(me^(4))\/(8epsi_(0)^(2)ch^(3))<\/asciimath><latex style=\"display: none\">R=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} c h^{3}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.181ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4499.8 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2092.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(585.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1369.6, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1802.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2167.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mi>c<\/mi><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1013 preview-line 1013\" data_line_start=\"1013\" data_line_end=\"1013\" data_line=\"1013,1014\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R<\/asciimath><latex style=\"display: none\">R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.048ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 704\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called Rydberg constant. For hydrogen atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1015 preview-line 1015\" data_line_start=\"1015\" data_line_end=\"1015\" data_line=\"1015,1016\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=(-Rch)\/(n^(2))<\/asciimath><latex style=\"display: none\">E_{n}=\\frac{-R c h}{n^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.828ex\" height=\"3ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4786.1 1326.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2545.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(765.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1017 preview-line 1017\" data_line_start=\"1017\" data_line_end=\"1017\" data_line=\"1017,1018\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the quantum numbers of initial and final states and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are energies of electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n <mi mathvariant=\"normal\">H<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">\\mathrm{H}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 750 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H302Q262 636 251 634T233 622L232 500V378H517V622Q510 629 506 631T490 634T447 637H414V683H425Q446 680 569 680Q704 680 713 683H724V637H691Q651 636 640 634T622 622V61Q628 51 639 49T691 46H724V0H713Q692 3 569 3Q434 3 425 0H414V46H447Q489 47 498 49T517 61V332H232V197L233 61Q239 51 250 49T302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mi mathvariant=\"normal\">H<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom in initial and final state, we have<\/div>\n<div class=\"preview-paragraph-1019 preview-line 1019\" data_line_start=\"1019\" data_line_end=\"1019\" data_line=\"1019,1020\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)=(-Rch)\/(n_(i)^(2))<\/asciimath><latex style=\"display: none\">E_{i}=\\frac{-R c h}{n_{i}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.44ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.42ex\" height=\"3.45ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4605.8 1525\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1309.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2365.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(765.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -284.4) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)=(-Rch)\/(n_(f)^(2))<\/asciimath><latex style=\"display: none\">E_{f}=\\frac{-R c h}{n_{f}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.709ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.748ex\" height=\"3.719ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -888.7 4750.8 1644\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1454.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2510.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(752.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -315.5) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><rect width=\"2000.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>c<\/mi><mi>h<\/mi><\/mrow><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1021 preview-line 1021\" data_line_start=\"1021\" data_line_end=\"1021\" data_line=\"1021,1022\" count_line=\"1\">If <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the frequency of emitted radiation.<\/div>\n<div class=\"preview-paragraph-1023 preview-line 1023 1024\" data_line_start=\"1023\" data_line_end=\"1024\" data_line=\"1023,1025\" count_line=\"2\">we get <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mi>h<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(E_(i)-E_(f))\/(h)<\/asciimath><latex style=\"display: none\">v=\\frac{E_{i}-E_{f}}{h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.888ex\" height=\"3.127ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1029.4 4370.6 1382.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 548.6) scale(0.707)\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1032, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1810, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1072.4, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"2312\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/mrow><mi>h<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><br>\nfrom eq. (i)<\/div>\n<div class=\"preview-paragraph-1026 preview-line 1026\" data_line_start=\"1026\" data_line_end=\"1026\" data_line=\"1026,1027\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>h<\/mi>\n <\/mfrac>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>h<\/mi>\n <\/mfrac>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>+<\/mo> \n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=(1)\/(h)((-Rch)\/(n_(i)^(2))+(Rch)\/(n_(f)^(2)))<\/asciimath><latex style=\"display: none\">v=\\frac{1}{h}\\left(\\frac{-R c h}{n_{i}^{2}}+\\frac{R c h}{n_{f}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.02ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 9290.8 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1818.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(246.9, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><rect width=\"607.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mrow\" transform=\"translate(2665.8, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(736, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1970, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(765.3, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mi>R<\/mi><mi>c<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"21\" class=\"preview-paragraph-1030 preview-line 1030 1031\" data_line_start=\"1030\" data_line_end=\"1031\" data_line=\"1030,1032\" count_line=\"2\">\n<li>(a) Speed of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 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694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit : The centripetal force required for revolution is provided by the electrostatic force of attraction between the electron and the nucleus.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1032 preview-line 1032 1033 1034 1035 1036 1037\" data_line_start=\"1032\" data_line_end=\"1037\" data_line=\"1032,1038\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>∴<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mtext> where, <\/mtext>\n <mi>K<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>\u2234<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mtext>\u00a0where,\u00a0<\/mtext> \n <mi>K<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[:.(mv^(2))\/(r)=(KZe^(2))\/(r^(2))quad[” where, “K=(1)\/(4piepsi_(0))]],[=>r=(KZe^(2))\/(mv^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\therefore \\frac{m v^{2}}{r}=\\frac{K Z e^{2}}{r^{2}} \\quad\\left[\\text { where, } K=\\frac{1}{4 \\pi \\varepsilon_{0}}\\right] \\\\\n&\\Rightarrow r=\\frac{K Z e^{2}}{m v^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.175ex\" 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385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2681.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>\u2234<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mtext>\u00a0where,\u00a0<\/mtext><mi>K<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo stretchy=\"false\">\u21d2<\/mo><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1039 preview-line 1039\" data_line_start=\"1039\" data_line_end=\"1039\" data_line=\"1039,1040\" count_line=\"1\">The angular momentum for any permitted (stationary) orbit is<\/div>\n<div class=\"preview-paragraph-1041 preview-line 1041\" data_line_start=\"1041\" data_line_end=\"1041\" data_line=\"1041,1042\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.998ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4419.1 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 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694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1043 preview-line 1043\" data_line_start=\"1043\" data_line_end=\"1043\" data_line=\"1043,1044\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is any positive integer.<\/div>\n<div class=\"preview-paragraph-1045 preview-line 1045\" data_line_start=\"1045\" data_line_end=\"1045\" data_line=\"1045,1046\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(nh)\/(2pi mv)<\/asciimath><latex style=\"display: none\">r=\\frac{n h}{2 \\pi m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.925ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3944.9 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1948, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1920.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1047 preview-line 1047\" data_line_start=\"1047\" data_line_end=\"1047\" data_line=\"1047,1048\" count_line=\"1\">From (i) and (ii), we get<\/div>\n<div class=\"preview-paragraph-1049 preview-line 1049\" data_line_start=\"1049\" data_line_end=\"1049\" data_line=\"1049,1050\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>∴<\/mo>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>\u2234<\/mo>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>K<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(KZe^(2))\/(mv^(2))=(nh)\/(2pi mv):.v=(2pi KZe^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\frac{K Z e^{2}}{m v^{2}}=\\frac{n h}{2 \\pi m v} \\therefore v=\\frac{2 \\pi K Z e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.428ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 11681.1 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 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2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1612, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(472.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1954.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(2472.5, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3528.3, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(664.4, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 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388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"2711.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mo>\u2234<\/mo><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>K<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1051 preview-line 1051\" data_line_start=\"1051\" data_line_end=\"1051\" data_line=\"1051,1052\" count_line=\"1\">For hydrogen atom, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=1<\/asciimath><latex style=\"display: none\">Z=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.784ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2556.6 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2056.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1053 preview-line 1053\" data_line_start=\"1053\" data_line_end=\"1053\" data_line=\"1053,1054\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>ν<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>K<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bd<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>K<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad nu=(2pi Ke^(2))\/(nh)<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\nu=\\frac{2 \\pi K e^{2}}{n h}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.137ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6248.4 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 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129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 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562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(804.3, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><rect width=\"2200.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bd<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>K<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1055 preview-line 1055\" data_line_start=\"1055\" data_line_end=\"1055\" data_line=\"1055,1056\" count_line=\"1\">(b) Refer to answer 14.<\/div>\n<ol start=\"22\" class=\"preview-paragraph-1057 preview-line 1057 1058\" data_line_start=\"1057\" data_line_end=\"1058\" data_line=\"1057,1059\" count_line=\"2\">\n<li>Bohr’s postulates of atomic model : Bohr introduced three postulates and laid the foundations of quantum mechanics.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1059 preview-line 1059\" data_line_start=\"1059\" data_line_end=\"1059\" data_line=\"1059,1060\" count_line=\"1\">(i) In a hydrogen atom, an electron revolves in certain stable orbits called stationary orbits without the emission of radiant energy.<\/div>\n<div class=\"preview-paragraph-1061 preview-line 1061\" data_line_start=\"1061\" data_line_end=\"1061\" data_line=\"1061,1062\" count_line=\"1\">(ii) The angular momentum in the stationary orbits is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi)<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.707ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 1196.6 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(394.7, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1063 preview-line 1063\" data_line_start=\"1063\" data_line_end=\"1063\" data_line=\"1063,1064\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad L=mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">\\therefore \\quad L=m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.956ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 8378.4 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2903.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3959.3, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4837.3, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(5322.3, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6051.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(7106.9, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1065 preview-line 1065\" data_line_start=\"1065\" data_line_end=\"1065\" data_line=\"1065,1066\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is an integer called a quantum number.<\/div>\n<div class=\"preview-paragraph-1067 preview-line 1067\" data_line_start=\"1067\" data_line_end=\"1067\" data_line=\"1067,1068\" count_line=\"1\">In second excited state i.e., <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, three spectral lines can be obtained corresponding to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1,n=3<\/asciimath><latex style=\"display: none\">n=1, n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.018ex\" height=\"1.946ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 5311.8 860\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2878.2, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3756, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4811.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1069 preview-line 1069\" data_line_start=\"1069\" data_line_end=\"1069\" data_line=\"1069,1070\" count_line=\"1\">For Lyman series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for minimum wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>9<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>9<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(min))=R[(1)\/(1^(2))-(1)\/(3^(2))]=(8R)\/(9)<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\min }}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{8 R}{9}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.438ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10801.7 1799\" aria-hidden=\"true\"><g 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673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><rect width=\"1481.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1998.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3054.7, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(3813.7, 0)\"><g data-mml-node=\"mo\"><path data-c=\"5B\" d=\"M224 -649V1150H455V1099H275V-598H455V-649H224Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(472, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1773.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2773.4, 0)\"><g data-mml-node=\"mn\" transform=\"translate(362.7, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"838.9\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3852.3, 0)\"><path data-c=\"5D\" d=\"M16 1099V1150H247V-649H16V-598H196V1099H16Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(8415.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(9471.5, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(488.3, -345) scale(0.707)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><rect width=\"1090.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>8<\/mn><mi>R<\/mi><\/mrow><mn>9<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1071 preview-line 1071\" data_line_start=\"1071\" data_line_end=\"1071\" data_line=\"1071,1072\" count_line=\"1\">For Balmer series, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for maximum wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(max))=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\max }}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.961ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 11474.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(732.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 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556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 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-22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mi\" transform=\"translate(10715.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Dividing eq. (i) by (ii), we get<\/div>\n<div class=\"preview-paragraph-1073 preview-line 1073\" data_line_start=\"1073\" data_line_end=\"1073\" data_line=\"1073,1074\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>9<\/mn>\n <\/mrow>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>36<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>5<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>8<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>9<\/mn>\n <\/mrow>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>36<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>32<\/mn>\n <mn>5<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(max))\/(lambda_(min))=(8R\/\/9)\/(5R\/\/36)=(32)\/(5)<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{\\max }}{\\lambda_{\\min }}=\\frac{8 R \/ 9}{5 R \/ 36}=\\frac{32}{5}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.152ex\" height=\"3.607ex\" 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2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 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movablelimits=\"true\">max<\/mo><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>8<\/mn><mi>R<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>9<\/mn><\/mrow><mrow><mn>5<\/mn><mi>R<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>36<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>32<\/mn><mn>5<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1075 preview-line 1075\" data_line_start=\"1075\" data_line_end=\"1075\" data_line=\"1075,1076\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>:<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>32<\/mn>\n <mo>:<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>:<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>32<\/mn>\n <mo>:<\/mo>\n <mn>5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(max):lambda_(min)=32:5<\/asciimath><latex style=\"display: none\">\\lambda_{\\max }: \\lambda_{\\min }=32: 5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"18.691ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 8261.3 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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-11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"78\" d=\"M201 0Q189 3 102 3Q26 3 17 0H11V46H25Q48 47 67 52T96 61T121 78T139 96T160 122T180 150L226 210L168 288Q159 301 149 315T133 336T122 351T113 363T107 370T100 376T94 379T88 381T80 383Q74 383 44 385H16V431H23Q59 429 126 429Q219 429 229 431H237V385Q201 381 201 369Q201 367 211 353T239 315T268 274L272 270L297 304Q329 345 329 358Q329 364 327 369T322 376T317 380T310 384L307 385H302V431H309Q324 428 408 428Q487 428 493 431H499V385H492Q443 385 411 368Q394 360 377 341T312 257L296 236L358 151Q424 61 429 57T446 50Q464 46 499 46H516V0H510H502Q494 1 482 1T457 2T432 2T414 3Q403 3 377 3T327 1L304 0H295V46H298Q309 46 320 51T331 63Q331 65 291 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249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4872, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5927.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7205.6, 0)\"><path data-c=\"3A\" d=\"M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(7761.3, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>:<\/mo><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>32<\/mn><mo>:<\/mo><mn>5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"23\" class=\"preview-paragraph-1077 preview-line 1077 1078 1079 1080\" data_line_start=\"1077\" data_line_end=\"1080\" data_line=\"1077,1081\" count_line=\"4\">\n<li>\n<div>Refer to answer 19.<\/div>\n<\/li>\n<li>\n<div>(a) Limitation of Rutherford’s model:<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1081 preview-line 1081\" data_line_start=\"1081\" data_line_end=\"1081\" data_line=\"1081,1082\" count_line=\"1\">(i) Rutherford’s atomic model is inconsistent with classical physics. According to electromagnetic theory, an electron is a charged particle moving in the circular orbit around the nucleus and<\/div>\n<div class=\"preview-paragraph-1083 preview-line 1083 1084\" data_line_start=\"1083\" data_line_end=\"1084\" data_line=\"1083,1085\" count_line=\"2\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-15.jpg?height=254&width=251&top_left_y=770&top_left_x=751\" alt=\"\"><br>\nis accelerated, so it should emit radiation continuously and thereby loose energy. Due to this, radius of the electron would decrease continuously and also the atom should then produce continuous spectrum, and ultimately electron will fall into the nucleus and atom will collapse in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">10^(-8)s<\/asciimath><latex style=\"display: none\">10^{-8} \\mathrm{~s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.877ex\" height=\"2.005ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 2597.7 886\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1953.7, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>. But the atom is fairly stable and it emits line spectrum.<\/div>\n<div class=\"preview-paragraph-1086 preview-line 1086\" data_line_start=\"1086\" data_line_end=\"1086\" data_line=\"1086,1087\" count_line=\"1\">(ii) Rutherford’s model is not able to explain the spectrum of even most simplest H-spectrum.