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<title>Rydberg-Formel</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Rydberg-Formel</span></h1>

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<p>Die <b>Rydberg-Formel</b> (auch <b>Rydberg-Ritz-Formel</b>) wird in der <a href="Atomphysik" title="Atomphysik">Atomphysik</a> benutzt, um das <a href="Elektromagnetisches_Spektrum" title="Elektromagnetisches Spektrum">Linienspektrum</a> des vom <a href="Wasserstoff" title="Wasserstoff">Wasserstoff</a> <a href="Spontane_Emission" title="Spontane Emission">emittierten</a> Lichtes zu bestimmen. Sie zeigt, dass die <a href="Bindungsenergie" title="Bindungsenergie">Bindungsenergie</a> des <a href="Elektron" title="Elektron">Elektrons</a> im Wasserstoffatom <a href="Reziproke_Proportionalit%C3%A4t" class="mw-redirect" title="Reziproke Proportionalität">umgekehrt proportional</a> zum <a href="Quadrat_(Arithmetik)" class="mw-redirect" title="Quadrat (Arithmetik)">Quadrat</a> der <a href="Hauptquantenzahl" class="mw-redirect" title="Hauptquantenzahl">Hauptquantenzahl</a> ist.

</p><p>Die Formel wurde am 5. November 1888 vom <a href="Schweden" title="Schweden">schwedischen</a> <a href="Physiker" title="Physiker">Physiker</a> <a href="Johannes_Rydberg" title="Johannes Rydberg">Johannes Rydberg</a> vorgestellt; auch <a href="Walter_Ritz" title="Walter Ritz">Walter Ritz</a> arbeitete an ihr.

</p><p>Korrekturen aufgrund von <a href="Drehimpuls" title="Drehimpuls">Drehimpulsen</a> oder <a href="Relativistisch" class="mw-redirect" title="Relativistisch">relativistischen</a> Effekten werden in der Rydberg-Formel <i>nicht</i> berücksichtigt. Später wurde sie erweitert, um das Spektrum anderer <a href="Chemisches_Element" title="Chemisches Element">Elemente</a> zu bestimmen (s. u. Erweiterungen).

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<div class="mw-heading mw-heading2"><h2 id="Rydberg-Formel_für_Wasserstoff"><span id="Rydberg-Formel_f.C3.BCr_Wasserstoff"></span>Rydberg-Formel für Wasserstoff</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Formulierung">Formulierung</h3></div>

<p>Die Rydberg-Formel lautet:

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<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\lambda _{\mathrm {vac} }}}=R_{\infty }\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0d946409a23e1fd9958e87af67ca3cb81f24023f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:25.06ex; height:7.509ex;" alt="{\displaystyle {\frac {1}{\lambda _{\mathrm {vac} }}}=R_{\infty }\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right)}" loading="lazy"></span></dd></dl>

<p>Dabei sind

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<annotation encoding="application/x-tex">{\displaystyle \lambda _{\mathrm {vac} }}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/92f14f71061408985102d3d119a358b71094d749.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.007ex; height:2.509ex;" alt="{\displaystyle \lambda _{\mathrm {vac} }}" loading="lazy"></span> die <a href="Wellenl%C3%A4nge" title="Wellenlänge">Wellenlänge</a> des Lichts im <a href="Vakuum" title="Vakuum">Vakuum</a></li>

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<annotation encoding="application/x-tex">{\displaystyle R}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> die Rydberg-Konstante für das betrachtete Wasserstoff-Isotop: <span class="mwe-math-element mwe-math-element-inline"><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={\tfrac {R_{\infty }}{1+{\frac {m_{\mathrm {e} }}{M}}}}}">

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<annotation encoding="application/x-tex">{\displaystyle R={\tfrac {R_{\infty }}{1+{\frac {m_{\mathrm {e} }}{M}}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/966812cf0c73da76135ea7cc1df0d929cbda531c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:10.533ex; height:5.343ex;" alt="{\displaystyle R={\tfrac {R_{\infty }}{1+{\frac {m_{\mathrm {e} }}{M}}}}}" loading="lazy"></span> mit

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<annotation encoding="application/x-tex">{\displaystyle M}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f82cade9898ced02fdd08712e5f0c0151758a0dd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" loading="lazy"></span> die <a href="Kernmasse" title="Kernmasse">Kernmasse</a> des vorliegenden Wasserstoff-<a href="Isotop" title="Isotop">Isotops</a></li>

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<annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {e} }}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7c3e1e197589f439bac0126262d62a0c6b5926cd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.003ex; height:2.009ex;" alt="{\displaystyle m_{\mathrm {e} }}" loading="lazy"></span> die Masse des Elektrons</li>

