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class="vector-toc-link" href="#Tingkatan_energi_elektron_dalam_atom_hidrogen"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tingkatan energi elektron dalam atom hidrogen</span> </div> </a> <ul id="toc-Tingkatan_energi_elektron_dalam_atom_hidrogen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pranala_luar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pranala_luar"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Pranala luar</span> </div> </a> <ul id="toc-Pranala_luar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-(Indonesia)_Teori_Atom_Bohr" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#(Indonesia)_Teori_Atom_Bohr"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span><span>(Indonesia)</span> Teori Atom Bohr</span> </div> </a> <ul id="toc-(Indonesia)_Teori_Atom_Bohr-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Daftar isi" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Gulingkan daftar isi" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Gulingkan daftar isi</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Model Bohr</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Pergi ke artikel dalam bahasa lain. Terdapat 69 bahasa" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-69" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">69 bahasa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Bohrsches_Atommodell" title="Bohrsches Atommodell – Jerman (Swiss)" lang="gsw" hreflang="gsw" data-title="Bohrsches Atommodell" data-language-autonym="Alemannisch" data-language-local-name="Jerman (Swiss)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Modelo_atomico_de_Bohr" title="Modelo atomico de Bohr – Aragon" lang="an" hreflang="an" data-title="Modelo atomico de Bohr" data-language-autonym="Aragonés" data-language-local-name="Aragon" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%85%D9%88%D8%B0%D8%AC_%D8%A8%D9%88%D8%B1" title="نموذج بور – Arab" lang="ar" hreflang="ar" data-title="نموذج بور" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Modelu_at%C3%B3micu_de_Bohr" title="Modelu atómicu de Bohr – Asturia" lang="ast" hreflang="ast" data-title="Modelu atómicu de Bohr" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Bor_modeli" title="Bor modeli – Azerbaijani" lang="az" hreflang="az" data-title="Bor modeli" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%B0%D1%9E%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%B0%D0%B4%D1%8D%D0%BB%D1%8C_%D0%B0%D1%82%D0%B0%D0%BC%D0%B0" title="Бораўская мадэль атама – Belarusia" lang="be" hreflang="be" data-title="Бораўская мадэль атама" data-language-autonym="Беларуская" data-language-local-name="Belarusia" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB_%D0%BD%D0%B0_%D0%91%D0%BE%D1%80" title="Модел на Бор – Bulgaria" lang="bg" hreflang="bg" data-title="Модел на Бор" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8B%E0%A6%B0_%E0%A6%AE%E0%A6%A1%E0%A7%87%E0%A6%B2" title="বোর মডেল – Bengali" lang="bn" hreflang="bn" data-title="বোর মডেল" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Bohrov_model_atoma" title="Bohrov model atoma – Bosnia" lang="bs" hreflang="bs" data-title="Bohrov model atoma" data-language-autonym="Bosanski" data-language-local-name="Bosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Model_at%C3%B2mic_de_Bohr" title="Model atòmic de Bohr – Katalan" lang="ca" hreflang="ca" data-title="Model atòmic de Bohr" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bohr%C5%AFv_model_atomu" title="Bohrův model atomu – Cheska" lang="cs" hreflang="cs" data-title="Bohrův model atomu" data-language-autonym="Čeština" data-language-local-name="Cheska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Bohrs_atommodel" title="Bohrs atommodel – Dansk" lang="da" hreflang="da" data-title="Bohrs atommodel" data-language-autonym="Dansk" data-language-local-name="Dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bohrsches_Atommodell" title="Bohrsches Atommodell – Jerman" lang="de" hreflang="de" data-title="Bohrsches Atommodell" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%84%CE%BF%CE%BC%CE%B9%CE%BA%CF%8C_%CF%80%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF_%CF%84%CE%BF%CF%85_%CE%9C%CF%80%CE%BF%CF%81" title="Ατομικό πρότυπο του Μπορ – Yunani" lang="el" hreflang="el" data-title="Ατομικό πρότυπο του Μπορ" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Bohr_model" title="Bohr model – Inggris" lang="en" hreflang="en" data-title="Bohr model" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Modelo_at%C3%B3mico_de_Bohr" title="Modelo atómico de Bohr – Spanyol" lang="es" hreflang="es" data-title="Modelo atómico de Bohr" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Bohri_aatomiteooria" title="Bohri aatomiteooria – Esti" lang="et" hreflang="et" data-title="Bohri aatomiteooria" data-language-autonym="Eesti" data-language-local-name="Esti" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bohrren_eredu_atomikoa" title="Bohrren eredu atomikoa – Basque" lang="eu" hreflang="eu" data-title="Bohrren eredu atomikoa" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%84_%D8%A8%D9%88%D8%B1" title="مدل بور – Persia" lang="fa" hreflang="fa" data-title="مدل