<\/div>\n<div class=\"preview-paragraph-1088 preview-line 1088\" data_line_start=\"1088\" data_line_end=\"1088\" data_line=\"1088,1089\" count_line=\"1\">Bohr’s postulates to resolve observed features of atomic spectrum :<\/div>\n<div class=\"preview-paragraph-1090 preview-line 1090\" data_line_start=\"1090\" data_line_end=\"1090\" data_line=\"1090,1091\" count_line=\"1\">(i) Quantum condition: Of all the possible circular orbits allowed by the classical theory, the electrons are permitted to circulate only in those orbits in which the angular momentum of an electron is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(h)\/(2pi),h<\/asciimath><latex style=\"display: none\">\\frac{h}{2 \\pi}, h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.016ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 2217.3 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(394.7, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1196.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1641.3, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> being Planck’s constant. Therefore, for any permitted orbit,<\/div>\n<div class=\"preview-paragraph-1092 preview-line 1092 1093 1094\" data_line_start=\"1092\" data_line_end=\"1094\" data_line=\"1092,1095\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>…<\/mo>\n <mo>…<\/mo>\n <mo>,<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>,<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>\u2026<\/mo>\n <mo>\u2026<\/mo>\n <mo>,<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=mvr=(nh)\/(2pi),n=1,2,3dots dots,<\/asciimath><latex style=\"display: none\">L=m v r=\\frac{n h}{2 \\pi}, n=1,2,3 \\ldots \\ldots,<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"33.185ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 14667.7 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 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285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(273, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1376\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(6778.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(7222.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8100.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9156.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9656.3, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(10101, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10601, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(11045.7, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11712.3, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(13051, 0)\"><path data-c=\"2026\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(14389.7, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>\u2026<\/mo><mo>\u2026<\/mo><mo>,<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1096 preview-line 1096\" data_line_start=\"1096\" data_line_end=\"1096\" data_line=\"1096,1097\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is called the principal quantum number, and this equation is called Bohr’s quantisation condition.<\/div>\n<div class=\"preview-paragraph-1098 preview-line 1098\" data_line_start=\"1098\" data_line_end=\"1098\" data_line=\"1098,1099\" count_line=\"1\">(ii) Stationary orbits: While resolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.<\/div>\n<div class=\"preview-paragraph-1100 preview-line 1100\" data_line_start=\"1100\" data_line_end=\"1100\" data_line=\"1100,1101\" count_line=\"1\">(iii) Frequency condition: An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.<\/div>\n<div class=\"preview-paragraph-1102 preview-line 1102 1103 1104\" data_line_start=\"1102\" data_line_end=\"1104\" data_line=\"1102,1105\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mrow>\n <mi mathvariant=\"normal\">i<\/mi>\n <\/mrow>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mrow>\n <mi mathvariant=\"normal\">i<\/mi>\n <\/mrow>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">h v=E_{\\mathrm{i}}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.073ex\" height=\"2.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 5778.5 989\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1338.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2394.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3601.4, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4601.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mrow><mi mathvariant=\"normal\">i<\/mi><\/mrow><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1106 preview-line 1106\" data_line_start=\"1106\" data_line_end=\"1106\" data_line=\"1106,1107\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is frequency of radiation emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(i)<\/asciimath><latex style=\"display: none\">E_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.335ex\" height=\"1.895ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1032 837.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(f)<\/asciimath><latex style=\"display: none\">E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.663ex\" height=\"2.206ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 1176.9 975\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the energies associated with stationary orbits of principal quantum number <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)<\/asciimath><latex style=\"display: none\">n_{i}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.023ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 894 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)<\/asciimath><latex style=\"display: none\">n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.35ex\" height=\"1.667ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 1038.9 737\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> respectively (where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>><\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i) > n_(f)<\/asciimath><latex style=\"display: none\">n_{i}>n_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.39ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -540 3266.4 835\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3E\" d=\"M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2227.5, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>><\/mo><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ).<\/div>\n<div class=\"preview-paragraph-1108 preview-line 1108\" data_line_start=\"1108\" data_line_end=\"1108\" data_line=\"1108,1109\" count_line=\"1\">(b) Refer to answer 13.<\/div>\n<ol start=\"25\" class=\"preview-paragraph-1110 preview-line 1110 1111 1112 1113\" data_line_start=\"1110\" data_line_end=\"1113\" data_line=\"1110,1114\" count_line=\"4\">\n<li>\n<div>Refer to answer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">17(i)<\/asciimath><latex style=\"display: none\">17(i)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.803ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2123 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1389, 0)\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1734, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>17<\/mn><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<\/li>\n<li>\n<div>(a) Refer to answer <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>17<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mi>i<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">17(i)<\/asciimath><latex style=\"display: none\">17(i)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.803ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2123 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1389, 0)\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1734, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>17<\/mn><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1114 preview-line 1114\" data_line_start=\"1114\" data_line_end=\"1114\" data_line=\"1114,1115\" count_line=\"1\">(b) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:’<\/asciimath><latex style=\"display: none\">\\because<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2235<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r=(n^(2)h^(2)epsi_(0))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">r=\\frac{n^{2} h^{2} \\varepsilon_{0}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.597ex\" height=\"3.358ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1046.7 4241.7 1484.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 457.1) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 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383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(1983.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" 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318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(570, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1448, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2217.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>m<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mi>m<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r prop(1)\/(m)<\/asciimath><latex style=\"display: none\">r \\propto \\frac{1}{m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.438ex\" height=\"2.755ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 2845.4 1217.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(728.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1784.6, 0)\"><g data-mml-node=\"mn\" transform=\"translate(353.6, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"820.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><mo>\u221d<\/mo><mfrac><mn>1<\/mn><mi>m<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1116 preview-line 1116\" data_line_start=\"1116\" data_line_end=\"1116\" data_line=\"1116,1117\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> when we increase the mass 200 times, the radius reduces to 200 times.<\/div>\n<div class=\"preview-paragraph-1118 preview-line 1118\" data_line_start=\"1118\" data_line_end=\"1118\" data_line=\"1118,1119\" count_line=\"1\">Similarly, ground state energy for hydrogen, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-me^(4))\/(8epsi_(0)^(2)n^(2)h^(2))<\/asciimath><latex style=\"display: none\">E=\\frac{-m e^{4}}{8 \\varepsilon_{0}^{2} n^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.105ex\" height=\"3.705ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -993.2 4908.2 1637.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(512.4, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" 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data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(2373.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2570.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1120 preview-line 1120\" data_line_start=\"1120\" data_line_end=\"1120\" data_line=\"1120,1121\" count_line=\"1\">i.e. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>∝<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>\u221d<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E prop m<\/asciimath><latex style=\"display: none\">E \\propto m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.732ex\" height=\"1.563ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 2975.6 691\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2097.6, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>\u221d<\/mo><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1122 preview-line 1122\" data_line_start=\"1122\" data_line_end=\"1122\" data_line=\"1122,1123\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.<\/asciimath><latex style=\"display: none\">\\therefore<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> when we increase the mass 200 times, the ground state energy also increases by a factor 200.<\/div>\n<ol start=\"27\" class=\"preview-paragraph-1124 preview-line 1124 1125 1126 1127\" data_line_start=\"1124\" data_line_end=\"1127\" data_line=\"1124,1128\" count_line=\"4\">\n<li>\n<div>Refer to answer 17(i).<\/div>\n<\/li>\n<li>\n<div>For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1128 preview-line 1128\" data_line_start=\"1128\" data_line_end=\"1128\" data_line=\"1128,1129\" count_line=\"1\">Ground state energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-13.6eV<\/asciimath><latex style=\"display: none\">E_{1}=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.084ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 6225.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2475.1, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3253.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5031.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1130 preview-line 1130\" data_line_start=\"1130\" data_line_end=\"1130\" data_line=\"1130,1131\" count_line=\"1\">Excited state energy, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(2)=-1.5eV<\/asciimath><latex style=\"display: none\">E_{2}=-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.953ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 5725.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 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120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(4531.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1132 preview-line 1132\" data_line_start=\"1132\" data_line_end=\"1132\" data_line=\"1132,1133\" count_line=\"1\">Energy of photon emitted, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=E_(2)-E_(1)<\/asciimath><latex style=\"display: none\">E=E_{2}-E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.677ex\" height=\"1.878ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 5603.1 830\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 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550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3461.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(4461.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1134 preview-line 1134\" data_line_start=\"1134\" data_line_end=\"1134\" data_line=\"1134,1135\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-1.5-(-13.6)=-1.5+13.6=12.1eV<\/asciimath><latex style=\"display: none\">=-1.5-(-13.6)=-1.5+13.6=12.1 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.547ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 18363.8 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 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680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>+<\/mo><mn>13.6<\/mn><mo>=<\/mo><mn>12.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1136 preview-line 1136\" data_line_start=\"1136\" data_line_end=\"1136\" data_line=\"1136,1137\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.<\/asciimath><latex style=\"display: none\">\\therefore<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.509ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 667 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Wavelength of photon emitted,<\/div>\n<div class=\"preview-paragraph-1138 preview-line 1138\" data_line_start=\"1138\" data_line_end=\"1138\" data_line=\"1138,1139\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>19.36<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>19.36<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/(E)=(6.62 xx10^(-34)xx3xx10^(8))\/(12.1 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(19.36)<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{E}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{12.1 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{19.36}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.3ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 16044.6 1476.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 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transform=\"translate(1000, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1778, 0)\"><\/path><\/g><rect width=\"3742.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>E<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>12.1<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>19.36<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1140 preview-line 1140\" data_line_start=\"1140\" data_line_end=\"1140\" data_line=\"1140,1141\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.027<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>1.027<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=1.027 xx10^(-7)=102.7nm<\/asciimath><latex style=\"display: none\">=1.027 \\times 10^{-7}=102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" 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402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>1.027<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mo>=<\/mo><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1142 preview-line 1142\" data_line_start=\"1142\" data_line_end=\"1142\" data_line=\"1142,1143\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>C<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>C<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">C<\/asciimath><latex style=\"display: none\">C<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.719ex\" height=\"1.645ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 760 727\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>C<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1144 preview-line 1144\" data_line_start=\"1144\" data_line_end=\"1144\" data_line=\"1144,1145\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-3.4eV,E_(2)=-1.5eV<\/asciimath><latex style=\"display: none\">E_{1}=-3.4 \\mathrm{eV}, E_{2}=-1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.912ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 11894.9 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 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599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 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245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1146 preview-line 1146\" data_line_start=\"1146\" data_line_end=\"1146\" data_line=\"1146,1147\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-1.5-(-3.4)=-1.5+3.4=1.9eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-1.5-(-3.4)=-1.5+3.4=1.9 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"44.91ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 19850.3 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2986.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 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data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>+<\/mo><mn>3.4<\/mn><mo>=<\/mo><mn>1.9<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1148 preview-line 1148\" data_line_start=\"1148\" data_line_end=\"1148\" data_line=\"1148,1149\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>3.04<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>3.04<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(1.9 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(3.04)<\/asciimath><latex style=\"display: none\">\\therefore \\lambda=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{1.9 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{3.04}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.811ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 14502.4 1476.9\" aria-hidden=\"true\"><g 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96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(1278, 0)\"><\/path><\/g><rect width=\"3742.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>1.9<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>3.04<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1150 preview-line 1150\" data_line_start=\"1150\" data_line_end=\"1150\" data_line=\"1150,1151\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.539<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>653.9<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.539<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>653.9<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=6.539 xx10^(-7)m=653.9nm<\/asciimath><latex style=\"display: none\">=6.539 \\times 10^{-7} \\mathrm{~m}=653.9 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" 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472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>6.539<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>653.9<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1152 preview-line 1152\" data_line_start=\"1152\" data_line_end=\"1152\" data_line=\"1152,1153\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>B<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">B<\/asciimath><latex style=\"display: none\">B<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.717ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 759 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-3.4eV,E_(2)=-0.85eV<\/asciimath><latex style=\"display: none\">E_{1}=-3.4 \\mathrm{eV}, E_{2}=-0.85 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.439ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.043ex\" height=\"1.984ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 12394.9 877\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 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429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(7589.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8644.9, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9422.9, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11200.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1156 preview-line 1156\" data_line_start=\"1156\" data_line_end=\"1156\" data_line=\"1156,1157\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>2.55<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo>=<\/mo>\n <mn>2.55<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-0.85-(-3.4)=-0.85+3.4=2.55eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-0.85-(-3.4)=-0.85+3.4=2.55 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.304ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 21350.3 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 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transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(20156.3, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mo>+<\/mo><mn>3.4<\/mn><mo>=<\/mo><mn>2.55<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1158 preview-line 1158\" data_line_start=\"1158\" data_line_end=\"1158\" data_line=\"1158,1159\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2.55<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4.08<\/mn>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>2.55<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>4.08<\/mn>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(2.55 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(4.08)<\/asciimath><latex style=\"display: none\">\\therefore \\lambda=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{2.55 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{4.08}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.811ex\" height=\"3.341ex\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2.55<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>4.08<\/mn><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1160 preview-line 1160\" data_line_start=\"1160\" data_line_end=\"1160\" data_line=\"1160,1161\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.867<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>486.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.867<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>486.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=4.867 xx10^(-7)m=486.7nm<\/asciimath><latex style=\"display: none\">=4.867 \\times 10^{-7} \\mathrm{~m}=486.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" 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2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>4.867<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>486.