Datei:Hydrogen eigenstate n2 l1 m-1.png

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class="fileinfo-paramfield" lang="de">Beschreibung<span class="summary fn" style="display:none">Hydrogen eigenstate n2 l1 m-1.png</span></td> <td class="description"> <div class="description en" dir="ltr" lang="en"><span class="language en" title="Englisch"><b>English: </b></span> Calculated 2p<sub>-1</sub> <a href="https://en.wikipedia.org/wiki/Atomic_orbital" class="extiw" title="en:Atomic orbital">orbital</a> of an electron's eigenstate in the Coulomb-field of a hydrogen nucleus. An <a href="https://en.wikipedia.org/wiki/Eigenfunction" class="extiw" title="en:Eigenfunction">eigenstate</a> is a state which keeps it's shape except for a complex phase when the <a href="https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)" class="extiw" title="en:Hamiltonian (quantum mechanics)">Hamilton operator</a> is applied, thus being invariant in time while obeying the <a href="https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" class="extiw" title="en:Schrödinger equation">Schrödinger equation</a>. The orbital is aligned around the z-axis, but remains an eigenfunction if rotated to any direction.<br> <p>The <a href="https://en.wikipedia.org/wiki/Hydrogen_atom#Wavefunction" class="extiw" title="en:Hydrogen atom">wavefunction</a> is: </p> <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 \psi _{2,1,-1}(r,\vartheta ,\varphi )={\sqrt {{\left({\frac {1}{a_{0}}}\right)}^{3}{\frac {1}{24}}}}\cdot e^{\textstyle -r/(2\,a_{0})}\cdot \left({\frac {r}{a_{0}}}\right)\cdot Y_{1}^{-1}(\vartheta ,\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>ϑ</mi> <mo>,</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>24</mn> </mfrac> </mrow> </msqrt> </mrow> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> </msup> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>ϑ</mi> <mo>,</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{2,1,-1}(r,\vartheta ,\varphi )={\sqrt {{\left({\frac {1}{a_{0}}}\right)}^{3}{\frac {1}{24}}}}\cdot e^{\textstyle -r/(2\,a_{0})}\cdot \left({\frac {r}{a_{0}}}\right)\cdot Y_{1}^{-1}(\vartheta ,\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10b8184cb50ca1a7aea4ce22bfd3b5e6bdb63a0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:62.93ex; height:7.676ex;" alt="{\displaystyle \psi _{2,1,-1}(r,\vartheta ,\varphi )={\sqrt {{\left({\frac {1}{a_{0}}}\right)}^{3}{\frac {1}{24}}}}\cdot e^{\textstyle -r/(2\,a_{0})}\cdot \left({\frac {r}{a_{0}}}\right)\cdot Y_{1}^{-1}(\vartheta ,\varphi )}"></span></dd></dl> <p>The state is an eigenstate of H, L² and L<sub>z</sub>, which constitute a <a href="https://en.wikipedia.org/wiki/complete_set_of_commuting_observables" class="extiw" title="en:complete set of commuting observables">complete set of commuting observables</a>.<br> The <a href="https://en.wikipedia.org/wiki/quantum_number" class="extiw" title="en:quantum number">quantum numbers</a> mean that the following quantities have a sharp certain value: </p> <ul><li>n = 2: <a href="https://en.wikipedia.org/wiki/Principal_quantum_number" class="extiw" title="en:Principal quantum number">Energy</a>: <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=-1\,\mathrm {Ry} /n^{2}=-13.6\,\mathrm {eV} /4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>13.6</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=-1\,\mathrm {Ry} /n^{2}=-13.6\,\mathrm {eV} /4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12d4356e3d35be023277035d2aa3250829032759" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.31ex; height:3.176ex;" alt="{\displaystyle E=-1\,\mathrm {Ry} /n^{2}=-13.6\,\mathrm {eV} /4}"></span></li> <li>l = 1: <a href="https://en.wikipedia.org/wiki/Azimuthal_quantum_number" class="extiw" title="en:Azimuthal quantum number">Angular momentum</a>: <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|={\sqrt {l\,(l+1)}}\,\hbar ={\sqrt {2}}\,\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>l</mi> <mspace width="thinmathspace"></mspace> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |L|={\sqrt {l\,(l+1)}}\,\hbar ={\sqrt {2}}\,\hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c04bf1b33179aa5a1f6cea0768f39241f6d2ed6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.468ex; height:4.843ex;" alt="{\displaystyle |L|={\sqrt {l\,(l+1)}}\,\hbar ={\sqrt {2}}\,\hbar }"></span></li> <li>m = -1: <a href="https://en.wikipedia.org/wiki/Magnetic_quantum_number" class="extiw" title="en:Magnetic quantum number">Angular momentum in z-direction</a>: <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_{z}=m\,\hbar =-\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mspace width="thinmathspace"></mspace> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{z}=m\,\hbar =-\hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/618895ef15d52fb79d280d6c80359ff5b6c58341" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.63ex; height:2.509ex;" alt="{\displaystyle L_{z}=m\,\hbar =-\hbar }"></span></li></ul> <p>Since l=1, this is called a p-orbital. <br><br> The depicted rigid body is where the probability density exceeds a certain value. The color shows the complex phase of the wavefunction, where blue means real positive, red means imaginary positive, yellow means real negative and green means imaginary negative. The image is <a href="https://en.wikipedia.org/wiki/Ray_tracing_(graphics)" class="extiw" title="en:Ray tracing (graphics)">raytraced</a> using modified <a href="https://en.wikipedia.org/wiki/Phong_reflection_model" class="extiw" title="en:Phong reflection model">Phong lighting</a>. <br> </p> The <a href="https://en.wikipedia.org/wiki/fine_structure" class="extiw" title="en:fine structure">fine structure</a> is neglected.</div></td> </tr> <tr> <td id="fileinfotpl_date" class="fileinfo-paramfield" lang="de">Datum</td> <td lang="de"> <time class="dtstart" datetime="2010-08" lang="de" dir="ltr" style="white-space:nowrap">August 2010</time></td> </tr> <tr> <td id="fileinfotpl_src" class="fileinfo-paramfield" lang="de">Quelle</td> <td> <p><span class="int-own-work" lang="de">Eigenes Werk</span>, </p> Created with <a href="//commons.wikimedia.org/wiki/User:Geek3/hydrogen" title="User:Geek3/hydrogen">hydrogen</a> 1.0</td> </tr> <tr> <td id="fileinfotpl_aut" class="fileinfo-paramfield" lang="de">Urheber</td> <td> <a href="//commons.wikimedia.org/wiki/User:Geek3" title="User:Geek3">Geek3</a></td> </tr> <tr> <td id="fileinfotpl_ver" class="fileinfo-paramfield" lang="de">Andere Versionen</td> <td> <span typeof="mw:File"><a href="//commons.wikimedia.org/wiki/File:Atomic-orbital-cloud_n2_l1_m-1.png" class="mw-file-description" title="Orbital cloud with actual probability density distribution."><img alt="Orbital cloud with actual probability density distribution." src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Atomic-orbital-cloud_n2_l1_m-1.png/100px-Atomic-orbital-cloud_n2_l1_m-1.png" decoding="async" width="100" height="100" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Atomic-orbital-cloud_n2_l1_m-1.png/150px-Atomic-orbital-cloud_n2_l1_m-1.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Atomic-orbital-cloud_n2_l1_m-1.png/200px-Atomic-orbital-cloud_n2_l1_m-1.png 2x" data-file-width="1024" data-file-height="1024"></a></span></td> </tr> </tbody></table> </div> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2></div> <table class="wikitable" style="text-align:right"> <tbody><tr> <th>Scale</th> <th>Surface probability density</th> <th>Probability inside the solid shape </th></tr> <tr> <td>240px / <a href="https://en.wikipedia.org/wiki/Bohr_radius" class="extiw" title="en:Bohr radius">a<sub>0</sub></a></td> <td>1.97·10<sup>-3</sup> / <a href="https://en.wikipedia.org/wiki/Bohr_radius" class="extiw" title="en:Bohr radius">a<sub>0</sub></a><sup>3</sup></td> <td>13.4% </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Lizenz">Lizenz</h2></div> <div style="clear:both; 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href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q11240141\">p-Orbital<\/a>"}},"text\/plain":{"de":{"P180":"p-Orbital"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P180 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h3 class="wbmi-statements-title">In dieser Datei abgebildete Objekte</h3><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P180" href="https://www.wikidata.org/wiki/Special:EntityPage/P180">Motiv</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M11272751$af166665-4b72-fd72-c332-86735111eade" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q11240141" href="https://www.wikidata.org/wiki/Special:EntityPage/Q11240141">p-Orbital</a></bdi></h4></div></div></div></div></div></div></div></div><div