{"id":1896,"date":"2026-09-27T19:22:22","date_gmt":"2026-09-27T10:22:22","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=1896"},"modified":"2026-09-27T19:22:23","modified_gmt":"2026-09-27T10:22:23","slug":"post-1896","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=1896","title":{"rendered":"\u30dc\u30fc\u30a2\u306e\u539f\u5b50\u6a21\u578b"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_88 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E3%83%90%E3%83%AB%E3%83%9E%E3%83%BC%E3%81%AE%E5%85%AC%E5%BC%8F\" >\u30d0\u30eb\u30de\u30fc\u306e\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E3%83%AA%E3%83%A5%E3%83%BC%E3%83%89%E3%83%99%E3%83%AA%E3%81%AE%E5%85%AC%E5%BC%8F\" >\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u306e\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E3%83%9C%E3%83%BC%E3%82%A2%E3%81%AE%E5%8E%9F%E5%AD%90%E6%A8%A1%E5%9E%8B\" >\u30dc\u30fc\u30a2\u306e\u539f\u5b50\u6a21\u578b<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E5%89%8D%E6%8F%90%E6%9D%A1%E4%BB%B6\" >\u524d\u63d0\u6761\u4ef6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E6%B0%B4%E7%B4%A0%E5%8E%9F%E5%AD%90%E3%81%AE%E4%BE%8B\" >\u6c34\u7d20\u539f\u5b50\u306e\u4f8b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/daba-no-heya.com\/?p=1896\/#%E3%83%9C%E3%83%BC%E3%82%A2%E3%81%AE%E9%87%8F%E5%AD%90%E6%9D%A1%E4%BB%B6\" >\u30dc\u30fc\u30a2\u306e\u91cf\u5b50\u6761\u4ef6<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%90%E3%83%AB%E3%83%9E%E3%83%BC%E3%81%AE%E5%85%AC%E5%BC%8F\"><\/span>\u30d0\u30eb\u30de\u30fc\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c34\u7d20\u539f\u5b50\u304c\u653e\u51fa\u3059\u308b\u5149\u306e\u6ce2\u9577\u306b\u3064\u3044\u3066\u3001\u53ef\u8996\u5149\u7dda\u306e4\u672c\u306e\u7dda\u30b9\u30da\u30af\u30c8\u30eb\u306e\u6ce2\u9577\u306f\u4ee5\u4e0b\u306e\u898f\u5247\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\lambda_n=364.56\\frac{n^2}{n^2-4}\\space \\text{nm}\\quad(n=3,4,5,6)\n<br>$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%AA%E3%83%A5%E3%83%BC%E3%83%89%E3%83%99%E3%83%AA%E3%81%AE%E5%85%AC%E5%BC%8F\"><\/span>\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ce2\u9577\u306e\u9006\u6570\u3092\u7528\u3044\u308b\u3068\u3001\u6c34\u7d20\u539f\u5b50\u306e\u7dda\u30b9\u30da\u30af\u30c8\u30eb\u3092\u5c11\u6570\u306e\u9805\u3067\u8aac\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\frac{1}{\\lambda_n}=R_H\\left( \\frac{1}{n&#8217;^2}-\\frac{1}{n^2} \\right)\n\\quad\n\\begin{cases}\nn&#8217;&amp;=1,2,3,\\dots \\\\\nn&amp;=n&#8217;+1,n&#8217;+2,\\dots\n\\end{cases}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u3001$R_H$\u306f\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u5b9a\u6570\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d0\u30eb\u30de\u30fc\u306e\u516c\u5f0f\u306f\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u306e\u516c\u5f0f\u306e\u7279\u5225\u306a\u5834\u5408\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<br>\u30d0\u30eb\u30de\u30fc\u306e\u516c\u5f0f\u3067\u4e21\u8fba\u306e\u9006\u6570\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\n\\frac{1}{\\lambda_n}&amp;=\\frac{1}{364.56}\\frac{n^2-4}{n^2} \\\\\n&amp;=\\frac{1}{364.56}\\left( 1-\\frac{4}{n^2} \\right) \\\\\n&amp;=\\frac{1}{364.56}\\cdot 