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1162 preview-line 1162\" data_line_start=\"1162\" data_line_end=\"1162\" data_line=\"1162,1163\" count_line=\"1\">For element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1164 preview-line 1164\" data_line_start=\"1164\" data_line_end=\"1164\" data_line=\"1164,1165\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>,<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n 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311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11200.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>,<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>0.85<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1166 preview-line 1166\" data_line_start=\"1166\" data_line_end=\"1166\" data_line=\"1166,1167\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>1.5<\/mn>\n <mo>=<\/mo>\n <mn>0.65<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>+<\/mo>\n <mn>1.5<\/mn>\n <mo>=<\/mo>\n <mn>0.65<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad E=-0.85-(-1.5)=-0.85+1.5=0.65<\/asciimath><latex style=\"display: none\">\\therefore \\quad E=-0.85-(-1.5)=-0.85+1.5=0.65<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"45.603ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 20156.3 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" 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1168 1169 1170 1171 1172 1173\" data_line_start=\"1168\" data_line_end=\"1173\" data_line=\"1168,1174\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>0.65<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>1.04<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>19.096<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1909.6<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>0.65<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.86<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mn>1.04<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>19.096<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1909.6<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[:.quad lambda=(6.62 xx10^(-34)xx3xx10^(8))\/(0.65 xx1.6 xx10^(-19))=(19.86 xx10^(-7))\/(1.04)],[=19.096 xx10^(-7)m=1909.6nm]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n\\therefore \\quad \\lambda &=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{0.65 \\times 1.6 \\times 10^{-19}}=\\frac{19.86 \\times 10^{-7}}{1.04} \\\\\n&=19.096 \\times 10^{-7} \\mathrm{~m}=1909.6 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410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>\u03bb<\/mi><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>0.65<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>19.86<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mn>1.04<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>19.096<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>1909.6<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1175 preview-line 1175\" data_line_start=\"1175\" data_line_end=\"1175\" data_line=\"1175,1176\" count_line=\"1\">The element <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>D<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">D<\/asciimath><latex style=\"display: none\">D<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> corresponds to a spectral line of wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>102.7<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">102.7nm<\/asciimath><latex style=\"display: none\">102.7 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.862ex\" height=\"1.579ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -676 3917 698\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2278, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>102.7<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<ol start=\"29\" class=\"preview-paragraph-1177 preview-line 1177 1178 1179 1180\" data_line_start=\"1177\" data_line_end=\"1180\" data_line=\"1177,1181\" count_line=\"4\">\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>α<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>H<\/mi>\n <mrow>\n <mi>\u03b1<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H_(alpha)<\/asciimath><latex style=\"display: none\">H_{\\alpha}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.017ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1333.5 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(831, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3B1\" d=\"M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>H<\/mi><mrow><mi>\u03b1<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> line of the Balmer series in the emission spectrum of hydrogen atoms obtained when the transition occurs from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state.<\/div>\n<\/li>\n<li>\n<div>Number of spectral lines obtained due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd <\/mtext>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd\u00a0<\/mtext>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4(3^(“rd “):}<\/asciimath><latex style=\"display: none\">n=4\\left(3^{\\text {rd }}\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.703ex\" height=\"2.722ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 4288.7 1203.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2433.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M152 251Q152 646 388 850H416Q422 844 422 841Q422 837 403 816T357 753T302 649T255 482T236 250Q236 124 255 19T301 -147T356 -251T403 -315T422 -340Q422 -343 416 -349H388Q359 -325 332 -296T271 -213T212 -97T170 56T152 251Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(458, 0)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(392, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(948, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1855.1, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msup><mn>3<\/mn><mrow><mtext>rd\u00a0<\/mtext><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state) to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (ground state) is<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1181 preview-line 1181\" data_line_start=\"1181\" data_line_end=\"1181\" data_line=\"1181,1182\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=314&width=714&top_left_y=997&top_left_x=288\" alt=\"\"><\/div>\n<ol start=\"31\" class=\"preview-paragraph-1183 preview-line 1183 1184\" data_line_start=\"1183\" data_line_end=\"1184\" data_line=\"1183,1185\" count_line=\"2\">\n<li>The minimum energy, required to free the electron from the ground state of the hydrogen atom, is known as ionization energy of that atom.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1185 preview-line 1185\" data_line_start=\"1185\" data_line_end=\"1185\" data_line=\"1185,1186\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(0)=(me^(4))\/(8epsi_(0)^(2)h^(2))<\/asciimath><latex style=\"display: none\">E_{0}=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.353ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4576.2 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 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489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1861.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> i.e..<span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(0)prop m<\/asciimath><latex style=\"display: none\">E_{0} \\propto m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.586ex\" height=\"1.913ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 3353.1 845.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1419.3, 0)\"><path data-c=\"221D\" d=\"M56 124T56 216T107 375T238 442Q260 442 280 438T319 425T352 407T382 385T406 361T427 336T442 315T455 297T462 285L469 297Q555 442 679 442Q687 442 722 437V398H718Q710 400 694 400Q657 400 623 383T567 343T527 294T503 253T495 235Q495 231 520 192T554 143Q625 44 696 44Q717 44 719 46H722V-5Q695 -11 678 -11Q552 -11 457 141Q455 145 454 146L447 134Q362 -11 235 -11Q157 -11 107 56ZM93 213Q93 143 126 87T220 31Q258 31 292 48T349 88T389 137T413 178T421 196Q421 200 396 239T362 288Q322 345 288 366T213 387Q163 387 128 337T93 213Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2475.1, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><mo>\u221d<\/mo><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, so when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron, ionization energy increases by 200 times.<\/div>\n<ol start=\"32\" class=\"preview-paragraph-1187 preview-line 1187 1188\" data_line_start=\"1187\" data_line_end=\"1188\" data_line=\"1187,1189\" count_line=\"2\">\n<li>Number of spectral lines obtained due to transition of electron from <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd <\/mtext>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n <mfenced open=\"(\" close=\"\" separators=\"|\">\n <mrow>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mtext>rd\u00a0<\/mtext>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=4(3^(“rd “):}<\/asciimath><latex style=\"display: none\">n=4\\left(3^{\\text {rd }}\\right.<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.791ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.703ex\" height=\"2.722ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 4288.7 1203.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(2433.6, 0)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M152 251Q152 646 388 850H416Q422 844 422 841Q422 837 403 816T357 753T302 649T255 482T236 250Q236 124 255 19T301 -147T356 -251T403 -315T422 -340Q422 -343 416 -349H388Q359 -325 332 -296T271 -213T212 -97T170 56T152 251Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(458, 0)\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"72\" d=\"M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(392, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(948, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1855.1, 0)\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msup><mn>3<\/mn><mrow><mtext>rd\u00a0<\/mtext><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\" fence=\"true\" stretchy=\"true\" symmetric=\"true\"><\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state) to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (ground state) is<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1189 preview-line 1189\" data_line_start=\"1189\" data_line_end=\"1189\" data_line=\"1189,1190\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=314&width=699&top_left_y=1805&top_left_x=290\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1191 preview-line 1191\" data_line_start=\"1191\" data_line_end=\"1191\" data_line=\"1191,1192\" count_line=\"1\">These lines correspond to Lyman series.<\/div>\n<ol start=\"33\" class=\"preview-paragraph-1193 preview-line 1193 1194\" data_line_start=\"1193\" data_line_end=\"1194\" data_line=\"1193,1195\" count_line=\"2\">\n<li>(a) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>496<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=496nm=496 xx10^(-9)m<\/asciimath><latex style=\"display: none\">\\lambda=496 \\mathrm{~nm}=496 \\times 10^{-9} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.485ex\" height=\"2.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 12148.2 946\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"34\" 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mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1195 preview-line 1195 1196 1197 1198 1199 1200\" data_line_start=\"1195\" data_line_end=\"1200\" data_line=\"1195,1201\" count_line=\"6\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mi>E<\/mi>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n 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<mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>2.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <mi>E<\/mi>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>496<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>496<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>2.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E=(hc)\/(lambda)=(6.62 xx10^(-34)xx3xx10^(8))\/(496 xx10^(-9))J],[=(6.6 xx10^(-34)xx3xx10^(8))\/(496 xx10^(-9)xx1.6 xx10^(-19))=2.5eV]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\nE &=\\frac{h c}{\\lambda}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{496 \\times 10^{-9}} \\mathrm{~J} \\\\\n&=\\frac{6.6 \\times 10^{-34} \\times 3 \\times 10^{8}}{496 \\times 10^{-9} \\times 1.6 \\times 10^{-19}}=2.5 \\mathrm{eV}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -5.189ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"38.573ex\" height=\"11.51ex\" role=\"img\" focusable=\"false\" 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573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"10906.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" 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224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(15091.4, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 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rowspacing=\"3pt\"><mtr><mtd><mi>E<\/mi><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mfrac><mrow><mn>6.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>496<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>2.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1202 preview-line 1202\" data_line_start=\"1202\" data_line_end=\"1202\" data_line=\"1202,1203\" count_line=\"1\">This energy corresponds to the transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A(n=4<\/asciimath><latex style=\"display: none\">A(n=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.083ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3572.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(750, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1139, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2016.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3072.6, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3)<\/asciimath><latex style=\"display: none\">n=3)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.386ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2822.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2433.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> for which the energy change <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2eV<\/asciimath><latex style=\"display: none\">=2 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.221ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2749.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1555.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (b) Energy of emitted photon is given by,<\/div>\n<div class=\"preview-paragraph-1204 preview-line 1204 1205 1206\" data_line_start=\"1204\" data_line_end=\"1206\" data_line=\"1204,1207\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>∝<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>\u221d<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(hc)\/(lambda)quad:.lambda_(max)prop(1)\/(E_(min))<\/asciimath><latex style=\"display: none\">E=\\frac{h c}{\\lambda} \\quad \\therefore \\lambda_{\\max } \\propto \\frac{1}{E_{\\min }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.891ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"25.924ex\" height=\"4.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 11458.3 2206\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 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625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z\" transform=\"translate(833, 0)\"><\/path><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(1111, 0)\"><\/path><\/g><\/g><\/g><rect width=\"2166.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>\u221d<\/mo><mfrac><mn>1<\/mn><msub><mi>E<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><\/mrow><\/msub><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1208 preview-line 1208\" data_line_start=\"1208\" data_line_end=\"1208\" data_line=\"1208,1209\" count_line=\"1\">Transition <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>A<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">A<\/asciimath><latex style=\"display: none\">A<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.697ex\" height=\"1.62ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 750 716\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, for which the energy emission is minimum, corresponds to the emission of radiation of maximum wavelength.<\/div>\n<ol start=\"34\" class=\"preview-paragraph-1210 preview-line 1210 1211\" data_line_start=\"1210\" data_line_end=\"1211\" data_line=\"1210,1212\" count_line=\"2\">\n<li>(i) An electron undergoes transition from 2nd excited state to the first excited state is Balmer series and then to the ground state is Lyman series.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1212 preview-line 1212\" data_line_start=\"1212\" data_line_end=\"1212\" data_line=\"1212,1213\" count_line=\"1\">(ii) The wavelength of the emitted radiations in the two cases.<\/div>\n<div class=\"preview-paragraph-1214 preview-line 1214\" data_line_start=\"1214\" data_line_end=\"1214\" data_line=\"1214,1215\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-16.jpg?height=540&width=605&top_left_y=961&top_left_x=1134\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1216 preview-line 1216\" data_line_start=\"1216\" data_line_end=\"1216\" data_line=\"1216,1217\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"REL\">\n <mover>\n <mrow data-mjx-texclass=\"OP\">\n <mo stretchy=\"false\">⟶<\/mo>\n <\/mrow>\n <mrow>\n <mi>λ<\/mi>\n <\/mrow>\n <\/mover>\n <\/mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mrow data-mjx-texclass=\"REL\">\n <mover accent=\"true\" accentunder=\"false\">\n <mrow data-mjx-texclass=\"OP\">\n <mo stretchy=\"false\">\u27f6<\/mo>\n <\/mrow>\n <mrow>\n <mi>\u03bb<\/mi>\n <\/mrow>\n <\/mover>\n <\/mrow>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(2)longrightarrow^(lambda)n_(1)<\/asciimath><latex style=\"display: none\">n_{2} \\stackrel{\\lambda}{\\longrightarrow} n_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.504ex\" height=\"3.284ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1301.7 4200.7 1451.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"REL\" transform=\"translate(1281.3, 0)\"><g data-mml-node=\"mover\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"OP\"><g data-mml-node=\"mo\"><path data-c=\"27F6\" d=\"M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(612.9, 711) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(3197.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"REL\"><mover><mrow data-mjx-texclass=\"OP\"><mo stretchy=\"false\">\u27f6<\/mo><\/mrow><mrow><mi>\u03bb<\/mi><\/mrow><\/mover><\/mrow><msub><mi>n<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1218 preview-line 1218\" data_line_start=\"1218\" data_line_end=\"1218\" data_line=\"1218,1219\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>10.20<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>10.20<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=(-3.40+13.6)=10.20eV<\/asciimath><latex style=\"display: none\">\\Delta E=(-3.40+13.6)=10.20 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"31.834ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14070.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 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52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 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mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1220 preview-line 1220\" data_line_start=\"1220\" data_line_end=\"1220\" data_line=\"1220,1221\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.626<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.626<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=(6.626 xx10^(-34)xx3xx10^(8))\/(10.2 xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda_{2}=\\frac{6.626 \\times 10^{-34} \\times 3 \\times 10^{8}}{10.2 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" 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65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"6438.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>6.626<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>10.2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1222 preview-line 1222\" data_line_start=\"1222\" data_line_end=\"1222\" data_line=\"1222,1223\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.218<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1218<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>10.2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.218<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>1218<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(2)=(19.878 xx10^(-7))\/(10.2 xx1.6)=1.218 xx10^(-7)m=1218″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda_{2}=\\frac{19.878 \\times 10^{-7}}{10.2 \\times 1.6}=1.218 \\times 10^{-7} \\mathrm{~m}=1218 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.816ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.765ex\" height=\"3.101ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1009.9 18460.3 1370.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 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data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>19.878<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>10.2<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>1.218<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>1218<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1224 preview-line 1224\" data_line_start=\"1224\" data_line_end=\"1224\" data_line=\"1224,1225\" count_line=\"1\">For <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">→<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo stretchy=\"false\">\u2192<\/mo>\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(3)rarrn_(2)<\/asciimath><latex style=\"display: none\">n_{3} \\rightarrow n_{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.375ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.06ex\" height=\"1.531ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -511 3562.7 676.6\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1281.3, 0)\"><path data-c=\"2192\" d=\"M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2559.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><mo stretchy=\"false\">\u2192<\/mo><msub><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1226 preview-line 1226\" data_line_start=\"1226\" data_line_end=\"1226\" data_line=\"1226,1227\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.9<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=(-1.5+3.4)=1.9eV<\/asciimath><latex style=\"display: none\">\\Delta E=(-1.5+3.4)=1.9 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.309ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12070.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 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mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1228 preview-line 1228\" data_line_start=\"1228\" data_line_end=\"1228\" data_line=\"1228,1229\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>6.538<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>6538<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>19.878<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>1.9<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>6.538<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>6538<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda_(1)=(19.878 xx10^(-7))\/(1.9 xx1.6)=6.538 xx10^(-7)m=6538″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda_{1}=\\frac{19.878 \\times 10^{-7}}{1.9 \\times 1.6}=6.538 \\times 10^{-7} \\mathrm{~m}=6538 \\AA<\/latex><mjx-container 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511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10489.