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<annotation encoding="application/x-tex">{\displaystyle R_{\infty }}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/639146705058e9d335aed47b55a9f802bc290b5f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.639ex; height:2.509ex;" alt="{\displaystyle R_{\infty }}" loading="lazy"></span> die <a href="Rydberg-Konstante" title="Rydberg-Konstante">Rydberg-Konstante</a> für unendliche Kernmasse. Da</li></ul></li></ul>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}m_{\mathrm {e} }\,&\ll M\\[4pt]\Rightarrow {\frac {m_{\mathrm {e} }}{M}}&\ll 1\quad (\mathrm {Quotient} \approx {\tfrac {1}{1835}}\mathrm {\;bei\;leichtem\;Wasserstoff,\;} {\tfrac {1}{3670}}\mathrm {\;bei\;Deuterium\;und\;} {\tfrac {1}{5497}}\mathrm {\;bei\;Tritium} )\\\Rightarrow 1+{\frac {m_{\mathrm {e} }}{M}}&\approx 1\\[4pt]\Rightarrow R\;&\approx R_{\infty }\end{aligned}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/70f347f122e13620284b96653df17df8a891d7bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.171ex; width:104.283ex; height:17.509ex;" alt="{\displaystyle {\begin{aligned}m_{\mathrm {e} }\,&\ll M\\[4pt]\Rightarrow {\frac {m_{\mathrm {e} }}{M}}&\ll 1\quad (\mathrm {Quotient} \approx {\tfrac {1}{1835}}\mathrm {\;bei\;leichtem\;Wasserstoff,\;} {\tfrac {1}{3670}}\mathrm {\;bei\;Deuterium\;und\;} {\tfrac {1}{5497}}\mathrm {\;bei\;Tritium} )\\\Rightarrow 1+{\frac {m_{\mathrm {e} }}{M}}&\approx 1\\[4pt]\Rightarrow R\;&\approx R_{\infty }\end{aligned}}}" loading="lazy"></span></dd></dl></dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle n_{1}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee784b70e772f55ede5e6e0bdc929994bff63413.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{1}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{2}}">

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<annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span> ganzzahlige Werte der <a href="Hauptquantenzahl" class="mw-redirect" title="Hauptquantenzahl">Hauptquantenzahl</a> (mit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1}<n_{2}}">

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<annotation encoding="application/x-tex">{\displaystyle n_{1}<n_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/58e3737206604f516374f27b1199a26a3df8625a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.996ex; height:2.176ex;" alt="{\displaystyle n_{1}<n_{2}}" loading="lazy"></span>): <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{2}}">

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span> ist die Quantenzahl des Orbits, von dem aus das Elektron in den tiefer gelegenen Orbit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1}}">

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee784b70e772f55ede5e6e0bdc929994bff63413.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{1}}" loading="lazy"></span> übergeht – also etwa vom dritten Orbit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{2}=3}">

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/171b6ed858e2fa9568482337ebc8d6eab20f489d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.71ex; height:2.509ex;" alt="{\displaystyle n_{2}=3}" loading="lazy"></span> in den zweiten <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1}=2}">

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3d78e0d9d3fa3ffa0401a62e2be14b009da6e6db.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.71ex; height:2.509ex;" alt="{\displaystyle n_{1}=2}" loading="lazy"></span> (siehe <a href="Bohrsches_Atommodell" title="Bohrsches Atommodell">Bohrsches Atommodell</a>).</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Energie">Energie</h3></div>

<p>Für die Energie des emittierten <a href="Photon" title="Photon">Photons</a> gilt:

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<annotation encoding="application/x-tex">{\displaystyle E={\frac {1}{\lambda _{\mathrm {vac} }}}\cdot c\cdot h}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/70ae0669812338746c34e652175044f505a42368.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.422ex; height:5.676ex;" alt="{\displaystyle E={\frac {1}{\lambda _{\mathrm {vac} }}}\cdot c\cdot h}" loading="lazy"></span></dd></dl>

<p>mit

</p>

<ul><li><a href="Lichtgeschwindigkeit" title="Lichtgeschwindigkeit">Lichtgeschwindigkeit</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}">

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<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"></span> im Vakuum</li>

<li><a href="Plancksche_Konstante" class="mw-redirect" title="Plancksche Konstante">Planckscher Konstante</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}">

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<annotation encoding="application/x-tex">{\displaystyle h}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b26be3e694314bc90c3215047e4a2010c6ee184a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" loading="lazy"></span>.</li></ul>

<p>Entsprechend gilt für die Energiestufen der beiden o. g. Orbits im Atom (siehe <a href="Rydberg-Energie#Anwendung" class="mw-redirect" title="Rydberg-Energie">Rydberg-Energie</a>):