بور" data-language-autonym="فارسی" data-language-local-name="Persia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Bohrin_atomimalli" title="Bohrin atomimalli – Suomi" lang="fi" hreflang="fi" data-title="Bohrin atomimalli" data-language-autonym="Suomi" data-language-local-name="Suomi" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Mod%C3%A8le_de_Bohr" title="Modèle de Bohr – Prancis" lang="fr" hreflang="fr" data-title="Modèle de Bohr" data-language-autonym="Français" data-language-local-name="Prancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Samhail_Bohr" title="Samhail Bohr – Irlandia" lang="ga" hreflang="ga" data-title="Samhail Bohr" data-language-autonym="Gaeilge" data-language-local-name="Irlandia" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Modelo_at%C3%B3mico_de_Bohr" title="Modelo atómico de Bohr – Galisia" lang="gl" hreflang="gl" data-title="Modelo atómico de Bohr" data-language-autonym="Galego" data-language-local-name="Galisia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AB%89%E0%AA%B9%E0%AA%B0%E0%AA%A8%E0%AB%8B_%E0%AA%B8%E0%AA%BF%E0%AA%A6%E0%AB%8D%E0%AA%A7%E0%AA%BE%E0%AA%82%E0%AA%A4" title="બૉહરનો સિદ્ધાંત – Gujarat" lang="gu" hreflang="gu" data-title="બૉહરનો સિદ્ધાંત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarat" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%95%D7%93%D7%9C_%D7%94%D7%90%D7%98%D7%95%D7%9D_%D7%A9%D7%9C_%D7%91%D7%95%D7%94%D7%A8" title="מודל האטום של בוהר – Ibrani" lang="he" hreflang="he" data-title="מודל האטום של בוהר" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8B%E0%A4%B0_%E0%A4%95%E0%A4%BE_%E0%A4%AA%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A3%E0%A5%81_%E0%A4%AE%E0%A5%89%E0%A4%A1%E0%A4%B2" title="बोर का परमाणु मॉडल – Hindi" lang="hi" hreflang="hi" data-title="बोर का परमाणु मॉडल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Bohrov_model_atoma" title="Bohrov model atoma – Kroasia" lang="hr" hreflang="hr" data-title="Bohrov model atoma" data-language-autonym="Hrvatski" data-language-local-name="Kroasia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Bohr-f%C3%A9le_atommodell" title="Bohr-féle atommodell – Hungaria" lang="hu" hreflang="hu" data-title="Bohr-féle atommodell" data-language-autonym="Magyar" data-language-local-name="Hungaria" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%B8%D6%80%D5%AB_%D5%B4%D5%B8%D5%A4%D5%A5%D5%AC" title="Բորի մոդել – Armenia" lang="hy" hreflang="hy" data-title="Բորի մոդել" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Modello_atomico_di_Bohr" title="Modello atomico di Bohr – Italia" lang="it" hreflang="it" data-title="Modello atomico di Bohr" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9C%E3%83%BC%E3%82%A2%E3%81%AE%E5%8E%9F%E5%AD%90%E6%A8%A1%E5%9E%8B" title="ボーアの原子模型 – Jepang" lang="ja" hreflang="ja" data-title="ボーアの原子模型" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%91%E1%83%9D%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%9D%E1%83%93%E1%83%94%E1%83%9A%E1%83%98" title="ბორის მოდელი – Georgia" lang="ka" hreflang="ka" data-title="ბორის მოდელი" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%BE%D1%80_%D2%9B%D0%B0%D2%93%D0%B8%D0%B4%D0%B0%D0%BB%D0%B0%D1%80%D1%8B" title="Бор қағидалары – Kazakh" lang="kk" hreflang="kk" data-title="Бор қағидалары" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B4%EC%96%B4_%EB%AA%A8%ED%98%95" title="보어 모형 – Korea" lang="ko" hreflang="ko" data-title="보어 모형" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Boro_teorija" title="Boro teorija – Lituavi" lang="lt" hreflang="lt" data-title="Boro teorija" data-language-autonym="Lietuvių" data-language-local-name="Lituavi" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bora_atoma_uzb%C5%ABves_modelis" title="Bora atoma uzbūves modelis – Latvi" lang="lv" hreflang="lv" data-title="Bora atoma uzbūves modelis" data-language-autonym="Latviešu" data-language-local-name="Latvi" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%BE%D0%B2_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Боров модел – Makedonia" lang="mk" hreflang="mk" data-title="Боров модел" data-language-autonym="Македонски" data-language-local-name="Makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%8B%E0%B5%BC_%E0%B4%AE%E0%B4%BE%E0%B4%A4%E0%B5%83%E0%B4%95" title="ബോർ മാതൃക – Malayalam" lang="ml" hreflang="ml" data-title="ബോർ മാതൃക" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8B%E0%A4%B0%E0%A4%9A%E0%A5%80_%E0%A4%85%E0%A4%A3%E0%A5%82%E0%A4%9A%E0%A5%80_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A5%80" title="बोरची अणूची प्रतिकृती – Marathi" lang="mr" hreflang="mr" data-title="बोरची अणूची प्रतिकृती" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Model_Bohr" title="Model Bohr – Melayu" lang="ms" hreflang="ms" data-title="Model Bohr" data-language-autonym="Bahasa Melayu" data-language-local-name="Melayu" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Atoommodel_van_Bohr" title="Atoommodel van Bohr – Belanda" lang="nl" hreflang="nl" data-title="Atoommodel van Bohr" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Atommodell" title="Atommodell – Nynorsk Norwegia" lang="nn" hreflang="nn" data-title="Atommodell" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norwegia" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bohrs_atommodell" title="Bohrs