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(11490, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 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263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17860.3, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>19.878<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>1.9<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>6.538<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>6538<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1230 preview-line 1230\" data_line_start=\"1230\" data_line_end=\"1230\" data_line=\"1230,1231\" count_line=\"1\">The ratio <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>6538<\/mn>\n <mn>1218<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>5.36<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>6538<\/mn>\n <mn>1218<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>5.36<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(lambda_(1))\/(lambda_(2))=(6538)\/(1218)=5.36<\/asciimath><latex style=\"display: none\">\\frac{\\lambda_{1}}{\\lambda_{2}}=\\frac{6538}{1218}=5.36<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.021ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.826ex\" height=\"3.14ex\" role=\"img\" focusable=\"false\" 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136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"897.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1415.4, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2471.2, 0)\"><g data-mml-node=\"mn\" transform=\"translate(220, 394) scale(0.707)\"><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(1500, 0)\"><\/path><\/g><rect width=\"1614.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4603.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5658.9, 0)\"><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>6538<\/mn><mn>1218<\/mn><\/mfrac><mo>=<\/mo><mn>5.36<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"35\" class=\"preview-paragraph-1232 preview-line 1232 1233\" data_line_start=\"1232\" data_line_end=\"1233\" data_line=\"1232,1234\" count_line=\"2\">\n<li>For longest wavelength of Lyman series <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=2<\/asciimath><latex style=\"display: none\">n_{i}=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.864ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2727.5 823.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1234 preview-line 1234 1235 1236 1237 1238 1239 1240\" data_line_start=\"1234\" data_line_end=\"1240\" data_line=\"1234,1241\" count_line=\"7\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1215<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>1215<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[(1)\/(lambda_(max))=R((1)\/(1^(2))-(1)\/(2^(2)))=(3R)\/(4)],[lambda_(max)=(4)\/(3R)=(4)\/(3xx1.097 xx10^(7))=1.215 xx10^(-7)m],[lambda_(max)=1215″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&\\frac{1}{\\lambda_{\\max }}=R\\left(\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right)=\\frac{3 R}{4} \\\\\n&\\lambda_{\\max }=\\frac{4}{3 R}=\\frac{4}{3 \\times 1.097 \\times 10^{7}}=1.215 \\times 10^{-7} \\mathrm{~m} \\\\\n&\\lambda_{\\max }=1215 \\AA\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -6.454ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.082ex\" height=\"14.039ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -3352.5 21252.2 6205.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g 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22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5282.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><mn>4<\/mn><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mn>1.215<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mn>1215<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1242 preview-line 1242\" data_line_start=\"1242\" data_line_end=\"1242\" data_line=\"1242,1243\" count_line=\"1\">The lines of the Lyman series are found in ultraviolet region. (ii) For longest wavelength of Balmer series <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=3<\/asciimath><latex style=\"display: none\">n_{i}=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.861ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2727.5 822.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1171.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2227.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1244 preview-line 1244\" data_line_start=\"1244\" data_line_end=\"1244\" data_line=\"1244,1245\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda_(max))=R((1)\/(2^(2))-(1)\/(3^(2)))=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda_{\\max }}=R\\left(\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right)=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.526ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 11724.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" 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data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1246 preview-line 1246\" data_line_start=\"1246\" data_line_end=\"1246\" data_line=\"1246,1247\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>×<\/mo>\n <mn>1.097<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.563<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6563<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.097<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6.563<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <mi><\/mi>\n <mo>=<\/mo>\n <mn>6563<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[lambda_(max)=(36)\/(5R)=(36)\/(5xx1.097 xx10^(7))=6.563 xx10^(-7)m],[=6563″\u212b”]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned} \\lambda_{\\max }=\\frac{36}{5 R}=\\frac{36}{5 \\times 1.097 \\times 10^{7}} &=6.563 \\times 10^{-7} \\mathrm{~m} \\\\ &=6563 \\AA \\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -3.388ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.082ex\" height=\"7.907ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1997.5 21252.2 3495.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 655.5)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" 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380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3333.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><msub><mi>\u03bb<\/mi><mrow><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">max<\/mo><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mn>1.097<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6.563<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mi><\/mi><mo>=<\/mo><mn>6563<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1248 preview-line 1248\" data_line_start=\"1248\" data_line_end=\"1248\" data_line=\"1248,1249\" count_line=\"1\">Balmer series lie in the visible region of electromagnetic spectrum.<\/div>\n<ol start=\"36\" class=\"preview-paragraph-1250 preview-line 1250 1251\" data_line_start=\"1250\" data_line_end=\"1251\" data_line=\"1250,1252\" count_line=\"2\">\n<li>Here, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=12.5eV<\/asciimath><latex style=\"display: none\">\\Delta E=12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1252 preview-line 1252\" data_line_start=\"1252\" data_line_end=\"1252\" data_line=\"1252,1253\" count_line=\"1\">Energy of an electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit of hydrogen atom is, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.061ex\" height=\"2.947ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864.9 6215.1 1302.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1490, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 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82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(493.8, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1457.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5021.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1254 preview-line 1254\" data_line_start=\"1254\" data_line_end=\"1254\" data_line=\"1254,1255\" count_line=\"1\">In ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1256 preview-line 1256\" data_line_start=\"1256\" data_line_end=\"1256\" data_line=\"1256,1257\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(1)=-13.6eV<\/asciimath><latex style=\"display: none\">E_{1}=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.084ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 6225.1 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 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624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1258 preview-line 1258\" data_line_start=\"1258\" data_line_end=\"1258\" data_line=\"1258,1259\" count_line=\"1\">Energy of an electron in the excited state after absorbing a photon of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>12.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">12.5eV<\/asciimath><latex style=\"display: none\">12.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.05ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.724ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 2972 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(1778, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>12.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> energy will be<\/div>\n<div class=\"preview-paragraph-1260 preview-line 1260\" data_line_start=\"1260\" data_line_end=\"1260\" data_line=\"1260,1261\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo>+<\/mo>\n <mn>12.5<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo>+<\/mo>\n <mn>12.5<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-13.6+12.5=-1.1eV<\/asciimath><latex style=\"display: none\">E_{n}=-13.6+12.5=-1.1 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.701ex\" height=\"1.902ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 12685.8 840.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 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d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo>+<\/mo><mn>12.5<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>1.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1262 preview-line 1262\" data_line_start=\"1262\" data_line_end=\"1262\" data_line=\"1262,1263\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mrow>\n <mo>−<\/mo>\n <mn>1.1<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>12.36<\/mn>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3.5<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>1.1<\/mn>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>12.36<\/mn>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3.5<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadn^(2)=(-13.6)\/(E_(n))=(-13.6)\/(-1.1)=12.36=>n=3.5<\/asciimath><latex style=\"display: none\">\\therefore \\quad n^{2}=\\frac{-13.6}{E_{n}}=\\frac{-13.6}{-1.1}=12.36 \\Rightarrow n=3.5<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"41.83ex\" height=\"2.999ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 18488.8 1325.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><mrow><mo>\u2212<\/mo><mn>1.1<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>12.36<\/mn><mo stretchy=\"false\">\u21d2<\/mo><mi>n<\/mi><mo>=<\/mo><mn>3.5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1264 preview-line 1264\" data_line_start=\"1264\" data_line_end=\"1264\" data_line=\"1264,1265\" count_line=\"1\">Here, state of electron cannot be fraction.<\/div>\n<div class=\"preview-paragraph-1266 preview-line 1266\" data_line_start=\"1266\" data_line_end=\"1266\" data_line=\"1266,1267\" count_line=\"1\">So, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>3<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=3<\/asciimath><latex style=\"display: none\">n=3<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.69ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -665 2433.6 747\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> ( <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mtext>nd\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2^(“nd “)<\/asciimath><latex style=\"display: none\">2^{\\text {nd }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.423ex\" height=\"1.932ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1513.1 853.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><path data-c=\"64\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\" transform=\"translate(556, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(1112, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>2<\/mn><mrow><mtext>nd\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> exited state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">)<\/asciimath><latex style=\"display: none\">)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.88ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 389 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<div class=\"preview-paragraph-1268 preview-line 1268\" data_line_start=\"1268\" data_line_end=\"1268\" data_line=\"1268,1269\" count_line=\"1\">The wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda<\/asciimath><latex style=\"display: none\">\\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.027ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.319ex\" height=\"1.597ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 583 706\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the first member of Lyman series is given by<\/div>\n<div class=\"preview-paragraph-1270 preview-line 1270\" data_line_start=\"1270\" data_line_end=\"1270\" data_line=\"1270,1271\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>3<\/mn>\n <mn>4<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda)=R[(1)\/(1^(2))-(1)\/(2^(2))]=(3)\/(4)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda}=R\\left[\\frac{1}{1^{2}}-\\frac{1}{2^{2}}\\right]=\\frac{3}{4} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.975ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10155.2 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(249.3, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"612.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1130, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2185.8, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 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data_line=\"1272,1273\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>4<\/mn>\n <mrow>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.09<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.215<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda=(4)\/(3R)=(4)\/(3xx1.09 xx10^(7))=>lambda=1.215 xx10^(-7)m<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda=\\frac{4}{3 R}=\\frac{4}{3 \\times 1.09 \\times 10^{7}} \\Rightarrow \\lambda=1.215 \\times 10^{-7} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.067ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>1.215<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1274 preview-line 1274\" data_line_start=\"1274\" data_line_end=\"1274\" data_line=\"1274,1275\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">⇒<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>121<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda=121 xx10^(-9)m=>lambda=121nm<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda=121 \\times 10^{-9} \\mathrm{~m} \\Rightarrow \\lambda=121 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"35.214ex\" height=\"2.14ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 15564.6 946\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1277.8, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2138.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3194.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4916.6, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5916.8, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(7870.5, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(9231.2, 0)\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(10509, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(11369.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(12425.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13925.6, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>121<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>121<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1276 preview-line 1276\" data_line_start=\"1276\" data_line_end=\"1276\" data_line=\"1276,1277\" count_line=\"1\">The wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda^(‘)<\/asciimath><latex style=\"display: none\">\\lambda^{\\prime}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.027ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.872ex\" height=\"1.744ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -759 827.5 771\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"2032\" d=\"M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>\u03bb<\/mi><mrow><mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the first member of the Balmer series is given by<\/div>\n<div class=\"preview-paragraph-1278 preview-line 1278\" data_line_start=\"1278\" data_line_end=\"1278\" data_line=\"1278,1279\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msup>\n <mn>3<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mn>5<\/mn>\n <mn>36<\/mn>\n <\/mfrac>\n <mi>R<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(1)\/(lambda^(‘))=R[(1)\/(2^(2))-(1)\/(3^(2))]=(5)\/(36)R<\/asciimath><latex style=\"display: none\">\\frac{1}{\\lambda^{\\prime}}=R\\left[\\frac{1}{2^{2}}-\\frac{1}{3^{2}}\\right]=\\frac{5}{36} R<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.166ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 10681.6 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mn\" transform=\"translate(335.8, 394) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(220, -376.7) 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32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(220, -345) scale(0.707)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(500, 0)\"><\/path><\/g><rect width=\"907.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mi\" transform=\"translate(9922.6, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><msup><mi>\u03bb<\/mi><mrow><mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mi>R<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msup><mn>3<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>5<\/mn><mn>36<\/mn><\/mfrac><mi>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1280 preview-line 1280\" data_line_start=\"1280\" data_line_end=\"1280\" data_line=\"1280,1281\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <msup>\n <mi>λ<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">′<\/mi>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>×<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mn>1.09<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msup>\n <mi>\u03bb<\/mi>\n <mrow>\n <mi data-mjx-alternate=\"1\" mathvariant=\"normal\">\u2032<\/mi>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mi>R<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>36<\/mn>\n <mrow>\n <mn>5<\/mn>\n <mo>\u00d7<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1.09<\/mn> \n <mo>\u00d7<\/mo> \n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup> \n <\/mrow> \n <\/mfenced>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>lambda^(‘)=(36)\/(5R)=(36)\/(5xx(1.09 xx10^(7)))<\/asciimath><latex style=\"display: none\">\\Rightarrow \\lambda^{\\prime}=\\frac{36}{5 R}=\\frac{36}{5 \\times\\left(1.09 \\times 10^{7}\\right)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" 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mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mi>R<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>36<\/mn><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>1.09<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>7<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1282 preview-line 1282\" data_line_start=\"1282\" data_line_end=\"1282\" data_line=\"1282,1283\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.56<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>6.56<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>9<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>656<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n 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396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1000, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(17019.1, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"6E\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(806, 0)\"><path data-c=\"6D\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>6.56<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>656<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>9<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>656<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"37\" class=\"preview-paragraph-1284 preview-line 1284 1285\" data_line_start=\"1284\" data_line_end=\"1285\" data_line=\"1284,1286\" count_line=\"2\">\n<li>(i) <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:’E_(n)=(-13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">\\because E_{n}=\\frac{-13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.683ex\" height=\"2.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -868.9 6932 1306.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2434.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3490.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 398) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 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data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2007.4\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(5738, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2235<\/mo><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1286 preview-line 1286\" data_line_start=\"1286\" data_line_end=\"1286\" data_line=\"1286,1287\" count_line=\"1\">Energy of the photon emitted during a transition of the electron from the first excited state to its ground state is,<\/div>\n<div class=\"preview-paragraph-1288 preview-line 1288\" data_line_start=\"1288\" data_line_end=\"1288\" data_line=\"1288,1289\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=E_(2)-E_(1)<\/asciimath><latex style=\"display: none\">\\Delta E=E_{2}-E_{1}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.561ex\" height=\"1.959ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 6436.1 866\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 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<\/mrow>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>−<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>2<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mn>1<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.40<\/mn>\n <mo>+<\/mo>\n <mn>13.6<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(-13.6)\/(2^(2))-((-13.6)\/(1^(2)))=(-13.6)\/(4)+(13.6)\/(1)=-3.40+13.6<\/asciimath><latex style=\"display: none\">=\\frac{-13.6}{2^{2}}-\\left(\\frac{-13.6}{1^{2}}\\right)=\\frac{-13.6}{4}+\\frac{13.6}{1}=-3.40+13.6<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"48.32ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 21357.6 1799\" aria-hidden=\"true\"><g 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d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" 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-22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mn>2<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>\u2212<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><mn>4<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>13.6<\/mn><mn>1<\/mn><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mn>3.40<\/mn><mo>+<\/mo><mn>13.6<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1292 preview-line 1292\" data_line_start=\"1292\" data_line_end=\"1292\" data_line=\"1292,1293\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>10.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>10.