4\\left( \\frac{1}{4}-\\frac{1}{n^2} \\right) \\\\\n&amp;=\\frac{1}{364.56}\\left( \\frac{1}{2^2}-\\frac{1}{n^2} \\right)\n\\end{align}\n<br>$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%9C%E3%83%BC%E3%82%A2%E3%81%AE%E5%8E%9F%E5%AD%90%E6%A8%A1%E5%9E%8B\"><\/span>\u30dc\u30fc\u30a2\u306e\u539f\u5b50\u6a21\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%89%8D%E6%8F%90%E6%9D%A1%E4%BB%B6\"><\/span>\u524d\u63d0\u6761\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u539f\u5b50\u306f\u6570\u591a\u304f\u306e\u5b9a\u5e38\u72b6\u614b(stationary state)\u3092\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<br>\u5b9a\u5e38\u72b6\u614b\u306b\u304a\u3044\u3066\u306f\u3001\u96fb\u5b50\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u306b\u5f93\u3063\u3066\u8ecc\u9053\u904b\u52d5\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u539f\u5b50\u304c\u3042\u308b\u5b9a\u5e38\u72b6\u614b\u304b\u3089\u5225\u306e\u5b9a\u5e38\u72b6\u614b\u306b\u79fb\u308b\u3053\u3068\u306f\u3001\u96fb\u5b50\u304c\u4e00\u3064\u306e\u8ecc\u9053\u304b\u3089\u5225\u306e\u8ecc\u9053\u306b\u79fb\u308b(\u9077\u79fb(transition))\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u3066\u8d77\u3053\u308b\u3002<br>\u305d\u306e\u3068\u304d\u4e00\u3064\u306e\u5149\u5b50\u304c\u653e\u51fa\u3055\u308c\u308b\u3002<br>\u5149\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u539f\u5b50\u306e\u4e8c\u3064\u306e\u5b9a\u5e38\u72b6\u614b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5dee\u306b\u7b49\u3057\u304f\u3001\u632f\u52d5\u6570\u306f$E=h\\nu$\u3067\u6c7a\u307e\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%B0%B4%E7%B4%A0%E5%8E%9F%E5%AD%90%E3%81%AE%E4%BE%8B\"><\/span>\u6c34\u7d20\u539f\u5b50\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"305\" src=\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2026\/09\/\u6c34\u7d20\u539f\u5b50.png\" alt=\"\" class=\"wp-image-1900\" srcset=\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2026\/09\/\u6c34\u7d20\u539f\u5b50.png 345w, https:\/\/daba-no-heya.com\/wp-content\/uploads\/2026\/09\/\u6c34\u7d20\u539f\u5b50-300x265.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">\u96fb\u5b50\u306b\u4f5c\u7528\u3059\u308b\u529b\u306f\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\nF=ma=\\frac{mv^2}{r}=\\frac{e^2}{4\\pi\\epsilon_0 r^2}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\epsilon_0$\u306f\u771f\u7a7a\u306e\u8a98\u96fb\u7387\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u529b\u306e\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb$U(r)$\u306f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\nU(r)=-\\frac{e^2}{4\\pi\\epsilon_0}\\frac{1}{r}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u306e\u3067\u3001\u96fb\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\nE&amp;=\\frac{1}{2}mv^2-\\frac{e^2}{4\\pi\\epsilon_0 r} \\\\\n&amp;=\\frac{e^2}{8\\pi\\epsilon_0 r}-\\frac{e^2}{4\\pi\\epsilon_0 r} \\\\\n&amp;=-\\frac{e^2}{8\\pi\\epsilon_0 