atommodell – Bokmål Norwegia" lang="nb" hreflang="nb" data-title="Bohrs atommodell" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmål Norwegia" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A9%8B%E0%A8%B9%E0%A8%B0_%E0%A8%AE%E0%A8%BE%E0%A8%A1%E0%A8%B2" title="ਬੋਹਰ ਮਾਡਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਬੋਹਰ ਮਾਡਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Model_atomu_Bohra" title="Model atomu Bohra – Polski" lang="pl" hreflang="pl" data-title="Model atomu Bohra" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D9%88%DB%81%D8%B1_%D9%85%D8%A7%DA%88%D9%84" title="بوہر ماڈل – Western Punjabi" lang="pnb" hreflang="pnb" data-title="بوہر ماڈل" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81tomo_de_Bohr" title="Átomo de Bohr – Portugis" lang="pt" hreflang="pt" data-title="Átomo de Bohr" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modelul_atomic_Bohr" title="Modelul atomic Bohr – Rumania" lang="ro" hreflang="ro" data-title="Modelul atomic Bohr" data-language-autonym="Română" data-language-local-name="Rumania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%BE%D0%B2%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C_%D0%B0%D1%82%D0%BE%D0%BC%D0%B0" title="Боровская модель атома – Rusia" lang="ru" hreflang="ru" data-title="Боровская модель атома" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Mud%C3%A8llu_at%C3%B2micu_di_Bohr" title="Mudèllu atòmicu di Bohr – Sisilia" lang="scn" hreflang="scn" data-title="Mudèllu atòmicu di Bohr" data-language-autonym="Sicilianu" data-language-local-name="Sisilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Bohr_model" title="Bohr model – Skotlandia" lang="sco" hreflang="sco" data-title="Bohr model" data-language-autonym="Scots" data-language-local-name="Skotlandia" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Bohrov_model_atoma" title="Bohrov model atoma – Serbo-Kroasia" lang="sh" hreflang="sh" data-title="Bohrov model atoma" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroasia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Bohr_model" title="Bohr model – Simple English" lang="en-simple" hreflang="en-simple" data-title="Bohr model" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Bohrov_model_at%C3%B3mu" title="Bohrov model atómu – Slovak" lang="sk" hreflang="sk" data-title="Bohrov model atómu" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Bohrov_model_atoma" title="Bohrov model atoma – Sloven" lang="sl" hreflang="sl" data-title="Bohrov model atoma" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%BE%D0%B2_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB_%D0%B0%D1%82%D0%BE%D0%BC%D0%B0" title="Боров модел атома – Serbia" lang="sr" hreflang="sr" data-title="Боров модел атома" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bohrs_atommodell" title="Bohrs atommodell – Swedia" lang="sv" hreflang="sv" data-title="Bohrs atommodell" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%8B%E0%AE%B0%E0%AF%8D_%E0%AE%85%E0%AE%A3%E0%AF%81_%E0%AE%AE%E0%AE%BE%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AE%BF" title="போர் அணு மாதிரி – Tamil" lang="ta" hreflang="ta" data-title="போர் அணு மாதிரி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%8B%E0%B0%B0%E0%B1%8D_%E0%B0%A8%E0%B0%AE%E0%B1%82%E0%B0%A8%E0%B0%BE" title="బోర్ నమూనా – Telugu" lang="te" hreflang="te" data-title="బోర్ నమూనా" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%88%E0%B8%B3%E0%B8%A5%E0%B8%AD%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%82%E0%B8%9B%E0%B8%A3%E0%B9%8C" title="แบบจำลองของโปร์ – Thai" lang="th" hreflang="th" data-title="แบบจำลองของโปร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Modelong_Bohr" title="Modelong Bohr – Tagalog" lang="tl" hreflang="tl" data-title="Modelong Bohr" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bohr_modeli" title="Bohr modeli – Turki" lang="tr" hreflang="tr" data-title="Bohr modeli" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%B0_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C_%D0%91%D0%BE%D1%80%D0%B0" title="Атомна модель Бора – Ukraina" lang="uk" hreflang="uk" data-title="Атомна модель Бора" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Bor_postulatlari" title="Bor postulatlari – Uzbek" lang="uz" hreflang="uz" data-title="Bor postulatlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%B4_h%C3%ACnh_Bohr" title="Mô hình Bohr – Vietnam" lang="vi" hreflang="vi" data-title="Mô hình Bohr" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%8E%BB%E5%B0%94%E6%A8%A1%E5%9E%8B" title="玻尔模型 – Wu Tionghoa" lang="wuu" hreflang="wuu" data-title="玻尔模型" data-language-autonym="吴语" data-language-local-name="Wu Tionghoa" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%8E%BB%E5%B0%94%E6%A8%A1%E5%9E%8B" title="玻尔模型 – Tionghoa" lang="zh" hreflang="zh" data-title="玻尔模型" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%8E%BB%E7%88%BE%E6%A8%A1%E5%9E%8B" title="玻爾模型 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="玻爾模型" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%8E%BB%E7%88%BE%E6%A8%A1%E5%9E%8B" title="玻爾模型 – Kanton" lang="yue" hreflang="yue" data-title="玻爾模型" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q172948#sitelinks-wikipedia" title="Sunting pranala interwiki" class="wbc-editpage">Sunting pranala</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ruang nama"> <div id="p-associated-pages" 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Artikel ini <b>tidak memiliki <a href="/wiki/Wikipedia:Kutip_sumber_tulisan" title="Wikipedia:Kutip sumber tulisan">referensi</a> atau <a href="/wiki/Wikipedia:Sumber_tepercaya" title="Wikipedia:Sumber tepercaya">sumber tepercaya</a></b> sehingga isinya tidak bisa <a href="/wiki/Wikipedia:Pemastian" title="Wikipedia:Pemastian">dipastikan</a>.