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=10.2eV<\/asciimath><latex style=\"display: none\">=10.2 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.113ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4027.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2833.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>10.2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1294 preview-line 1294\" data_line_start=\"1294\" data_line_end=\"1294\" data_line=\"1294,1295\" count_line=\"1\">This transition lies in the region of Lyman series. (ii) (a) The energy levels of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>H<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">H<\/asciimath><latex style=\"display: none\">H<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: 0\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.009ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 888 683\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>-atom are given by <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mrow>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(n)=-(Rhc)\/(n^(2))=-(13.6)\/(n^(2))eV<\/asciimath><latex style=\"display: none\">E_{n}=-\\frac{R h c}{n^{2}}=-\\frac{13.6}{n^{2}} \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.662ex\" height=\"2.991ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 10016.8 1322.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" 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class=\"preview-paragraph-1296 preview-line 1296\" data_line_start=\"1296\" data_line_end=\"1296\" data_line=\"1296,1297\" count_line=\"1\">For first excited state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=2<\/asciimath><latex style=\"display: none\">n=2<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(877.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1933.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1298 preview-line 1298\" data_line_start=\"1298\" data_line_end=\"1298\" data_line=\"1298,1299\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>13.6<\/mn>\n <mrow>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n 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126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>13.6<\/mn><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mo>\u2212<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1300 preview-line 1300\" data_line_start=\"1300\" data_line_end=\"1300\" data_line=\"1300,1301\" count_line=\"1\">Kinetic energy of electron in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(n=2)<\/asciimath><latex style=\"display: none\">(n=2)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.266ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3211.6 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1266.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2322.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2822.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> state is<\/div>\n<div class=\"preview-paragraph-1302 preview-line 1302\" data_line_start=\"1302\" data_line_end=\"1302\" data_line=\"1302,1303\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>K<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>+<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">K_(2)=-E_(2)=+3.4eV<\/asciimath><latex style=\"display: none\">K_{2}=-E_{2}=+3.4 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.339ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.564ex\" height=\"1.885ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 9089.2 833\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 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566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(7895.2, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>K<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mo>+<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1304 preview-line 1304\" data_line_start=\"1304\" data_line_end=\"1304\" data_line=\"1304,1305\" count_line=\"1\">(b) Radius in the first excited state<\/div>\n<div class=\"preview-paragraph-1306 preview-line 1306\" data_line_start=\"1306\" data_line_end=\"1306\" data_line=\"1306,1307\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">(<\/mo>\n <mn>0.53<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mn>2<\/mn>\n <msup>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mo stretchy=\"false\">(<\/mo>\n <mn>0.53<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(1)=(2)^(2)(0.53)”\u212b”<\/asciimath><latex style=\"display: none\">r_{1}=(2)^{2}(0.53) \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.895ex\" height=\"2.452ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 7025.7 1083.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2188.1, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2577.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3077.1, 0)\"><g data-mml-node=\"mo\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(389, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3869.7, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4258.7, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(6036.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6425.7, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mrow><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>0.53<\/mn><mo stretchy=\"false\">)<\/mo><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1308 preview-line 1308\" data_line_start=\"1308\" data_line_end=\"1308\" data_line=\"1308,1309\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2.12<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2.12<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(1)=2.12″\u212b”<\/asciimath><latex style=\"display: none\">r_{1}=2.12 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.331ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 4566.1 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1132.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2188.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3966.1, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2.12<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"38\" class=\"preview-paragraph-1310 preview-line 1310 1311 1312 1313 1314 1315\" data_line_start=\"1310\" data_line_end=\"1315\" data_line=\"1310,1316\" count_line=\"6\">\n<li>\n<div>Refer to answer 19.<\/div>\n<\/li>\n<li>\n<div>Refer to answer 32.<\/div>\n<\/li>\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">hv=(hc)\/(lambda)=(E_(2)-E_(1))<\/asciimath><latex style=\"display: none\">h v=\\frac{h c}{\\lambda}=\\left(E_{2}-E_{1}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.8ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20.736ex\" height=\"2.801ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 9165.1 1238.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 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248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 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440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3894.6, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/((E_(2)-E_(1)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{\\left(E_{2}-E_{1}\\right)}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.238ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.473ex\" height=\"3.239ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 5071.2 1431.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(1220.6, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -370.3) scale(0.707)\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1530.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2308.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3450.1, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><rect width=\"2914.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1316 preview-line 1316\" data_line_start=\"1316\" data_line_end=\"1316\" data_line=\"1316,1317\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>−<\/mo>\n <mn>0.85<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mo stretchy=\"false\">[<\/mo>\n <mo>\u2212<\/mo>\n <mn>0.85<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.4<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo stretchy=\"false\">]<\/mo>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mrow>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad lambda=[(6.63 xx10^(-34)xx3xx10^(8))\/([-0.85-(-3.4)]xx1.6 xx10^(-19))]m<\/asciimath><latex style=\"display: none\">\\therefore \\quad \\lambda=\\left[\\frac{6.63 \\times 10^{-34} \\times 3 \\times 10^{8}}{[-0.85-(-3.4)] \\times 1.6 \\times 10^{-19}}\\right] \\mathrm{m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.469ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.734ex\" height=\"4.07ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1149.5 14468.3 1799\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" 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class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.875<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4875<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>4.875<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>4875<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=4.875 xx10^(-7)m=4875″\u212b”<\/asciimath><latex style=\"display: none\">=4.875 \\times 10^{-7} \\mathrm{~m}=4875 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.078ex\" height=\"2.423ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 11526.5 1071.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path 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9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(4556.2, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 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46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\"><\/path><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(7870.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(8926.5, 0)\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(10926.5, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>4.875<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>4875<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1320 preview-line 1320\" data_line_start=\"1320\" data_line_end=\"1320\" data_line=\"1320,1321\" count_line=\"1\">Balmer series<\/div>\n<ol start=\"41\" class=\"preview-paragraph-1322 preview-line 1322 1323\" data_line_start=\"1322\" data_line_end=\"1323\" data_line=\"1322,1324\" count_line=\"2\">\n<li>(i) The kinetic energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E_(k))<\/asciimath><latex style=\"display: none\">\\left(E_{k}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.376ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1934.4 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1545.4, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in an orbit is equal to negative of its total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1324 preview-line 1324\" data_line_start=\"1324\" data_line_end=\"1324\" data_line=\"1324,1325\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>k<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>1.5<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(k)=-E=-(-1.5)=1.5eV<\/asciimath><latex style=\"display: none\">E_{k}=-E=-(-1.5)=1.5 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"28.921ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12783.1 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 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data-mml-node=\"mn\" transform=\"translate(10311.1, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11589.1, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>k<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1.5<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1326 preview-line 1326\" data_line_start=\"1326\" data_line_end=\"1326\" data_line=\"1326,1327\" count_line=\"1\">(ii) The potential energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E_(p))<\/asciimath><latex style=\"display: none\">\\left(E_{p}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.348ex\" height=\"2.347ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1921.7 1037.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mrow\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"70\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1532.7, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> of the electron in an orbit is equal to twice of its total energy <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">(<\/mo>\n <mi>E<\/mi>\n <mo stretchy=\"false\">)<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(E)<\/asciimath><latex style=\"display: none\">(E)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.489ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 1542 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(389, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1153, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1328 preview-line 1328\" data_line_start=\"1328\" data_line_end=\"1328\" data_line=\"1328,1329\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>×<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>3.0<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>p<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u00d7<\/mo>\n <mn>2<\/mn>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>3.0<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(p)=2E=-1.5 xx2=-3.0eV<\/asciimath><latex style=\"display: none\">E_{p}=2 E=-1.5 \\times 2=-3.0 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.65ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.4ex\" height=\"2.195ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 13436.8 970.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 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d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4019, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 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95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(9131, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10186.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(10964.8, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(12242.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>p<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>3.0<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1330 preview-line 1330\" data_line_start=\"1330\" data_line_end=\"1330\" data_line=\"1330,1331\" count_line=\"1\">(iii) Here, ground state energy of the H-atom <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-13.6eV<\/asciimath><latex style=\"display: none\">=-13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.873ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 4805.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1833.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3611.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1332 preview-line 1332\" data_line_start=\"1332\" data_line_end=\"1332\" data_line=\"1332,1333\" count_line=\"1\">When the electron goes from the excited state to the ground state, energy emitted is given by<\/div>\n<div class=\"preview-paragraph-1334 preview-line 1334\" data_line_start=\"1334\" data_line_end=\"1334\" data_line=\"1334,1335\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>1.5<\/mn>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>1.5<\/mn>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=-1.5-(-13.6)=12.1eV=12.1 xx1.6 xx10^(-19)J<\/asciimath><latex style=\"display: none\">E=-1.5-(-13.6)=12.1 \\mathrm{eV}=12.1 \\times 1.6 \\times 10^{-19} \\mathrm{~J}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"51.858ex\" height=\"2.52ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 22921.2 1114\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2097.6, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 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313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8321, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8987.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 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18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(18849.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(19850, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(22157.2, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"4A\" d=\"M89 177Q115 177 133 160T152 112Q152 88 137 72T102 52Q99 51 101 49Q106 43 129 29Q159 15 190 15Q232 15 256 48T286 126Q286 127 286 142T286 183T286 238T287 306T287 378Q287 403 287 429T287 479T287 524T286 563T286 593T286 614V621Q281 630 263 633T182 637H154V683H166Q187 680 332 680Q439 680 457 683H465V637H449Q422 637 401 634Q393 631 389 623Q388 621 388 376T387 123Q377 61 322 20T194 -22Q188 -22 177 -21T160 -20Q96 -9 61 29T25 110Q25 144 44 160T89 177Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1.5<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>12.1<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>12.1<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1336 preview-line 1336\" data_line_start=\"1336\" data_line_end=\"1336\" data_line=\"1336,1337\" count_line=\"1\">Now, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>λ<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>\u03bb<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(hc)\/(lambda)<\/asciimath><latex style=\"display: none\">E=\\frac{h c}{\\lambda}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.8ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.355ex\" height=\"2.801ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3251 1238.2\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1041.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2097.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(576, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(370.6, -345) scale(0.707)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><rect width=\"913.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>\u03bb<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1338 preview-line 1338\" data_line_start=\"1338\" data_line_end=\"1338\" data_line=\"1338,1339\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <mi>E<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.62<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>12.1<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(hc)\/(E)=(6.62 xx10^(-34)xx3xx10^(8))\/(12.1 xx1.6 xx10^(-19))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h c}{E}=\\frac{6.62 \\times 10^{-34} \\times 3 \\times 10^{8}}{12.1 \\times 1.6 \\times 10^{-19}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.055ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"24.273ex\" height=\"3.341ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 10728.7 1476.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" 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552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><\/g><rect width=\"6085.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><mi>E<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.62<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>12.1<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1340 preview-line 1340\" data_line_start=\"1340\" data_line_end=\"1340\" data_line=\"1340,1341\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1.025<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1.025<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>7<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1.025 xx10^(-7)<\/asciimath><latex style=\"display: none\">\\lambda=1.025 \\times 10^{-7}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.676ex\" height=\"2.156ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -871.1 7370.7 953.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(778, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4416.8, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(5417, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1.025<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>7<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1342 preview-line 1342\" data_line_start=\"1342\" data_line_end=\"1342\" data_line=\"1342,1343\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mn>1025<\/mn>\n <mrow>\n <mtext>Å<\/mtext>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mn>1025<\/mn>\n <mrow>\n <mtext>\u212b<\/mtext>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=1025″\u212b”<\/asciimath><latex style=\"display: none\">\\lambda=1025 \\AA<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.452ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.218ex\" height=\"2.149ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 4516.6 950\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1916.6, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\" transform=\"translate(1500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3916.6, 0)\"><g data-mml-node=\"mtext\"><text data-variant=\"normal\" transform=\"matrix(1 0 0 -1 0 0)\" font-size=\"884px\" font-family=\"serif\">\u212b<\/text><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mn>1025<\/mn><mrow><mtext>\u212b<\/mtext><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"42\" class=\"preview-paragraph-1344 preview-line 1344 1345 1346 1347\" data_line_start=\"1344\" data_line_end=\"1347\" data_line=\"1344,1348\" count_line=\"4\">\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∵<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2235<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msubsup>\n <mrow>\n <mi>r<\/mi>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:'(mv^(2))\/(r_(n))=(1)\/(4piepsi_(0))(e^(2))\/(r_(n)^(2))<\/asciimath><latex style=\"display: none\">\\because \\frac{m v^{2}}{r_{n}}=\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.38ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.55ex\" height=\"3.605ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 6873.2 1593.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 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419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msubsup\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -247) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"854.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2235<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msubsup><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1348 preview-line 1348\" data_line_start=\"1348\" data_line_end=\"1348\" data_line=\"1348,1349\" count_line=\"1\">and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr_(n)=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r_{n}=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.071ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4893.4 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1363, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2566, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(257.5, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1031.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1350 preview-line 1350\" data_line_start=\"1350\" data_line_end=\"1350\" data_line=\"1350,1351\" count_line=\"1\">From eqn. (i) and (ii)<\/div>\n<div class=\"preview-paragraph-1352 preview-line 1352 1353 1354\" data_line_start=\"1352\" data_line_end=\"1354\" data_line=\"1352,1355\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quadr_(n)=(epsi_(0)h^(2)n^(2))\/(pi me^(2))<\/asciimath><latex style=\"display: none\">\\therefore \\quad r_{n}=\\frac{\\varepsilon_{0} h^{2} n^{2}}{\\pi m e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.96ex\" height=\"5.237ex\" 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357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3052.