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<annotation encoding="application/x-tex">{\displaystyle E_{1}={\frac {R}{n_{1}^{2}}}\cdot c\cdot h}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f4cc33b80db316273b93182a2d399f7de27756dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.857ex; height:6.176ex;" alt="{\displaystyle E_{1}={\frac {R}{n_{1}^{2}}}\cdot c\cdot h}" loading="lazy"></span></dd>

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<annotation encoding="application/x-tex">{\displaystyle E_{2}={\frac {R}{n_{2}^{2}}}\cdot c\cdot h}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d734c76e70422db7416f673d0bb38cbcb92580d1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.857ex; height:6.176ex;" alt="{\displaystyle E_{2}={\frac {R}{n_{2}^{2}}}\cdot c\cdot h}" loading="lazy"></span>.</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle n_{1}<n_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/58e3737206604f516374f27b1199a26a3df8625a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.996ex; height:2.176ex;" alt="{\displaystyle n_{1}<n_{2}}" loading="lazy"></span> folgt daraus:

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<annotation encoding="application/x-tex">{\displaystyle \Rightarrow E_{1}>E_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a534c544716985e4463a18210503de2b40376017.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.606ex; height:2.509ex;" alt="{\displaystyle \Rightarrow E_{1}>E_{2}}" loading="lazy"></span>.</dd></dl>

<p>Nachdem die Bedeutung der Hauptquantenzahl <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

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<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> im <a href="Term" title="Term">Term</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {R}{n^{2}}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\tfrac {R}{n^{2}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c86c04de940e867df8861df03777f0bf619d4b20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:2.654ex; height:4.009ex;" alt="{\displaystyle {\tfrac {R}{n^{2}}}}" loading="lazy"></span> für die Energieniveaus erkannt worden war, bürgerten sich die Begriffe <a href="Termsymbol" title="Termsymbol">Termsymbol</a> und <a href="Termschema" title="Termschema">Termschema</a> für damit zusammenhängende Werkzeuge ein.

</p>

<div class="mw-heading mw-heading3"><h3 id="Spektrallinien-Serien">Spektrallinien-Serien</h3></div>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{1}=1}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ac03fd3f78e3696025989e727d2453fa5861b719.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.71ex; height:2.509ex;" alt="{\displaystyle n_{1}=1}" loading="lazy"></span> (<a href="Grundzustand" title="Grundzustand">Grundzustand</a>) und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{2}\in (2...\infty )}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{2}\in (2...\infty )}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0b26b9200ab3d01370cd686d77a6fc2f130b8a3d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.526ex; height:2.843ex;" alt="{\displaystyle n_{2}\in (2...\infty )}" loading="lazy"></span> erhält man eine Serie von <a href="Spektrallinie" title="Spektrallinie">Spektrallinien</a>, die auch <a href="Lyman-Serie" title="Lyman-Serie">Lyman-Serie</a> genannt wird. Der erste Übergang der Serie hat eine Wellenlänge von 121 nm, die Seriengrenze liegt bei 91 nm. Analog ergeben sich die anderen Serien:

</p>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{1}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee784b70e772f55ede5e6e0bdc929994bff63413.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{1}}" loading="lazy"></span>

</th>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/840e456e3058bc0be28e5cf653b170cdbfcc3be4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}" loading="lazy"></span>

</th>

<th rowspan="2">Name

</th>

<th colspan="2">Wellenlänge

</th></tr>

<th>des ersten<br>Übergangs<br>(α-Linie)

</th>

<th>konvergiert<br>gegen<br>Grenzwert

</th></tr>

<tr>

<td><span style="visibility:hidden;">0</span>1

</td>

</td>

<td><a href="Lyman-Serie" title="Lyman-Serie">Lyman-Serie</a>

</td>

<td style="text-align:right">121 nm

</td>

<td style="text-align:right">91,13 nm

</td></tr>

<tr>

<td><span style="visibility:hidden;">0</span>2

</td>

</td>

<td><a href="Balmer-Serie" title="Balmer-Serie">Balmer-Serie</a>

</td>

<td style="text-align:right">656 nm

</td>

<td style="text-align:right">364,51 nm

</td></tr>

<tr>

<td><span style="visibility:hidden;">0</span>3

</td>

</td>

<td><a href="Paschen-Serie" title="Paschen-Serie">Paschen-Serie</a>

</td>

<td style="text-align:right">1.874 nm

</td>

<td style="text-align:right">820,14 nm

</td></tr>

<tr>

<td><span style="visibility:hidden;">0</span>4

</td>

</td>

<td><a href="Brackett-Serie" title="Brackett-Serie">Brackett-Serie</a>

</td>

<td style="text-align:right">4.051 nm

</td>

<td style="text-align:right">1458,03 nm

</td></tr>

<tr>

<td><span style="visibility:hidden;">0</span>5

</td>

</td>

<td><a href="Pfund-Serie" title="Pfund-Serie">Pfund-Serie</a>

</td>

<td style="text-align:right">7.456 nm

</td>

<td style="text-align:right">2278,17 nm

</td></tr>

<tr>

<td><span style="visibility:hidden;">0</span>6

</td>

</td>

<td><a href="Humphreys-Serie" title="Humphreys-Serie">Humphreys-Serie</a>

</td>

<td style="text-align:right">12.365 nm

</td>

<td style="text-align:right">3280,56 nm

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Erweiterungen">Erweiterungen</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Für_wasserstoffähnliche_Atome"><span id="F.C3.BCr_wasserstoff.C3.A4hnliche_Atome"></span>Für wasserstoffähnliche Atome</h3></div>