<span class="hide-when-compact"> Tolong bantu <span class="plainlinks"><a class="external text" href="https://id.wikipedia.org/w/index.php?title=Model_Bohr&action=edit">perbaiki artikel ini</a></span> dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.<br /><small><span class="plainlinks"><i>Cari sumber:</i> <a rel="nofollow" class="external text" href="//google.com/search?as_eq=wikipedia&q=%22Model+Bohr%22&num=50">"Model Bohr"</a> – <a rel="nofollow" class="external text" href="//google.com/search?q=%22Model+Bohr%22&tbm=nws">berita</a> <b>·</b> <a rel="nofollow" class="external text" href="//google.com/search?&q=%22Model+Bohr%22+site:news.google.com/newspapers&source=newspapers">surat kabar</a> <b>·</b> <a rel="nofollow" class="external text" href="//google.com/search?tbs=bks:1&q=%22Model+Bohr%22">buku</a> <b>·</b> <a rel="nofollow" class="external text" href="//scholar.google.com/scholar?q=%22Model+Bohr%22">cendekiawan</a> <b>·</b> <a rel="nofollow" class="external text" href="http://www.jstor.org/action/doBasicSearch?Query=%22Model+Bohr%22&acc=on&wc=on">JSTOR</a></span></small></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Bohr_atom_model_English.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bohr_atom_model_English.svg/langid-300px-Bohr_atom_model_English.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bohr_atom_model_English.svg/langid-450px-Bohr_atom_model_English.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bohr_atom_model_English.svg/langid-600px-Bohr_atom_model_English.svg.png 2x" data-file-width="600" data-file-height="600" /></a><figcaption><b>Model Bohr</b> dari <a href="/wiki/Atom_hidrogen" title="Atom hidrogen">atom hidrogen</a> menggambarkan <a href="/wiki/Elektron" title="Elektron">elektron</a>-elektron bermuatan negatif mengorbit pada <a href="/w/index.php?title=Kulit_atom&action=edit&redlink=1" class="new" title="Kulit atom (halaman belum tersedia)">kulit atom</a> dalam lintasan tertentu mengelilingi <a href="/wiki/Inti_atom" title="Inti atom">inti atom</a> yang bermuatan positif. Ketika elektron meloncat dari satu orbit ke orbit lainnya selalu disertai dengan pemancaran atau penyerapan sejumlah <a href="/w/index.php?title=Energi_elektromagnetik&action=edit&redlink=1" class="new" title="Energi elektromagnetik (halaman belum tersedia)">energi elektromagnetik</a> <i>hf</i>.</figcaption></figure> <p>Di dalam <a href="/wiki/Fisika_atom" title="Fisika atom">fisika atom</a>, <b>model Bohr</b> adalah <a href="/wiki/Model_atom" class="mw-redirect" title="Model atom">model atom</a> yang diperkenalkan oleh <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> pada <a href="/wiki/1913" title="1913">1913</a>. Model ini menggambarkan <a href="/wiki/Atom" title="Atom">atom</a> sebagai sebuah <a href="/wiki/Inti" class="mw-disambig" title="Inti">inti</a> kecil bermuatan positif yang dikelilingi oleh <a href="/wiki/Elektron" title="Elektron">elektron</a> yang bergerak dalam orbit sirkuler mengelilingi inti — mirip sistem <a href="/wiki/Tata_surya" class="mw-redirect" title="Tata surya">tata surya</a>, tetapi peran gaya <a href="/wiki/Gravitasi" title="Gravitasi">gravitasi</a> digantikan oleh <a href="/wiki/Gaya_elektrostatik" class="mw-redirect" title="Gaya elektrostatik">gaya elektrostatik</a>. Model ini adalah pengembangan dari <a href="/wiki/Model_puding_prem" title="Model puding prem">model puding prem</a> (1904), <a href="/w/index.php?title=Model_Saturnian&action=edit&redlink=1" class="new" title="Model Saturnian (halaman belum tersedia)">model Saturnian</a> (1904), dan <a href="/wiki/Model_Rutherford" title="Model Rutherford">model Rutherford</a> (1911). Karena model Bohr adalah pengembangan dari model Rutherford, banyak sumber mengkombinasikan kedua nama dalam penyebutannya menjadi model Rutherford-Bohr. Seperti sudah diketahui sebelumnya, Rutherford mengemukakan teori atom Rutherford berdasarkan percobaan hamburan sinar alfa oleh partikel emas yang dilakukannya. </p><p>Kunci sukses model ini adalah dalam menjelaskan <a href="/w/index.php?title=Formula_Rydberg&action=edit&redlink=1" class="new" title="Formula Rydberg (halaman belum tersedia)">formula Rydberg</a> mengenai garis-<a href="/w/index.php?title=Garis_emisi&action=edit&redlink=1" class="new" title="Garis emisi (halaman belum tersedia)">garis emisi</a> spektral atom <a href="/wiki/Hidrogen" title="Hidrogen">hidrogen</a>; walaupun formula Rydberg sudah dikenal secara eksperimental, tetapi tidak pernah mendapatkan landasan teoretis sebelum model Bohr diperkenalkan. Tidak hanya karena model Bohr menjelaskan alasan untuk struktur formula Rydberg, ia juga memberikan justifikasi hasil empirisnya dalam hal suku-suku <a href="/wiki/Konstanta_fisika" title="Konstanta fisika">konstanta fisika</a> fundamental. </p><p>Model Bohr adalah sebuah model primitif mengenai atom hidrogen. Sebagai sebuah teori, model Bohr dapat dianggap sebagai sebuah pendekatan orde pertama dari atom hidrogen menggunakan <a href="/wiki/Mekanika_kuantum" title="Mekanika kuantum">mekanika kuantum</a> yang lebih umum dan akurat, dan dengan demikian dapat dianggap sebagai model yang telah usang. Namun, karena kesederhanaannya, dan hasil yang tepat untuk sebuah sistem tertentu, model Bohr tetap diajarkan sebagai pengenalan pada mekanika kuantum. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Sejarah">Sejarah</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model_Bohr&veaction=edit&section=1" title="Sunting bagian: Sejarah" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Model_Bohr&action=edit&section=1" title="Sunting kode sumber bagian: Sejarah"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Di awal <a href="/wiki/Abad_20" class="mw-redirect" title="Abad 20">abad 20</a>, percobaan oleh <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> telah dapat menunjukkan bahwa <a href="/wiki/Atom" title="Atom">atom</a> terdiri dari sebentuk awan difus <a href="/wiki/Elektron" title="Elektron">elektron</a> bermuatan negatif mengelilingi inti yang kecil, padat, dan bermuatan positif. Berdasarkan data percobaan ini, sangat wajar jika fisikawan kemudian membayangkan sebuah model sistem keplanetan yang diterapkan pada atom, <a href="/wiki/Model_Rutherford" title="Model Rutherford">model Rutherford</a> tahun 1911, dengan elektron-elektron mengorbit inti seperti layaknya planet mengorbit matahari. Namun, model sistem keplanetan untuk atom menemui beberapa kesulitan. Sebagai contoh, hukum <a href="/wiki/Mekanika_klasik" title="Mekanika klasik">mekanika klasik</a> (Newtonian) memprediksi bahwa elektron akan melepas <a href="/wiki/Radiasi_elektromagnetik" title="Radiasi elektromagnetik">radiasi elektromagnetik</a> ketika sedang mengorbit inti. Karena dalam pelepasan tersebut elektron kehilangan energi, maka lama-kelamaan akan jatuh secara spiral menuju ke inti. Ketika ini terjadi, frekuensi radiasi elektromagnetik yang dipancarkan akan berubah. Namun percobaan pada akhir <a href="/wiki/Abad_19" class="mw-redirect" title="Abad 19">abad 19</a> menunjukkan bahwa loncatan bunga api listrik yang dilalukan dalam suatu <a href="/wiki/Gas" title="Gas">gas</a> bertekanan rendah di dalam sebuah tabung hampa akan membuat atom-atom gas memancarkan cahaya (yang berarti radiasi elektromagnetik) dalam frekuensi-frekuensi tetap yang diskret. </p><p>Untuk mengatasi hal ini dan kesulitan-kesulitan lainnya dalam menjelaskan gerak elektron di dalam atom, <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> mengusulkan, pada <a href="/wiki/1913" title="1913">1913</a>, apa yang sekarang disebut <b>model atom Bohr</b>. Dua gagasan kunci adalah: </p> <ol><li>Elektron-elektron bergerak di dalam orbit-orbit dan memiliki momenta yang terkuantisasi, dan dengan demikian energi yang terkuantisasi. Ini berarti tidak setiap orbit, melainkan hanya beberapa orbit spesifik yang dimungkinkan ada yang berada pada jarak yang spesifik dari inti.</li> <li>Elektron-elektron tidak akan kehilangan energi secara perlahan-lahan sebagaimana mereka bergerak di dalam orbit, melainkan akan tetap stabil di dalam sebuah orbit yang tidak meluruh.</li></ol> <p>Arti penting model ini terletak pada pernyataan bahwa <i>hukum mekanika klasik tidak berlaku pada gerak elektron di sekitar inti</i>. Bohr mengusulkan bahwa satu bentuk mekanika baru, atau <a href="/wiki/Mekanika_kuantum" title="Mekanika kuantum">mekanika kuantum</a>, menggambarkan gerak elektron di sekitar inti. Namun, model elektron yang bergerak dalam orbit yang terkuantisasi mengelilingi inti ini kemudian digantikan oleh model gerak elektron yang lebih akurat sekitar sepuluh tahun kemudian oleh fisikawan Austria <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a> dan fisikawan Jerman <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>. </p><p>Point-point penting lainnya adalah: </p> <ol><li>Ketika sebuah elektron meloncat dari satu orbit ke orbit lainnya, perbedaan energi dibawa (atau dipasok) oleh sebuah kuantum tunggal cahaya (disebut sebagai <a href="/wiki/Foton" title="Foton">foton</a>) yang memiliki energi sama dengan perbedaan energi antara kedua orbit.</li> <li>Orbit-orbit yang diperkenankan bergantung pada harga-harga terkuantisasi (diskret) dari <a href="/wiki/Momentum_sudut" title="Momentum sudut">momentum sudut</a> orbital, <i>L</i> menurut persamaan<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {L} =n\cdot \hbar =n\cdot {h \over 2\pi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">L</mi> </mrow> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {L} =n\cdot \hbar =n\cdot {h \over 2\pi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34c35dfb5a494ac6f71484544eeda82afc631d2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.59ex; height:5.343ex;" alt="{\displaystyle \mathbf {L} =n\cdot \hbar =n\cdot {h \over 2\pi }}"></span><br />dimana <i>n</i> = 1,2,3,… dan disebut sebagai <a href="/wiki/Bilangan_kuantum_utama" title="Bilangan kuantum utama">bilangan kuantum utama</a>, dan <i>h</i> adalah <a href="/wiki/Konstanta_Planck" title="Konstanta Planck">konstanta Planck</a>.