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>\u03c0<\/mi><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1356 preview-line 1356\" data_line_start=\"1356\" data_line_end=\"1356\" data_line=\"1356,1357\" count_line=\"1\">Total energy<\/div>\n<div class=\"preview-paragraph-1358 preview-line 1358 1359 1360 1361 1362 1363 1364\" data_line_start=\"1358\" data_line_end=\"1364\" data_line=\"1358,1365\" count_line=\"7\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msubsup>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd><\/mtd>\n <mtd>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\">\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mn>2<\/mn>\n <\/mfrac>\n <mi>m<\/mi>\n <msubsup>\n <mrow>\n <mi>v<\/mi>\n <\/mrow>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>4<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>\u03b5<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mrow>\n <\/mfrac>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <mtr>\n <mtd>\n <mrow>\n <mrow>\n <maligngroup\/>\n <\/mrow>\n <mrow>\n <maligngroup\/>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <\/mrow>\n <\/mrow>\n <\/mtd>\n <\/mtr>\n <\/mtable>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">{:[E_(n)=(1)\/(2)mv_(n)^(2)-(1)\/(4piepsi_(0))(e^(2))\/(r_(n))=(1)\/(8piepsi_(0))(e^(2))\/(r_(n))-(1)\/(4piepsi_(0))(e^(2))\/(r_(n))],[E_(n)=-(1)\/(8piepsi_(0))(e^(2))\/(r_(n))=-(1)\/(8epsi_(0)^(2))(me^(4))\/(h^(2)n^(2))],[E_(n)=(-Rhc)\/(n^(2))]:}<\/asciimath><latex style=\"display: none\">\\begin{aligned}\n&E_{n}=\\frac{1}{2} m v_{n}^{2}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}=\\frac{1}{8 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}-\\frac{1}{4 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}} \\\\\n&E_{n}=-\\frac{1}{8 \\pi \\varepsilon_{0}} \\frac{e^{2}}{r_{n}}=-\\frac{1}{8 \\varepsilon_{0}^{2}} \\frac{m e^{4}}{h^{2} n^{2}} \\\\\n&E_{n}=\\frac{-R h c}{n^{2}}\n\\end{aligned}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -8.203ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"46.009ex\" height=\"17.537ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -4125.8 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153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2545.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 676)\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(778, 0)\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1537, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2113, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(991.2, -793.9)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"2746\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\" columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" rowspacing=\"3pt\"><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>m<\/mi><msubsup><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><mi>\u03c0<\/mi><msub><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mfrac><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mrow><\/mfrac><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><msub><mi>E<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1366 preview-line 1366\" data_line_start=\"1366\" data_line_end=\"1366\" data_line=\"1366,1367\" count_line=\"1\">where Rydberg constant <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <mi>c<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>R<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <mi>c<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">R=(me^(4))\/(8epsi_(0)^(2)h^(3)c)<\/asciimath><latex style=\"display: none\">R=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{3} c}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.458ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.181ex\" height=\"3.696ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -989.2 4499.8 1633.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"52\" d=\"M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1036.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2092.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(585.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"38\" d=\"M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z\"><\/path><\/g><g data-mml-node=\"msubsup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3B5\" d=\"M190 -22Q124 -22 76 11T27 107Q27 174 97 232L107 239L99 248Q76 273 76 304Q76 364 144 408T290 452H302Q360 452 405 421Q428 405 428 392Q428 381 417 369T391 356Q382 356 371 365T338 383T283 392Q217 392 167 368T116 308Q116 289 133 272Q142 263 145 262T157 264Q188 278 238 278H243Q308 278 308 247Q308 206 223 206Q177 206 142 219L132 212Q68 169 68 112Q68 39 201 39Q253 39 286 49T328 72T345 94T362 105Q376 103 376 88Q376 79 365 62T334 26T275 -8T190 -22Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, -287.9) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1369.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(2349.1, 0)\"><path data-c=\"63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><rect width=\"2167.2\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><mi>c<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1368 preview-line 1368\" data_line_start=\"1368\" data_line_end=\"1368\" data_line=\"1368,1369\" count_line=\"1\">Energy emitted <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=E_(i)-E_(f)<\/asciimath><latex style=\"display: none\">\\Delta E=E_{i}-E_{f}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.393ex\" height=\"2.287ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 6361.9 1011\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2930.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 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634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><msub><mi>E<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1370 preview-line 1370 1371 1372\" data_line_start=\"1370\" data_line_end=\"1372\" data_line=\"1370,1373\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=Rhc[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))]<\/asciimath><latex style=\"display: none\">\\Delta E=R h c\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right]<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.646ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 10009.5 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 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scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><rect width=\"1203.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4727.9, 0)\"><path data-c=\"5D\" d=\"M5 1677V1750H313V-1249H5V-1176H240V1677H5Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mi>R<\/mi><mi>h<\/mi><mi>c<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1374 preview-line 1374\" data_line_start=\"1374\" data_line_end=\"1374\" data_line=\"1374,1375\" count_line=\"1\">But <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">Δ<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>h<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi mathvariant=\"normal\">\u0394<\/mi>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mi>h<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Delta E=hv<\/asciimath><latex style=\"display: none\">\\Delta E=h v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.031ex\" height=\"1.805ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 3991.6 798\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"394\" d=\"M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(833, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1874.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2930.6, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3506.6, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>E<\/mi><mo>=<\/mo><mi>h<\/mi><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1376 preview-line 1376 1377 1378\" data_line_start=\"1376\" data_line_end=\"1378\" data_line=\"1376,1379\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">[<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">]<\/mo>\n <\/mrow>\n <mtext> or <\/mtext>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mi>ε<\/mi>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo>−<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mi>R<\/mi>\n <mi>c<\/mi>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n <mtext>\u00a0or\u00a0<\/mtext>\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>4<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>8<\/mn>\n <msubsup>\n <mrow>\n <mi>\u03b5<\/mi>\n <\/mrow>\n <mrow>\n <mn>0<\/mn>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <mo>\u2212<\/mo> \n <mfrac>\n <mn>1<\/mn>\n <msubsup>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msubsup>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=Rc[(1)\/(n_(f)^(2))-(1)\/(n_(i)^(2))]” or “v=(me^(4))\/(8epsi_(0)^(2)h^(3))((1)\/(n_(f)^(2))-(1)\/(n_(i)^(2)))<\/asciimath><latex style=\"display: none\">v=R c\\left[\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right] \\text { or } v=\\frac{m e^{4}}{8 \\varepsilon_{0}^{2} h^{3}}\\left(\\frac{1}{n_{f}^{2}}-\\frac{1}{n_{i}^{2}}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.838ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"45.362ex\" height=\"6.796ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1749.5 20050 3003.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 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data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mtext>\u00a0or\u00a0<\/mtext><mi>v<\/mi><mo>=<\/mo><mfrac><mrow><mi>m<\/mi><msup><mi>e<\/mi><mrow><mn>4<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>8<\/mn><msubsup><mi>\u03b5<\/mi><mrow><mn>0<\/mn><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>h<\/mi><mrow><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msubsup><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msubsup><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1380 preview-line 1380\" data_line_start=\"1380\" data_line_end=\"1380\" data_line=\"1380,1381\" count_line=\"1\">When electron in hydrogen atom jumps from energy state <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>i<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>4<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(i)=4<\/asciimath><latex style=\"display: none\">n_{i}=4<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.171ex\" height=\"1.889ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -677 2727.5 834.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>i<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>4<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> to <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>n<\/mi>\n <mrow>\n <mi>f<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n_(f)=3,2,1<\/asciimath><latex style=\"display: none\">n_{f}=3,2,1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.667ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.773ex\" height=\"2.174ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 4761.8 961\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1316.7, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(2372.5, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2872.5, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(3317.1, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3817.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(4261.8, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>n<\/mi><mrow><mi>f<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>, the Paschen, Balmer and Lyman spectral series are found.<\/div>\n<ol start=\"44\" class=\"preview-paragraph-1382 preview-line 1382 1383 1384 1385 1386 1387\" data_line_start=\"1382\" data_line_end=\"1387\" data_line=\"1382,1388\" count_line=\"6\">\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div>Refer to answer 35.<\/div>\n<\/li>\n<li>\n<div>de-Broglie hypothesis : It states that a moving particle sometimes acts as a wave and sometimes as a particle or a wave is associated with moving particle which controls the particle in every respect. The wave associated with moving particle is called matter wave or de-Broglie wave whose wavelength is given by<\/div>\n<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1388 preview-line 1388\" data_line_start=\"1388\" data_line_end=\"1388\" data_line=\"1388,1389\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv)<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.512ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3320.3 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(498.2, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><rect width=\"1163.8\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1390 preview-line 1390\" data_line_start=\"1390\" data_line_end=\"1390\" data_line=\"1390,1391\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">m<\/asciimath><latex style=\"display: none\">m<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.986ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 878 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v<\/asciimath><latex style=\"display: none\">v<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.027ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 485 454\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> are the mass and velocity of the particle and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h<\/asciimath><latex style=\"display: none\">h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.303ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 576 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is Planck’s constant.<\/div>\n<ol start=\"47\" class=\"preview-paragraph-1392 preview-line 1392 1393\" data_line_start=\"1392\" data_line_end=\"1393\" data_line=\"1392,1394\" count_line=\"2\">\n<li>Kinetic energy of the electron in the second state of hydrogen atom<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1394 preview-line 1394\" data_line_start=\"1394\" data_line_end=\"1394\" data_line=\"1394,1395\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <\/mrow>\n <mn>4<\/mn>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(K)=(13.6eV)\/(n^(2))=(13.6eV)\/(4)=3.4 xx1.6 xx10^(-19)J<\/asciimath><latex style=\"display: none\">E_{K}=\\frac{13.6 \\mathrm{eV}}{n^{2}}=\\frac{13.6 \\mathrm{eV}}{4}=3.4 \\times 1.6 \\times 10^{-19} \\mathrm{~J}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"42.019ex\" height=\"2.974ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -877 18572.5 1314.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 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class=\"preview-paragraph-1396 preview-line 1396\" data_line_start=\"1396\" data_line_end=\"1396\" data_line=\"1396,1397\" count_line=\"1\">de Broglie wavelength <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(sqrt(2mE_(K)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{\\sqrt{2 m E_{K}}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.334ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.167ex\" height=\"3.335ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4935.8 1474.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 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-11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1378, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 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role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><msqrt><mn>2<\/mn><mi>m<\/mi><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><\/msqrt><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1398 preview-line 1398 1399 1400\" data_line_start=\"1398\" data_line_end=\"1400\" data_line=\"1398,1401\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(6.63 xx10^(-34))\/(sqrt(2xx9.1 xx10^(-31)xx3.4 xx1.6 xx10^(-19)))=0.67nm<\/asciimath><latex style=\"display: none\">=\\frac{6.63 \\times 10^{-34}}{\\sqrt{2 \\times 9.1 \\times 10^{-31} \\times 3.4 \\times 1.6 \\times 10^{-19}}}=0.67 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.76ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"50.514ex\" height=\"6.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1547.8 22327 2767.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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display=\"block\"><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><msqrt><mn>2<\/mn><mo>\u00d7<\/mo><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/msqrt><\/mfrac><mo>=<\/mo><mn>0.67<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"48\" class=\"preview-paragraph-1402 preview-line 1402 1403\" data_line_start=\"1402\" data_line_end=\"1403\" data_line=\"1402,1404\" count_line=\"2\">\n<li>According to Bohr’s postulates,<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1404 preview-line 1404 1405 1406\" data_line_start=\"1404\" data_line_end=\"1406\" data_line=\"1404,1407\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=(nh)\/(2pi)<\/asciimath><latex style=\"display: none\">m v r=\\frac{n h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.777ex\" 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17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(273, -686)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1376\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1408 preview-line 1408\" data_line_start=\"1408\" data_line_end=\"1408\" data_line=\"1408,1409\" count_line=\"1\">(where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mvr=<\/asciimath><latex style=\"display: none\">m v r=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.493ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 2869.8 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(878, 0)\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1363, 0)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2091.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> angular momentum of an electron and <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n<\/asciimath><latex style=\"display: none\">n<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is an integer).<\/div>\n<div class=\"preview-paragraph-1410 preview-line 1410\" data_line_start=\"1410\" data_line_end=\"1410\" data_line=\"1410,1411\" count_line=\"1\">Thus, the centripetal force, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.822ex\" height=\"3.024ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 1689.1 1336.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> (experienced by the electron) is due to the electrostatic attraction, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(kZe^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{k Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.377ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 1934.5 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1244, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(665.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1694.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Where, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>Z<\/mi>\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">Z=<\/asciimath><latex style=\"display: none\">Z=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.024ex\" height=\"1.731ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 1778.8 765\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1000.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Z<\/mi><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Atomic number<\/div>\n<div class=\"preview-paragraph-1412 preview-line 1412\" data_line_start=\"1412\" data_line_end=\"1412\" data_line=\"1412,1413\" count_line=\"1\">Therefore, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>m<\/mi>\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mi>r<\/mi>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(mv^(2))\/(r)=(kZe^(2))\/(r^(2))<\/asciimath><latex style=\"display: none\">\\frac{m v^{2}}{r}=\\frac{k Z e^{2}}{r^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.215ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4957.2 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(685.1, -345) scale(0.707)\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><rect width=\"1449.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(1966.9, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(3022.7, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(521, 0)\"><path data-c=\"5A\" d=\"M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(1244, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(665.1, -429.7) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"1694.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>m<\/mi><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mi>r<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1414 preview-line 1414\" data_line_start=\"1414\" data_line_end=\"1414\" data_line=\"1414,1415\" count_line=\"1\">Substituting the value of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>v<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v^(2)<\/asciimath><latex style=\"display: none\">v^{2}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.01ex\" height=\"1.912ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 888.6 844.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>v<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> from (i), we obtain:<\/div>\n<div class=\"preview-paragraph-1416 preview-line 1416 1417 1418\" data_line_start=\"1416\" data_line_end=\"1418\" data_line=\"1416,1419\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mfrac>\n <mi>m<\/mi>\n <mi>r<\/mi>\n <\/mfrac>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>m<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msup>\n <mi>r<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(m)\/(r)(n^(2)h^(2))\/(4pi^(2)m^(2)r^(2))=(kZe^(2))\/(r^(2))quad:.quad r=(n^(2)h^(2))\/(4pi^(2)mkZe^(2))<\/asciimath><latex style=\"display: none\">\\frac{m}{r} \\frac{n^{2} h^{2}}{4 \\pi^{2} m^{2} r^{2}}=\\frac{k Z e^{2}}{r^{2}} \\quad \\therefore \\quad r=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.821ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"43.364ex\" height=\"5.237ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1509.9 19167 2314.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mi\" transform=\"translate(220, 676)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 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x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mi>m<\/mi><mi>r<\/mi><\/mfrac><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>m<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><msup><mi>r<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>r<\/mi><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1420 preview-line 1420\" data_line_start=\"1420\" data_line_end=\"1420\" data_line=\"1420,1421\" count_line=\"1\">The relation for the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 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<mn>4<\/mn>\n <msup>\n <mi>π<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <msup>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>4<\/mn>\n <msup>\n <mi>\u03c0<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <mi>m<\/mi>\n <mi>k<\/mi>\n <mi>Z<\/mi>\n <msup>\n <mi>e<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(n^(2)h^(2))\/(4pi^(2)mkZe^(2))<\/asciimath><latex style=\"display: none\">=\\frac{n^{2} h^{2}}{4 \\pi^{2} m k Z e^{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.99ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.527ex\" height=\"3.215ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -983.7 4653.1 1421.1\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1055.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(1097.5, 394) scale(0.707)\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(1003.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(576, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"34\" d=\"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(500, 0)\"><g data-mml-node=\"mi\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 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data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2351.6, 0)\"><path data-c=\"6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 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448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 51Q452 60 500 100T579 247Q587 272 590 277T603 282H607Q628 282 628 271Q547 5 541 2Q538 0 300 0H124Q58 0 58 8Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(3595.