r}\n\\end{align}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c34\u7d20\u539f\u5b50\u304c\u3042\u308b\u6c7a\u307e\u3063\u305f\u6ce2\u9577\u306e\u5149\u3060\u3051\u3092\u653e\u51fa\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u304b\u3089\u3001\u539f\u5b50\u306e\u4e2d\u306e\u96fb\u5b50\u306b\u5bfe\u3057\u3066\u3001\u4e0d\u9023\u7d9a\u306a\u7279\u5b9a\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u3082\u3064\u8ecc\u9053\u3060\u3051\u304c\u8a31\u3055\u308c\u308b\u3068\u8003\u3048\u307e\u3059\u3002<br>\u6c34\u7d20\u539f\u5b50\u306e\u30b9\u30da\u30af\u30c8\u30eb\u9805\u3092\u533a\u5225\u3059\u308b$n$\u306b\u5bfe\u5fdc\u3057\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u72b6\u614b\u306b\u5236\u9650\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$n=1$\u306f\u6700\u5c0f\u306e\u8ecc\u9053\u534a\u5f84\u3092\u3082\u3064\u6700\u3082\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u4f4e\u3044\u72b6\u614b<\/li>\n\n\n\n<li>$n=2$\u306f\u6b21\u306b\u5c0f\u3055\u3044\u8ecc\u9053\u534a\u5f84\u3092\u3082\u30642\u756a\u76ee\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u4f4e\u3044\u72b6\u614b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">$n=n_i$\u304b\u3089$n=n_f$ ($n_i &gt; n_f$)\u3078\u96fb\u5b50\u304c\u79fb\u308b\u3068\u304d\u3001\u5149\u5b50\u304c\u4e00\u500b\u653e\u51fa\u3055\u308c\u3001\u305d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u4e8c\u3064\u306e\u8ecc\u9053\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5dee\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\nE&amp;=\\frac{hc}{\\lambda} \\\\\n&amp;=E_i-E_f \\\\\n&amp;=-\\frac{e^2}{8\\pi\\epsilon_0}\\left( \\frac{1}{r_i}-\\frac{1}{r_f} \\right) \\\\\n&amp;=\\frac{e^2}{8\\pi\\epsilon_0}\\left( \\frac{1}{r_f}-\\frac{1}{r_i} \\right)\n\\end{align}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ecc\u9053\u534a\u5f84\u304c$n^2$\u306b\u6bd4\u4f8b\u3059\u308b\u306a\u3089\u3001\u5149\u5b50\u306e\u6ce2\u9577\u306e\u9006\u6570\u3092<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\frac{1}{\\lambda_n}=R_H\\left( \\frac{1}{n&#8217;^2}-\\frac{1}{n^2} \\right)\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306e\u5f62\u3067\u8868\u305b\u308b\u306e\u3067\u3001$r_n=a_Bn^2\\quad(n=1,2,3,\\dots)$\u3068\u3057\u307e\u3059\u3002<br>$a_B$\u306f\u6700\u5c0f\u306e\u8ecc\u9053\u534a\u5f84\u3067\u3001\u30dc\u30fc\u30a2\u534a\u5f84(Bohr radius)\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\nE&amp;=\\frac{hc}{\\lambda_n} \\\\\n&amp;=\\frac{e^2}{8\\pi\\epsilon_0}\\left( \\frac{1}{r_f}-\\frac{1}{r_i} \\right) \\\\\n&amp;=\\frac{e^2}{8\\pi\\epsilon_0 a_B}\\left( \\frac{1}{n_f^2}-\\frac{1}{n_i^2} \\right) \\\\\n\\end{align}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\frac{1}{\\lambda_n}=\\frac{e^2}{8\\pi\\epsilon_0hca_B}\\left( \\frac{1}{n_f^2}-\\frac{1}{n_i^2} \\right)\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u5b9a\u6570$R_H$\u306f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>R_H=\\frac{e^2}{8\\pi\\epsilon_0hca_B}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%9C%E3%83%BC%E3%82%A2%E3%81%AE%E9%87%8F%E5%AD%90%E6%9D%A1%E4%BB%B6\"><\/span>\u30dc\u30fc\u30a2\u306e\u91cf\u5b50\u6761\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30dc\u30fc\u30a2\u534a\u5f84$a_B$\u304c\u672a\u77e5\u306e\u5024\u306a\u306e\u3067\u3001\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u5b9a\u6570$R_H$\u306e\u5024\u306f\u307e\u3060\u308f\u304b\u308a\u307e\u305b\u3093\u3002<br>\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u5b9a\u6570\u3092\u6c42\u3081\u308