</li></ol> <p>Point (2) menyatakan bahwa harga terendah dari <i>n</i> adalah 1. Ini berhubungan dengan radius terkecil yang mungkin yaitu 0.0529 nm. Radius ini dikenal sebagai <a href="/wiki/Radius_Bohr" class="mw-redirect" title="Radius Bohr">radius Bohr</a>. Sekali elektron berada pada orbit ini, dia tidak akan mungkin bertambah lebih dekat lagi ke proton. </p> <div class="mw-heading mw-heading2"><h2 id="Tingkatan_energi_elektron_dalam_atom_hidrogen">Tingkatan energi elektron dalam atom hidrogen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model_Bohr&veaction=edit&section=2" title="Sunting bagian: Tingkatan energi elektron dalam atom hidrogen" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Model_Bohr&action=edit&section=2" title="Sunting kode sumber bagian: Tingkatan energi elektron dalam atom hidrogen"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Model Bohr hanya akurat untuk sistem satu elektron seperti <a href="/wiki/Atom_hidrogen" title="Atom hidrogen">atom hidrogen</a> atau <a href="/wiki/Helium" title="Helium">helium</a> yang terionisasi satu kali. Bagian ini hendak menurunkan rumusan tingkat-tingkat energi atom hidrogen menggunakan model Bohr. </p><p>Penurunan rumus didasarkan pada tiga asumsi sederhana: </p> <dl><dd>1) Energi sebuah elektron dalam orbit adalah penjumlahan energi kinetik dan energi potensialnya:</dd></dl> <dl><dd><dl><dd><table> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9123abddc2ec35f72035ec59f443c79ee052c9ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.163ex; height:2.176ex;" alt="{\displaystyle E\,}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =E_{kinetik}+E_{potensial}\quad \quad \quad \quad \quad \quad (1)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mi>i</mi> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> <mi>i</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =E_{kinetik}+E_{potensial}\quad \quad \quad \quad \quad \quad (1)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5a6a9539dbfcc06e3ec24a38b8e8c41aa32eee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:38.346ex; height:3.009ex;" alt="{\displaystyle =E_{kinetik}+E_{potensial}\quad \quad \quad \quad \quad \quad (1)\,}"></span> </td></tr> <tr> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ade5cbcd442b8d49ba65246300c61cef04c0c7ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.105ex; height:5.676ex;" alt="{\displaystyle ={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}}"></span> </td></tr></tbody></table></dd></dl></dd></dl> <dl><dd><dl><dd>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k=1/({4\pi \epsilon _{0}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=1/({4\pi \epsilon _{0}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/317e660124880bb24305c1dcbc9bbfa6087e2c17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.937ex; height:2.843ex;" alt="{\displaystyle k=1/({4\pi \epsilon _{0}})}"></span>, dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d61b69f0737a387888ee5ca0b7e062d2e681e58e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.035ex; height:2.009ex;" alt="{\displaystyle q_{e}}"></span> adalah muatan elektron.</dd></dl></dd></dl> <dl><dd>2) Momentum sudut elektron hanya boleh memiliki harga diskret tertentu: <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L=m_{e}vr=n{\frac {h}{2\pi }}=n\hbar \quad \quad \quad \quad \quad (2)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>v</mi> <mi>r</mi> <mo>=</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>n</mi> <mi class="MJX-variant">ℏ</mi> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=m_{e}vr=n{\frac {h}{2\pi }}=n\hbar \quad \quad \quad \quad \quad (2)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b44322aa9d02533c80d52b082ee939ab0f0cefb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:38.492ex; height:5.343ex;" alt="{\displaystyle L=m_{e}vr=n{\frac {h}{2\pi }}=n\hbar \quad \quad \quad \quad \quad (2)\,}"></span></dd></dl></dd> <dd>dengan <i>n</i> = 1,2,3,… dan disebut <a href="/wiki/Bilangan_kuantum_utama" title="Bilangan kuantum utama">bilangan kuantum utama</a>, <i>h</i> adalah <a href="/wiki/Konstanta_Planck" title="Konstanta Planck">konstanta Planck</a>, dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar =h/(2\pi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar =h/(2\pi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c43c4e0cfef2829e9705d8da36c3f9093ad9b53e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.21ex; height:2.843ex;" alt="{\displaystyle \hbar =h/(2\pi )}"></span>.