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(466, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"3357.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><msup><mi>h<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>4<\/mn><msup><mi>\u03c0<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><mi>m<\/mi><mi>k<\/mi><mi>Z<\/mi><msup><mi>e<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/div>\n<ol start=\"49\" class=\"preview-paragraph-1422 preview-line 1422 1423\" data_line_start=\"1422\" data_line_end=\"1423\" data_line=\"1422,1424\" count_line=\"2\">\n<li>(i) Bohr’s quantization condition : The electron revolves around the nucleus only in those orbits for which the angular momentum is an integral multiple of <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h\/\/2pi<\/asciimath><latex style=\"display: none\">h \/ 2 \\pi<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.855ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 2146 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(576, 0)\"><g data-mml-node=\"mo\"><path data-c=\"2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1076, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1576, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><mrow><mo>\/<\/mo><\/mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span>.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1424 preview-line 1424 1425 1426\" data_line_start=\"1424\" data_line_end=\"1426\" data_line=\"1424,1427\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext> i.e., <\/mtext>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>…<\/mo>\n <mo>.<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mtext>\u00a0i.e.,\u00a0<\/mtext>\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>;<\/mo>\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n <mo>,<\/mo>\n <mn>2<\/mn>\n <mo>,<\/mo>\n <mn>3<\/mn>\n <mo>,<\/mo>\n <mo>\u2026<\/mo>\n <mo>.<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">” i.e., “L=mvr=n(h)\/(2pi);n=1,2,3,dots.<\/asciimath><latex style=\"display: none\">\\text { i.e., } L=m v r=n \\frac{h}{2 \\pi} ; n=1,2,3, \\ldots .<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.554ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 16157 2067\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><path data-c=\"69\" d=\"M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 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display=\"block\"><mtext>\u00a0i.e.,\u00a0<\/mtext><mi>L<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><mo>;<\/mo><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mn>3<\/mn><mo>,<\/mo><mo>\u2026<\/mo><mo>.<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1428 preview-line 1428\" data_line_start=\"1428\" data_line_end=\"1428\" data_line=\"1428,1429\" count_line=\"1\">de Broglie hypothesis may be used to derive Bohr’s formula by considering the electron to be a wave spread over the entire orbit, rather than as a particle which at any instant is located at a point in its orbit. The stable orbits in an atom are those which are standing waves. Formation of standing waves require that the circumference of the orbit is equal in length to an integral multiple of the wavelength. Thus, if <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>r<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r<\/asciimath><latex style=\"display: none\">r<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.02ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 451 453\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the radius of the orbit<\/div>\n<div class=\"preview-paragraph-1430 preview-line 1430 1431 1432\" data_line_start=\"1430\" data_line_end=\"1432\" data_line=\"1430,1433\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mi>p<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mo>∵<\/mo>\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>p<\/mi>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mi>p<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mo>\u2235<\/mo> \n <mi>\u03bb<\/mi> \n <mo>=<\/mo> \n <mfrac>\n <mi>h<\/mi>\n <mi>p<\/mi>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pi r=n lambda=(nh)\/(p)quad(:’lambda=(h)\/(p))<\/asciimath><latex style=\"display: none\">2 \\pi r=n \\lambda=\\frac{n h}{p} \\quad\\left(\\because \\lambda=\\frac{h}{p}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -2.148ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.173ex\" height=\"5.428ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1449.5 13336.4 2399\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 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-148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><\/g><rect width=\"776\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(4613.3, 0)\"><path data-c=\"29\" d=\"M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mn>2<\/mn><mi>\u03c0<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mi>p<\/mi><\/mfrac><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mo>\u2235<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mi>p<\/mi><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1434 preview-line 1434\" data_line_start=\"1434\" data_line_end=\"1434\" data_line=\"1434,1435\" count_line=\"1\">which gives the angular momentum quantization<\/div>\n<div class=\"preview-paragraph-1436 preview-line 1436 1437 1438\" data_line_start=\"1436\" data_line_end=\"1438\" data_line=\"1436,1439\" count_line=\"3\"><span class=\"math-block \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>p<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n <mi>L<\/mi>\n <mo>=<\/mo>\n <mi>p<\/mi>\n <mi>r<\/mi>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">L=pr=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">L=p r=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.577ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14.507ex\" height=\"4.676ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1370 6412.1 2067\" 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5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"1270\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>L<\/mi><mo>=<\/mo><mi>p<\/mi><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1441 preview-line 1441\" data_line_start=\"1441\" data_line_end=\"1441\" data_line=\"1441,1442\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=274&width=678&top_left_y=454&top_left_x=286\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1443 preview-line 1443\" data_line_start=\"1443\" data_line_end=\"1443\" data_line=\"1443,1444\" count_line=\"1\">(ii)<\/div>\n<div class=\"preview-paragraph-1445 preview-line 1445 1446\" data_line_start=\"1445\" data_line_end=\"1446\" data_line=\"1445,1447\" count_line=\"2\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=263&width=508&top_left_y=734&top_left_x=317\" alt=\"\"><br>\n<img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=542&width=648&top_left_y=454&top_left_x=316\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1448 preview-line 1448\" data_line_start=\"1448\" data_line_end=\"1448\" data_line=\"1448,1449\" count_line=\"1\">Clearly, from energy level diagram,<\/div>\n<div class=\"preview-paragraph-1450 preview-line 1450\" data_line_start=\"1450\" data_line_end=\"1450\" data_line=\"1450,1451\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n <mo>+<\/mo>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub>\n <mo>−<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub>\n <mo>\u2212<\/mo>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>C<\/mi>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n <mo>+<\/mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>B<\/mi>\n <\/mrow>\n <\/msub> \n <mo>\u2212<\/mo> \n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>A<\/mi>\n <\/mrow>\n <\/msub> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E_(C)-E_(A)=(E_(C)-E_(B))+(E_(B)-E_(A))<\/asciimath><latex style=\"display: none\">E_{C}-E_{A}=\\left(E_{C}-E_{B}\\right)+\\left(E_{B}-E_{A}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(389, 0)\"><g data-mml-node=\"mi\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 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61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 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0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -152.7) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"41\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4254.5, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>C<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>A<\/mi><\/mrow><\/msub><mo>=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>C<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>B<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>+<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msub><mi>E<\/mi><mrow><mi>B<\/mi><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>E<\/mi><mrow><mi>A<\/mi><\/mrow><\/msub><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1452 preview-line 1452\" data_line_start=\"1452\" data_line_end=\"1452\" data_line=\"1452,1453\" count_line=\"1\">(On the basis of energy of emitted photon).<\/div>\n<div class=\"preview-paragraph-1454 preview-line 1454\" data_line_start=\"1454\" data_line_end=\"1454\" data_line=\"1454,1455\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mrow>\n <mi>h<\/mi>\n <mi>c<\/mi>\n <\/mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">(hc)\/(lambda_(3))=(hc)\/(lambda_(1))+(hc)\/(lambda_(2))<\/asciimath><latex style=\"display: none\">\\frac{h c}{\\lambda_{3}}=\\frac{h c}{\\lambda_{1}}+\\frac{h c}{\\lambda_{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.612ex\" height=\"3.047ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6016.4 1346.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mfrac\"><g data-mml-node=\"mrow\" transform=\"translate(220, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 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-1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><rect width=\"913.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><g data-mml-node=\"mo\" transform=\"translate(3862.7, 0)\"><path data-c=\"2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4862.9, 0)\"><g 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394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/g><\/g><g data-mml-node=\"msub\" transform=\"translate(227.9, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(583, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><rect width=\"913.5\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>+<\/mo><mfrac><mrow><mi>h<\/mi><mi>c<\/mi><\/mrow><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1456 preview-line 1456\" data_line_start=\"1456\" data_line_end=\"1456\" data_line=\"1456,1457\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">⇒<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo stretchy=\"false\">⇒<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>λ<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo stretchy=\"false\">\u21d2<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo>+<\/mo>\n <mfrac>\n <mn>1<\/mn>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mfrac>\n <mo stretchy=\"false\">\u21d2<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>3<\/mn>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <mrow>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>1<\/mn>\n <\/mrow>\n <\/msub>\n <mo>+<\/mo>\n <msub>\n <mi>\u03bb<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=>(1)\/(lambda_(3))=(1)\/(lambda_(1))+(1)\/(lambda_(2))=>lambda_(3)=(lambda_(1)lambda_(2))\/(lambda_(1)+lambda_(2))<\/asciimath><latex style=\"display: none\">\\Rightarrow \\frac{1}{\\lambda_{3}}=\\frac{1}{\\lambda_{1}}+\\frac{1}{\\lambda_{2}} \\Rightarrow \\lambda_{3}=\\frac{\\lambda_{1} \\lambda_{2}}{\\lambda_{1}+\\lambda_{2}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.045ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"30.56ex\" height=\"3.165ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -936.8 13507.6 1398.9\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"21D2\" d=\"M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 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308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2145.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>3<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mrow><mrow><msub><mi>\u03bb<\/mi><mrow><mn>1<\/mn><\/mrow><\/msub><mo>+<\/mo><msub><mi>\u03bb<\/mi><mrow><mn>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1458 preview-line 1458\" data_line_start=\"1458\" data_line_end=\"1458\" data_line=\"1458,1459\" count_line=\"1\">which is the required relation between the three given wavelengths.<\/div>\n<ol start=\"50\" class=\"preview-paragraph-1460 preview-line 1460 1461\" data_line_start=\"1460\" data_line_end=\"1461\" data_line=\"1460,1462\" count_line=\"2\">\n<li>Kinetic energy in the first excited state of hydrogen atom<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1462 preview-line 1462\" data_line_start=\"1462\" data_line_end=\"1462\" data_line=\"1462,1463\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">J<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n <mo>=<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n 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317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(778, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(10556.4, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"><\/path><\/g><g data-mml-node=\"msup\" transform=\"translate(11556.6, 0)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" transform=\"translate(500, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(1000, 393.1) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mo\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(778, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(500, 0)\"><\/path><\/g><\/g><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13863.9, 0)\"><g data-mml-node=\"mtext\"><path data-c=\"A0\" d=\"\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(250, 0)\"><path data-c=\"4A\" d=\"M89 177Q115 177 133 160T152 112Q152 88 137 72T102 52Q99 51 101 49Q106 43 129 29Q159 15 190 15Q232 15 256 48T286 126Q286 127 286 142T286 183T286 238T287 306T287 378Q287 403 287 429T287 479T287 524T286 563T286 593T286 614V621Q281 630 263 633T182 637H154V683H166Q187 680 332 680Q439 680 457 683H465V637H449Q422 637 401 634Q393 631 389 623Q388 621 388 376T387 123Q377 61 322 20T194 -22Q188 -22 177 -21T160 -20Q96 -9 61 29T25 110Q25 144 44 160T89 177Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>3.4<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><mo>=<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">J<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1464 preview-line 1464\" data_line_start=\"1464\" data_line_end=\"1464\" data_line=\"1464,1465\" count_line=\"1\">De Broglie wavelength, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <msqrt>\n <mn>2<\/mn>\n <mi>m<\/mi>\n <msub>\n <mi>E<\/mi>\n <mrow>\n <mi>K<\/mi>\n <\/mrow>\n <\/msub>\n <\/msqrt>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(sqrt(2mE_(K)))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{\\sqrt{2 m E_{K}}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.334ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.167ex\" height=\"3.335ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4935.8 1474.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 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440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(738, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"4B\" d=\"M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z\"><\/path><\/g><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(0, 50.1)\"><path data-c=\"221A\" d=\"M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z\"><\/path><\/g><rect width=\"2794.6\" height=\"42.4\" x=\"853\" y=\"807.6\"><\/rect><\/g><rect width=\"2779.3\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><msqrt><mn>2<\/mn><mi>m<\/mi><msub><mi>E<\/mi><mrow><mi>K<\/mi><\/mrow><\/msub><\/msqrt><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1466 preview-line 1466\" data_line_start=\"1466\" data_line_end=\"1466\" data_line=\"1466,1467\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>×<\/mo>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>3.4<\/mn>\n <mo>×<\/mo>\n <mn>1.6<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <msqrt>\n <mn>2<\/mn>\n <mo>\u00d7<\/mo>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>3.4<\/mn>\n <mo>\u00d7<\/mo>\n <mn>1.6<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>19<\/mn>\n <\/mrow>\n <\/msup>\n <\/msqrt>\n <\/mfrac>\n <mo>=<\/mo>\n <mn>0.67<\/mn>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">n<\/mi>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=(6.63 xx10^(-34))\/(sqrt(2xx9.1 xx10^(-31)xx3.4 xx1.6 xx10^(-19)))=0.67nm<\/asciimath><latex style=\"display: none\">=\\frac{6.63 \\times 10^{-34}}{\\sqrt{2 \\times 9.1 \\times 10^{-31} \\times 3.4 \\times 1.6 \\times 10^{-19}}}=0.67 \\mathrm{~nm}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.654ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"36.303ex\" height=\"3.94ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -1010.4 16045.8 1741.4\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><msqrt><mn>2<\/mn><mo>\u00d7<\/mo><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>3.4<\/mn><mo>\u00d7<\/mo><mn>1.6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>19<\/mn><\/mrow><\/msup><\/msqrt><\/mfrac><mo>=<\/mo><mn>0.67<\/mn><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"51\" class=\"preview-paragraph-1468 preview-line 1468 1469\" data_line_start=\"1468\" data_line_end=\"1469\" data_line=\"1468,1470\" count_line=\"2\">\n<li><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>v<\/mi>\n <mo>=<\/mo>\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n <mrow>\n <mo>\/<\/mo>\n <\/mrow>\n <mrow>\n <mi mathvariant=\"normal\">s<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v=2.2 xx10^(8)m\/\/s<\/asciimath><latex style=\"display: none\">v=2.2 \\times 10^{8} \\mathrm{~m} \/ \\mathrm{s}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"17.42ex\" height=\"2.52ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -864 7699.6 1114\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(762.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 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transform=\"translate(7305.6, 0)\"><g data-mml-node=\"mi\"><path data-c=\"73\" d=\"M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mn>2.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><mrow><mtext>\u00a0<\/mtext><mi mathvariant=\"normal\">m<\/mi><\/mrow><mrow><mo>\/<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/li>\n<\/ol>\n<div class=\"preview-paragraph-1470 preview-line 1470\" data_line_start=\"1470\" data_line_end=\"1470\" data_line=\"1470,1471\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mo>?<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mo>?<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=?<\/asciimath><latex style=\"display: none\">\\lambda=?<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.776ex\" height=\"1.781ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 2110.8 787\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1638.8, 0)\"><path data-c=\"3F\" d=\"M226 668Q190 668 162 656T124 632L114 621Q116 621 119 620T130 616T145 607T157 591T162 567Q162 544 147 529T109 514T71 528T55 566Q55 625 100 661T199 704Q201 704 210 704T224 705H228Q281 705 320 692T378 656T407 612T416 567Q416 503 361 462Q267 395 247 303Q242 279 242 241V224Q242 205 239 202T222 198T205 201T202 218V249Q204 320 220 371T255 445T292 491T315 537Q317 546 317 574V587Q317 604 315 615T304 640T277 661T226 668ZM162 61Q162 89 180 105T224 121Q247 119 264 104T281 61Q281 31 264 16T222 1Q197 1 180 16T162 61Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mo>?<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1472 preview-line 1472\" data_line_start=\"1472\" data_line_end=\"1472\" data_line=\"1472,1473\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>P<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mi>P<\/mi>\n <\/mfrac>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>=<\/mo>\n <mi>m<\/mi>\n <mi>v<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(P)quad:.quad P=mv<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{P} \\quad \\therefore \\quad P=m v<\/latex><mjx-container 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367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(8194.7, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 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scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>P<\/mi><mo>=<\/mo><mi>m<\/mi><mi>v<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1474 preview-line 1474\" data_line_start=\"1474\" data_line_end=\"1474\" data_line=\"1474,1475\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>9.1<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>×<\/mo>\n <mn>2.2<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <mi>v<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mn>6.63<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>34<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <mrow>\n <mn>9.1<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>31<\/mn>\n <\/mrow>\n <\/msup>\n <mo>\u00d7<\/mo>\n <mn>2.2<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mn>8<\/mn>\n <\/mrow>\n <\/msup>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv)=(6.63 xx10^(-34))\/(9.1 xx10^(-31)xx2.2 xx10^(8))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v}=\\frac{6.63 \\times 10^{-34}}{9.1 \\times 10^{-31} \\times 2.2 \\times 10^{8}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><mi>v<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>6.63<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>34<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>9.1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo>\u2212<\/mo><mn>31<\/mn><\/mrow><\/msup><mo>\u00d7<\/mo><mn>2.2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mn>8<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1476 preview-line 1476\" data_line_start=\"1476\" data_line_end=\"1476\" data_line=\"1476,1477\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.331<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>3.3<\/mn>\n <mo>×<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>−<\/mo>\n <mn>12<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext> <\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>0.331<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>11<\/mn>\n <\/mrow>\n <\/msup>\n <mo>=<\/mo>\n <mn>3.3<\/mn>\n <mo>\u00d7<\/mo>\n <msup>\n <mn>10<\/mn>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>12<\/mn>\n <\/mrow>\n <\/msup>\n <mrow>\n <mtext><\/mtext>\n <mi mathvariant=\"normal\">m<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=0.331 xx10^(-11)=3.3 xx10^(-12)m<\/asciimath><latex style=\"display: none\">=0.331 \\times 10^{-11}=3.3 \\times 10^{-12} \\mathrm{~m}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" 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data_line_end=\"1479\" data_line=\"1478,1480\" count_line=\"2\">\n<li>According to Bohr’s second postulate quantization of angular momentum<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1480 preview-line 1480\" data_line_start=\"1480\" data_line_end=\"1480\" data_line=\"1480,1481\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv_(n)r_(n)=n(h)\/(2pi)<\/asciimath><latex style=\"display: none\">m v_{n} r_{n}=n \\frac{h}{2 \\pi}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"13.332ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 5892.7 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 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data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3040.