b\u305f\u3081\u3001\u3082\u3046\u4e00\u3064\u524d\u63d0\u6761\u4ef6\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u96fb\u5b50\u304c\u8ecc\u9053\u3092\u4e00\u5468\u3059\u308b\u524d\u3068\u5f8c\u3067\u4f4d\u76f8\u304c\u540c\u3058\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<br>\u3064\u307e\u308a\u3001\u8ecc\u9053\u306e\u4e00\u5468\u306e\u9577\u3055\u304c\u3001\u30c9\u30fb\u30d6\u30ed\u30a4\u6ce2\u306e\u6ce2\u9577$\\lambda=\\frac{h}{mv}$\u306e\u6574\u6570\u500d\u306b\u306a\u3063\u3066\u3044\u308b\u3082\u306e\u3068\u3057\u307e\u3059\u3002<br>\u96fb\u5b50\u304c\u4e00\u5468\u3059\u308b\u524d\u3068\u5f8c\u3067\u4f4d\u76f8\u304c\u305a\u308c\u3066\u3044\u308b\u3068\u6253\u3061\u6d88\u3057\u5408\u3063\u3066\u3057\u307e\u3046\u305f\u3081\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$2\\pi r=n\\lambda=n\\frac{h}{mv}$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>mvr=\\frac{nh}{2\\pi}=n\\hbar<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3088\u308a\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>v=\\frac{n\\hbar}{mr}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u96fb\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3088\u308a\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\n&amp;\\frac{mv^2}{r}=\\frac{e^2}{4\\pi\\epsilon_0r^2} \\\\\n&amp;\\frac{m}{r_n}\\left( \\frac{n\\hbar}{mr_n} \\right)^2=\\frac{e^2}{4\\pi\\epsilon_0r_n^2} \\\\\n&amp;\\frac{n^2\\hbar^2}{r_nm}=\\frac{e^2}{4\\pi\\epsilon_0} \\\\\n&amp;\\frac{e^2}{4\\pi\\epsilon_0}r_n=\\frac{n^2\\hbar^2}{m} \\\\\n&amp;r_n=\\frac{n^2\\hbar^2}{m}\\frac{4\\pi\\epsilon_0}{e^2}=\\frac{n^2h^2\\epsilon_0}{\\pi me^2}\n\\end{align}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u305f\u304c\u3063\u3066\u3001\u30dc\u30fc\u30a2\u534a\u5f84$r_1$\u306f\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\nr_1=\\frac{h^2\\epsilon_0}{\\pi me^2}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0a\u3088\u308a\u3001\u30ea\u30e5\u30fc\u30c9\u30d9\u30ea\u5b9a\u6570$R_H$\u306f\u3001<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\n\\begin{align}\nR_H&amp;=\\frac{e^2}{8\\pi\\epsilon_0hc}\\cdot\\frac{\\pi me^2}{h^2\\epsilon_0} \\\\\n&amp;=\\frac{me^4}{8\\epsilon_0^2h^3c} \\\\\n&#038;\\approx 1.10\\times10^7\\space\\text{m}^{-1}\n\\end{align}\n<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30d0\u30eb\u30de\u30fc\u306e\u516c\u5f0f \u6c34\u7d20\u539f\u5b50\u304c\u653e\u51fa\u3059\u308b\u5149\u306e\u6ce2\u9577\u306b\u3064\u3044\u3066\u3001\u53ef\u8996\u5149\u7dda\u306e4\u672c\u306e\u7dda\u30b9\u30da\u30af\u30c8\u30eb\u306e\u6ce2\u9577\u306f\u4ee5\u4e0b\u306e\u898f\u5247\u306b\u5f93\u3044\u307e\u3059\u3002 $$ \\lambda_n=364.56\\frac{n^2}{n^2-4}\\space \\text{nm}\\q [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36],"tags":[],"class_list":["post-1896","post","type-post","status-publish","format-standard","hentry","category-36"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1896","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1896"}],"version-history":[{"count":9,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1896\/revisions"}],"predecessor-version":[{"id":1906,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1896\/revisions\/1906"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}