<p>Für <a href="Wasserstoff%C3%A4hnliches_Ion" class="mw-redirect" title="Wasserstoffähnliches Ion">wasserstoffähnliche Ionen</a>, d. h. Ionen, die nur ein einziges Elektron besitzen, wie z. B. <sub>2</sub>He<sup>+</sup>, <sub>3</sub>Li<sup>2+</sup>, <sub>4</sub>Be<sup>3+</sup> oder <sub>11</sub>Na<sup>10+</sup>, lässt sich obige Formel erweitern zu:

</p>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<msup>

</mrow>

</msup>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<mfrac>

<msup>

</msup>

</mrow>

</mrow>

</mrow>

</msubsup>

</mfrac>

</mrow>

<mfrac>

<msup>

</msup>

</mrow>

</mrow>

</mrow>

</msubsup>

</mfrac>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\lambda _{\mathrm {vac} }}}=Z^{2}\cdot R_{\infty }\left({\frac {1}{{n'}_{1}^{2}}}-{\frac {1}{{n'}_{2}^{2}}}\right)}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f5ee7bc3bb09904fb9f53d7adec8676ca53b335e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:30.872ex; height:7.509ex;" alt="{\displaystyle {\frac {1}{\lambda _{\mathrm {vac} }}}=Z^{2}\cdot R_{\infty }\left({\frac {1}{{n'}_{1}^{2}}}-{\frac {1}{{n'}_{2}^{2}}}\right)}" loading="lazy"></span></dd></dl>

<p>mit

</p>

<ul><li>der <a href="Kernladungszahl" class="mw-redirect" title="Kernladungszahl">Kernladungszahl</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Z}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" loading="lazy"></span>, d. h. der Anzahl der <a href="Proton" title="Proton">Protonen</a> im <a href="Atomkern" title="Atomkern">Atomkern</a></li>

<li>die um den <a href="Quantendefekttheorie" title="Quantendefekttheorie">Quantendefekt</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{n}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \delta _{n}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/50acda784849200b94d62c19614b5e143adf169e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.251ex; height:2.676ex;" alt="{\displaystyle \delta _{n}}" loading="lazy"></span> korrigierten <a href="Effektive_Hauptquantenzahl" title="Effektive Hauptquantenzahl">effektiven Hauptquantenzahlen</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n'_{i}=n_{i}-\delta _{n}}">

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n'_{i}=n_{i}-\delta _{n}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/27db3b0814529b83b9625cc8ede5007282dea326.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.579ex; height:3.009ex;" alt="{\displaystyle n'_{i}=n_{i}-\delta _{n}}" loading="lazy"></span>.</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Für_Atome_mit_einem_Valenzelektron"><span id="F.C3.BCr_Atome_mit_einem_Valenzelektron"></span>Für Atome mit einem Valenzelektron</h3></div>

<p>Eine weitere Verallgemeinerung auf die Lichtemission von Atomen, die in ihrer <a href="Valenzschale" title="Valenzschale">äußersten Schale</a> ein einzelnes Elektron besitzen, darunter aber evtl. weitere Elektronen in <a href="Oktettregel" title="Oktettregel">abgeschlossenen Schalen</a>, führt zum <a href="Moseleysches_Gesetz" title="Moseleysches Gesetz">Moseleyschen Gesetz</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<ul><li>Joseph Reader, Charles H. Corliss: <i>Line Spectra of the Elements</i>. In: <i><a href="CRC_Handbook_of_Chemistry_and_Physics" title="CRC Handbook of Chemistry and Physics">CRC Handbook of Chemistry and Physics</a></i></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/ASD/lines1.pl?unit=1&line_out=0&bibrefs=1&show_obs_wl=1&show_calc_wl=1&A_out=1&intens_out=1&allowed_out=1&forbid_out=1&conf_out=1&term_out=1&enrg_out=1&J_out=1&g_out=0&spectra=H%20I">Umfangreiche Datenbank mit 568 Emissionslinien des Wasserstoffs</a> des <a href="National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">National Institute of Standards and Technology</a> (A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (2014). NIST Atomic Spectra Database (ver. 5.2))</li></ul></div><div><div class="zim-footer">

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