</dd></dl></dd></dl> <dl><dd>3) Elektron berada dalam orbit diatur oleh <a href="/wiki/Hukum_Coulomb" title="Hukum Coulomb">gaya coulomb</a>. Ini berarti gaya coulomb sama dengan <a href="/wiki/Gaya_sentripetal" title="Gaya sentripetal">gaya sentripetal</a>: <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {kq_{e}^{2}}{r^{2}}}={\frac {m_{e}v^{2}}{r}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (3)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>r</mi> </mfrac> </mrow> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {kq_{e}^{2}}{r^{2}}}={\frac {m_{e}v^{2}}{r}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (3)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8717d274a6f0bd8e6f2da4676f84b831ddfff14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:39.921ex; height:6.009ex;" alt="{\displaystyle {\frac {kq_{e}^{2}}{r^{2}}}={\frac {m_{e}v^{2}}{r}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (3)\,}"></span></dd></dl></dd></dl></dd></dl> <p>Dengan mengalikan ke-2 sisi persamaan (3) dengan <i>r</i> didapatkan: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {kq_{e}^{2}}{r}}=m_{e}v^{2}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (4)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {kq_{e}^{2}}{r}}=m_{e}v^{2}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (4)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7e166bfa32d612bf655d825be2edee253c39086" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:42.441ex; height:5.676ex;" alt="{\displaystyle {\frac {kq_{e}^{2}}{r}}=m_{e}v^{2}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (4)\,}"></span></dd></dl></dd></dl> <p>Suku di sisi kiri menyatakan <a href="/wiki/Energi_potensial" title="Energi potensial">energi potensial</a>, sehingga persamaan untuk energi menjadi: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}=-{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}\quad \quad \quad \quad (5)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}=-{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}\quad \quad \quad \quad (5)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa3112386f917e6e64318a1d8f59772f2e9d6674" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:44.712ex; height:5.676ex;" alt="{\displaystyle E={\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}-{\frac {kq_{e}^{2}}{r}}=-{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{e}v^{2}\quad \quad \quad \quad (5)\,}"></span></dd></dl></dd></dl> <p>Dengan menyelesaikan persamaan (2) untuk r, didapatkan harga jari-jari yang diperkenankan: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {n^{2}\hbar ^{2}}{m_{e}v^{2}}}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (6)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {n^{2}\hbar ^{2}}{m_{e}v^{2}}}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (6)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/661d1e1eaf98673cb5e009661dcc000a648464e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:44.79ex; height:6.343ex;" alt="{\displaystyle r={\frac {n^{2}\hbar ^{2}}{m_{e}v^{2}}}.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (6)\,}"></span></dd></dl></dd></dl> <p>Dengan memasukkan persamaan (6) ke persamaan (4), maka diperoleh: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle kq_{e}^{2}{\frac {m_{e}v}{n\hbar }}=m_{e}v^{2}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (7)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mi>v</mi> </mrow> <mrow> <mi>n</mi> <mi class="MJX-variant">ℏ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle kq_{e}^{2}{\frac {m_{e}v}{n\hbar }}=m_{e}v^{2}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (7)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0848521e5a36fd0441bec3d3b9daa61e218b7013" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:43.251ex; height:4.843ex;" alt="{\displaystyle kq_{e}^{2}{\frac {m_{e}v}{n\hbar }}=m_{e}v^{2}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (7)\,}"></span></dd></dl></dd></dl> <p>Dengan membagi kedua sisi persamaan (7) dengan <i>m<sub>e</sub>v</i> didapatkan </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {kq_{e}^{2}}{n\hbar }}=v\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (8)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mi>n</mi> <mi class="MJX-variant">ℏ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>v</mi> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>8</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {kq_{e}^{2}}{n\hbar }}=v\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (8)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41053ce1b115213e403a825b9c57662dfb59f5c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:44.282ex; height:5.843ex;" alt="{\displaystyle {\frac {kq_{e}^{2}}{n\hbar }}=v\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (8)\,}"></span></dd></dl></dd></dl> <p>Dengan memasukkan harga <i>v</i> pada persamaan energi (persamaan (5)), dan kemudian mensubstitusikan harga untuk <i>k</i> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span>, maka energi pada tingkatan orbit yang berbeda dari atom hidrogen dapat ditentukan sebagai berikut: </p> <dl><dd><dl><dd><dl><dd><table> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{n}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{n}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c621cabe4418802f7f26e069a046cd2270bff41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.321ex; height:2.509ex;" alt="{\displaystyle E_{n}\,}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {kq_{e}^{2}}{n\hbar }}\right)^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mi>n</mi> <mi class="MJX-variant">ℏ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {kq_{e}^{2}}{n\hbar }}\right)^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49dd986976dff504e68cbd2175ec0e359c9dd0d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.342ex; height:6.843ex;" alt="{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {kq_{e}^{2}}{n\hbar }}\right)^{2}\,}"></span> </td></tr> <tr> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {1}{4\pi \epsilon _{0}}}q_{e}^{2}{\frac {2\pi }{nh}}\right)^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mi>n</mi> <mi>h</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {1}{4\pi \epsilon _{0}}}q_{e}^{2}{\frac {2\pi }{nh}}\right)^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d871f5287f8ef93be8bebdfecd1c6a549c5aa86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.194ex; height:6.509ex;" alt="{\displaystyle ={\frac {-1}{2}}m_{e}\left({\frac {1}{4\pi \epsilon _{0}}}q_{e}^{2}{\frac {2\pi }{nh}}\right)^{2}\,}"></span> </td></tr> <tr> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {-m_{e}q_{e}^{4}}{8h^{2}\epsilon _{0}^{2}}}{\frac {1}{n^{2}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (9)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> </mrow> <mrow> <mn>8</mn> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>9</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {-m_{e}q_{e}^{4}}{8h^{2}\epsilon _{0}^{2}}}{\frac {1}{n^{2}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (9)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc7440f4c1e1d9f88b683c0e5d52603872142a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:40.14ex; height:6.843ex;" alt="{\displaystyle ={\frac {-m_{e}q_{e}^{4}}{8h^{2}\epsilon _{0}^{2}}}{\frac {1}{n^{2}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (9)\,}"></span> </td></tr></tbody></table></dd></dl></dd></dl></dd></dl> <p>Dengan memasukkan harga semua konstanta, didapatkan, </p> <dl><dd><dl><dd><dl><dd><table cellpadding="2" style="border:2px solid #ccccff"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{n}=(-13.6\ \mathrm {eV} ){\frac {1}{n^{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>13.6</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{n}=(-13.6\ \mathrm {eV} ){\frac {1}{n^{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/809298b88ef5c312bdf50c4051ca5d59f5ab8f4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.812ex; height:5.509ex;" alt="{\displaystyle E_{n}=(-13.6\ \mathrm {eV} ){\frac {1}{n^{2}}}\,}"></span> </td></tr></tbody></table></dd></dl></dd></dl></dd></dl> <p>Dengan demikian, tingkat energi terendah untuk atom hidrogen (<i>n</i> = 1) adalah -13.6 <a href="/wiki/Elektronvolt" title="Elektronvolt">eV</a>. Tingkat energi berikutnya (<i>n</i> = 2) adalah -3.4 eV. Tingkat energi ketiga (<i>n</i> = 3) adalah -1.51 eV, dan seterusnya. Harga-harga energi ini adalah negatif, yang menyatakan bahwa elektron berada dalam keadaan terikat dengan proton. Harga energi yang positif berhubungan dengan atom yang berada dalam keadaan ter<a href="/wiki/Ionisasi" title="Ionisasi">ionisasi</a> yaitu ketika elektron tidak lagi terikat, tetapi dalam keadaan tersebar. </p> <div class="mw-heading mw-heading2"><h2 id="Pranala_luar">Pranala luar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model_Bohr&veaction=edit&section=3" title="Sunting bagian: Pranala luar" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Model_Bohr&action=edit&section=3" title="Sunting kode sumber bagian: Pranala luar"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="(Indonesia)_Teori_Atom_Bohr"><span id=".28Indonesia.29_Teori_Atom_Bohr"></span><span style="font-size:0.95em; font-weight:bold; color:#777; cursor:help;" title="Bahasa Indonesia" lang="Indonesia">(Indonesia)</span> <a rel="nofollow" class="external text" href="http://www.ilmukimia.org/2013/01/teori-atom-bohr.html">Teori Atom Bohr</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model_Bohr&veaction=edit&section=4" title="Sunting bagian: (Indonesia) Teori Atom Bohr" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Model_Bohr&action=edit&section=4" title="Sunting kode sumber bagian: (Indonesia) Teori Atom Bohr"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Diperoleh dari "<a dir="ltr" href="https://id.wikipedia.org/w/index.php?title=Model_Bohr&oldid=26040488">https://id.wikipedia.org/w/index.php?title=Model_Bohr&oldid=26040488</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Istimewa:Daftar_kategori" title="Istimewa:Daftar kategori">Kategori</a>: <ul><li><a href="/wiki/Kategori:Fisika_atom" title="Kategori:Fisika atom">Fisika atom</a></li><li><a href="/wiki/Kategori:Fisika_kuantum" title="Kategori:Fisika kuantum">Fisika kuantum</a></li><li><a href="/wiki/Kategori:Hidrogen" title="Kategori:Hidrogen">Hidrogen</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Kategori tersembunyi: <ul><li><a href="/wiki/Kategori:Artikel_yang_tidak_memiliki_referensi_Juli_2024" title="Kategori:Artikel yang tidak memiliki referensi Juli 2024">Artikel yang tidak memiliki referensi Juli 2024</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Halaman ini terakhir diubah pada 16 Juli 2024, pukul 01.03.</li> <li id="footer-info-copyright">Teks tersedia di bawah <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Lisensi Atribusi-BerbagiSerupa Creative Commons</a>; ketentuan tambahan mungkin berlaku. 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