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(4096.1, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4696.1, 0)\"><g data-mml-node=\"mi\" transform=\"translate(394.7, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><\/g><rect width=\"956.6\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1482 preview-line 1482\" data_line_start=\"1482\" data_line_end=\"1482\" data_line=\"1482,1483\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)=(nh)\/(2pi mv_(n))<\/asciimath><latex style=\"display: none\">r_{n}=\\frac{n h}{2 \\pi m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.757ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 4754.6 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1203, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(2258.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(832.1, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1948, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2255.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>h<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">h<\/asciimath><latex style=\"display: none\">h<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.303ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 576 705\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>h<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is the Planck’s constant<\/div>\n<div class=\"preview-paragraph-1484 preview-line 1484\" data_line_start=\"1484\" data_line_end=\"1484\" data_line=\"1484,1485\" count_line=\"1\">Circumference of the electron in the <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbital state in hydrogen atom,<\/div>\n<div class=\"preview-paragraph-1486 preview-line 1486\" data_line_start=\"1486\" data_line_end=\"1486\" data_line=\"1486,1487\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=2pi(nh)\/(2pi mv_(n))<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=2 \\pi \\frac{n h}{2 \\pi m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.599ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 6894.6 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 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331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path 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429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(4398.8, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(832.1, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 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186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1070, 0)\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1948, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"2255.7\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1488 preview-line 1488\" data_line_start=\"1488\" data_line_end=\"1488\" data_line=\"1488,1489\" count_line=\"1\">(Using (i))<\/div>\n<div class=\"preview-paragraph-1490 preview-line 1490\" data_line_start=\"1490\" data_line_end=\"1490\" data_line=\"1490,1491\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12.823ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 5668 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 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50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1492 preview-line 1492\" data_line_start=\"1492\" data_line_end=\"1492\" data_line=\"1492,1493\" count_line=\"1\">But de Broglie wavelength of the electron<\/div>\n<div class=\"preview-paragraph-1494 preview-line 1494\" data_line_start=\"1494\" data_line_end=\"1494\" data_line=\"1494,1495\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.271ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3655.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(665.9, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1496 preview-line 1496\" data_line_start=\"1496\" data_line_end=\"1496\" data_line=\"1496,1497\" count_line=\"1\">From (ii) and (iii), we get<\/div>\n<div class=\"preview-paragraph-1498 preview-line 1498\" data_line_start=\"1498\" data_line_end=\"1498\" data_line=\"1498,1499\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n lambda<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.208ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4511.8 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3328.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3928.8, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<ol start=\"53\" class=\"preview-paragraph-1500 preview-line 1500 1501\" data_line_start=\"1500\" data_line_end=\"1501\" data_line=\"1500,1502\" count_line=\"2\">\n<li>(a) According to de-Broglie, a stationary orbit is that which contains an integral number of de-Broglie waves associated with the revolving electron.<\/li>\n<\/ol>\n<div class=\"preview-paragraph-1502 preview-line 1502\" data_line_start=\"1502\" data_line_end=\"1502\" data_line=\"1502,1503\" count_line=\"1\">For an electron revolving in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> circular orbit of radius <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">r_(n)<\/asciimath><latex style=\"display: none\">r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.093ex\" height=\"1.357ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 925.3 599.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1504 preview-line 1504\" data_line_start=\"1504\" data_line_end=\"1504\" data_line=\"1504,1505\" count_line=\"1\">Total distance covered <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=<\/asciimath><latex style=\"display: none\">=<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.76ex\" height=\"1.505ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -583 778 665\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> Circumference of the orbit <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2pir_(n)<\/asciimath><latex style=\"display: none\">=2 \\pi r_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.903ex\" height=\"1.864ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 3051 823.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1555.8, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(2125.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1506 preview-line 1506\" data_line_start=\"1506\" data_line_end=\"1506\" data_line=\"1506,1507\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> For the permissible orbit, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>λ<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mi>\u03bb<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">2pir_(n)=n lambda<\/asciimath><latex style=\"display: none\">2 \\pi r_{n}=n \\lambda<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10.208ex\" height=\"1.927ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4511.8 851.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(500, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(1070, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2273, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3328.8, 0)\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3928.8, 0)\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mi>n<\/mi><mi>\u03bb<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1508 preview-line 1508\" data_line_start=\"1508\" data_line_end=\"1508\" data_line=\"1508,1509\" count_line=\"1\">According to de-Broglie,<\/div>\n<div class=\"preview-paragraph-1510 preview-line 1510\" data_line_start=\"1510\" data_line_end=\"1510\" data_line=\"1510,1511\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>λ<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>\u03bb<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">lambda=(h)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\lambda=\\frac{h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.271ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 3655.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"3BB\" d=\"M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(860.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(1916.6, 0)\"><g data-mml-node=\"mi\" transform=\"translate(665.9, 394) scale(0.707)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><\/g><g data-mml-node=\"mrow\" transform=\"translate(220, -345) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><mo>=<\/mo><mfrac><mi>h<\/mi><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1512 preview-line 1512\" data_line_start=\"1512\" data_line_end=\"1512\" data_line=\"1512,1513\" count_line=\"1\"><img decoding=\"async\" src=\"https:\/\/cdn.mathpix.com\/cropped\/2022_11_04_7c02328ee062eff9e768g-19.jpg?height=445&width=442&top_left_y=1391&top_left_x=1184\" alt=\"\"><\/div>\n<div class=\"preview-paragraph-1514 preview-line 1514\" data_line_start=\"1514\" data_line_end=\"1514\" data_line=\"1514,1515\" count_line=\"1\">where <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">v_(n)<\/asciimath><latex style=\"display: none\">v_{n}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.357ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.17ex\" height=\"1.359ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -443 959.3 600.8\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> is speed of electron revolving in <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th <\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mtext>th\u00a0<\/mtext>\n <\/mrow>\n <\/msup>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n^(“th “)<\/asciimath><latex style=\"display: none\">n^{\\text {th }}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.025ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"3.382ex\" height=\"1.956ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -853.7 1495 864.7\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msup\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(600, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mtext\"><path data-c=\"74\" d=\"M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z\"><\/path><path data-c=\"68\" d=\"M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z\" transform=\"translate(389, 0)\"><\/path><path data-c=\"A0\" d=\"\" transform=\"translate(945, 0)\"><\/path><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>n<\/mi><mrow><mtext>th\u00a0<\/mtext><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> orbit.<\/div>\n<div class=\"preview-paragraph-1516 preview-line 1516\" data_line_start=\"1516\" data_line_end=\"1516\" data_line=\"1516,1517\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <\/mrow>\n <\/mfrac>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad2pir_(n)=(nh)\/(mv_(n))<\/asciimath><latex style=\"display: none\">\\therefore \\quad 2 \\pi r_{n}=\\frac{n h}{m v_{n}}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -1.033ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.866ex\" height=\"3.035ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 7012.7 1341.3\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mn\" transform=\"translate(1944.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(2444.8, 0)\"><path data-c=\"3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(3014.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(451, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4217.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mfrac\" transform=\"translate(5273.6, 0)\"><g data-mml-node=\"mrow\" transform=\"translate(453.8, 394) scale(0.707)\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(600, 0)\"><path data-c=\"68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 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-11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><g data-mml-node=\"msub\" transform=\"translate(878, 0)\"><g data-mml-node=\"mi\"><path data-c=\"76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(485, -150) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><path data-c=\"6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/g><\/g><\/g><\/g><rect width=\"1499.1\" height=\"60\" x=\"120\" y=\"220\"><\/rect><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mn>2<\/mn><mi>\u03c0<\/mi><msub><mi>r<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mi>h<\/mi><\/mrow><mrow><mi>m<\/mi><msub><mi>v<\/mi><mrow><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1518 preview-line 1518\" data_line_start=\"1518\" data_line_end=\"1518\" data_line=\"1518,1519\" count_line=\"1\">or <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mrow data-mjx-texclass=\"INNER\">\n <mo data-mjx-texclass=\"OPEN\">(<\/mo>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>π<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo data-mjx-texclass=\"CLOSE\">)<\/mo>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>m<\/mi>\n <msub>\n <mi>v<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <msub>\n <mi>r<\/mi>\n <mrow>\n <mi>n<\/mi>\n <\/mrow>\n <\/msub>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mi>n<\/mi>\n <mi>h<\/mi>\n <\/mrow>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac>\n <mo>=<\/mo>\n <mi>n<\/mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mfrac>\n <mi>h<\/mi>\n <mrow>\n <mn>2<\/mn>\n <mi>\u03c0<\/mi>\n <\/mrow>\n <\/mfrac> \n <\/mrow> \n <\/mfenced>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">mv_(n)r_(n)=(nh)\/(2pi)=n((h)\/(2pi))<\/asciimath><latex style=\"display: none\">m v_{n} r_{n}=\\frac{n h}{2 \\pi}=n\\left(\\frac{h}{2 \\pi}\\right)<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.798ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"21.298ex\" height=\"2.8ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -884.7 9413.8 1237.5\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 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preview-line 1520\" data_line_start=\"1520\" data_line_end=\"1520\" data_line=\"1520,1521\" count_line=\"1\">(b) For ground state, <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>n<\/mi>\n <mo>=<\/mo>\n <mn>1<\/mn>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">n=1<\/asciimath><latex style=\"display: none\">n=1<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.506ex\" height=\"1.692ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 2433.6 748\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g 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556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><mo>=<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1522 preview-line 1522\" data_line_start=\"1522\" data_line_end=\"1522\" data_line=\"1522,1523\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mi>n<\/mi>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mfrac>\n <mrow>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <\/mrow>\n <msup>\n <mn>1<\/mn>\n <mrow>\n <mn>2<\/mn>\n <\/mrow>\n <\/msup>\n <\/mfrac>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">E=(-13.6)\/(n^(2))=(-13.6)\/(1^(2))=-13.6eV<\/asciimath><latex style=\"display: none\">E=\\frac{-13.6}{n^{2}}=\\frac{-13.6}{1^{2}}=-13.6 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433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><\/g><g data-mml-node=\"msup\" transform=\"translate(804.2, -429.7) scale(0.707)\"><g data-mml-node=\"mn\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/g><g data-mml-node=\"TeXAtom\" transform=\"translate(500, 363) scale(0.707)\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mn\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 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556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11815.4, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mi>n<\/mi><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mfrac><mrow><mo>\u2212<\/mo><mn>13.6<\/mn><\/mrow><msup><mn>1<\/mn><mrow><mn>2<\/mn><\/mrow><\/msup><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1524 preview-line 1524\" data_line_start=\"1524\" data_line_end=\"1524\" data_line=\"1524,1525\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad<\/asciimath><latex style=\"display: none\">\\therefore \\quad<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> K.E. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mi>E<\/mi>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mn>13.6<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=-E=-(-13.6)=13.6eV<\/asciimath><latex style=\"display: none\">=-E=-(-13.6)=13.6 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"27.939ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 12348.9 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(1055.8, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1833.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2875.6, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3931.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4709.3, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(5098.3, 0)\"><path data-c=\"2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(5876.3, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(7654.3, 0)\"><path data-c=\"29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(8321.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(9376.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(11154.9, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 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<mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>∵<\/mo>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mo>\u2235<\/mo>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">quad:’<\/asciimath><latex style=\"display: none\">\\quad \\because<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.4ex\" height=\"1.251ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -471 1944.8 553\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mstyle\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1277.8, 0)\"><path data-c=\"2235\" d=\"M23 411Q23 437 41 454T84 471Q108 471 125 454T143 411T126 368T83 351Q57 351 40 368T23 411ZM523 411Q523 437 541 454T584 471Q608 471 625 454T643 411T626 368T583 351Q557 351 540 368T523 411ZM274 -22Q274 4 291 21T334 38Q356 38 374 22T392 -22T375 -65T333 -82Q307 -82 291 -65T274 -22Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mo>\u2235<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/span> P.E. <span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mi>E<\/mi>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">=2E<\/asciimath><latex style=\"display: none\">=2 E<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.186ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.248ex\" height=\"1.724ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -680 2319.8 762\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><\/g><g data-mml-node=\"mn\" transform=\"translate(1055.8, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(1555.8, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mn>2<\/mn><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n<div class=\"preview-paragraph-1528 preview-line 1528\" data_line_start=\"1528\" data_line_end=\"1528\" data_line=\"1528,1529\" count_line=\"1\"><span class=\"math-inline \"><mathml style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>∴<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>.<\/mo>\n <mi>E<\/mi>\n <mo>.<\/mo>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mo>−<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>−<\/mo>\n <mn>27.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathml><mathmlword style=\"display: none\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mo>\u2234<\/mo>\n <mstyle scriptlevel=\"0\">\n <mspace width=\"1em\"><\/mspace>\n <\/mstyle>\n <mi>P<\/mi>\n <mo>.<\/mo>\n <mi>E<\/mi>\n <mo>.<\/mo>\n <mo>=<\/mo>\n <mn>2<\/mn>\n <mo stretchy=\"false\">(<\/mo>\n <mo>\u2212<\/mo>\n <mn>13.6<\/mn>\n <mo stretchy=\"false\">)<\/mo>\n <mo>=<\/mo>\n <mo>\u2212<\/mo>\n <mn>27.2<\/mn>\n <mrow>\n <mi mathvariant=\"normal\">e<\/mi>\n <mi mathvariant=\"normal\">V<\/mi>\n <\/mrow>\n<\/math><\/mathmlword><asciimath style=\"display: none;\">:.quad P.E.=2(-13.6)=-27.2eV<\/asciimath><latex style=\"display: none\">\\therefore \\quad P . E .=2(-13.6)=-27.2 \\mathrm{eV}<\/latex><mjx-container class=\"MathJax\" jax=\"SVG\" role=\"presentation\" style=\"position: relative\"><svg style=\"vertical-align: -0.566ex\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"32.404ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 14322.4 1000\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\"><path data-c=\"2234\" d=\"M273 411Q273 437 291 454T334 471Q358 471 375 454T393 411T376 368T333 351Q307 351 290 368T273 411ZM84 38Q110 38 126 21T143 -22Q143 -46 127 -64T83 -82Q57 -82 41 -65T24 -22Q24 4 41 21T84 38ZM524 -22Q524 4 541 21T584 38Q608 38 625 21T643 -22Q643 -45 627 -63T583 -82Q557 -82 541 -65T524 -22Z\"><\/path><\/g><g data-mml-node=\"mstyle\" transform=\"translate(944.8, 0)\"><g data-mml-node=\"mspace\"><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(1944.8, 0)\"><path data-c=\"50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(2695.8, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(3140.4, 0)\"><path data-c=\"45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(3904.4, 0)\"><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><\/g><g data-mml-node=\"mo\" transform=\"translate(4349.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 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385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path data-c=\"37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\" transform=\"translate(500, 0)\"><\/path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(1000, 0)\"><\/path><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\" transform=\"translate(1278, 0)\"><\/path><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(13128.4, 0)\"><g data-mml-node=\"mi\"><path data-c=\"65\" d=\"M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z\"><\/path><\/g><g data-mml-node=\"mi\" transform=\"translate(444, 0)\"><path data-c=\"56\" d=\"M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z\"><\/path><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml role=\"presentation\" unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"><\/mspace><\/mstyle><mi>P<\/mi><mo>.<\/mo><mi>E<\/mi><mo>.<\/mo><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>13.6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>27.2<\/mn><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/span><\/div>\n\n <\/div>\n <\/div>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Atoms Atoms 12.2 Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom 12.3 Atomic Spectra 12.4 Bohr Model of the Hydrogen Atom 12.5 The Line Spectra of the Hydrogen Atom 12.6 De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation Topicwise Analysis of Last 10 Years’ CBSE Board Questions (2016-2007) M Maximum weightage is of Bohr … <a title=\"Atoms\" class=\"read-more\" href=\"https:\/\/successrouter.com\/articles\/atoms\/\" aria-label=\"More on Atoms\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260"}],"collection":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/comments?post=260"}],"version-history":[{"count":2,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260\/revisions"}],"predecessor-version":[{"id":262,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/260\/revisions\/262"}],"wp:attachment":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/media?parent=260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/categories?post=260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/tags?post=260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}