id="P170" data-property="P170" data-statements="[{"mainsnak":{"snaktype":"somevalue","property":"P170","hash":"d3550e860f988c6675fff913440993f58f5c40c5"},"type":"statement","qualifiers":{"P2699":[{"snaktype":"value","property":"P2699","hash":"debdaffdba74e4761bcf7a7423510dfea98b6c4e","datavalue":{"value":"https:\/\/commons.wikimedia.org\/wiki\/user:Geek3","type":"string"}}],"P4174":[{"snaktype":"value","property":"P4174","hash":"7726c708cd7dad4a3477de5c8a9297efaeba111f","datavalue":{"value":"Geek3","type":"string"}}],"P2093":[{"snaktype":"value","property":"P2093","hash":"999582aeb86724b98e2b7bcbef9e8e4c3b90e818","datavalue":{"value":"Geek3","type":"string"}}]},"qualifiers-order":["P2699","P4174","P2093"],"id":"M11272751$62F6D43F-1FAF-48E0-B9CD-9488F1C0D626","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":170,\"id\":\"P170\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P170\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P170\">Urheber<\/a>"}},"text\/plain":{"de":{"":"Urheber"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2699,\"id\":\"P2699\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P2699\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P2699\">URL<\/a>"}},"text\/plain":{"de":{"":"URL"}}},"{\"value\":\"https:\\\/\\\/commons.wikimedia.org\\\/wiki\\\/user:Geek3\",\"type\":\"string\"}":{"text\/html":{"de":{"P2699":"<a target=\"_blank\" rel=\"nofollow\" class=\"external free\" href=\"https:\/\/commons.wikimedia.org\/wiki\/user:Geek3\">https:\/\/commons.wikimedia.org\/wiki\/user:Geek3<\/a>"}},"text\/plain":{"de":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:Geek3"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P4174\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P4174\">Wikimedia-Benutzername<\/a>"}},"text\/plain":{"de":{"":"Wikimedia-Benutzername"}}},"{\"value\":\"Geek3\",\"type\":\"string\"}":{"text\/html":{"de":{"P4174":"<a target=\"_blank\" class=\"wb-external-id external\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:CentralAuth?target=Geek3\" rel=\"nofollow\">Geek3<\/a>","P2093":"Geek3"}},"text\/plain":{"de":{"P4174":"Geek3","P2093":"Geek3"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P2093\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P2093\">Autor (Text)<\/a>"}},"text\/plain":{"de":{"":"Autor (Text)"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P170 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P170" href="https://www.wikidata.org/wiki/Special:EntityPage/P170">Urheber</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M11272751$62F6D43F-1FAF-48E0-B9CD-9488F1C0D626" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi>Einige Werte ohne einen Wikidata-Eintrag</bdi></h4></div></div></div><div class="wbmi-item-qualifiers"><div class="wbmi-snaklist-container"><div class="wbmi-snaklist-content"><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P2699" href="https://www.wikidata.org/wiki/Special:EntityPage/P2699">URL</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value"><a target="_blank" rel="nofollow" class="external free" href="https://commons.wikimedia.org/wiki/user:Geek3">https://commons.wikimedia.org/wiki/user:Geek3</a></span></div></div><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P4174" href="https://www.wikidata.org/wiki/Special:EntityPage/P4174">Wikimedia-Benutzername</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value"><a target="_blank" class="wb-external-id external" href="https://www.wikidata.org/wiki/Special:CentralAuth?target=Geek3" rel="nofollow">Geek3</a></span></div></div><div class="wbmi-snak"><div class="wbmi-snak-value"><a target="_blank" title="d:Special:EntityPage/P2093" href="https://www.wikidata.org/wiki/Special:EntityPage/P2093">Autor (Text)</a><span class="wbmi-snak-value-separator">: </span><span class="wbmi-snak-value--value">Geek3</span></div></div></div></div></div></div></div></div></div></div><div id="P6216" data-property="P6216" data-statements="[{"mainsnak":{"snaktype":"value","property":"P6216","hash":"5570347fdc76d2a80732f51ea10ee4b144a084e0","datavalue":{"value":{"entity-type":"item","numeric-id":50423863,"id":"Q50423863"},"type":"wikibase-entityid"}},"type":"statement","id":"M11272751$C23063C8-F325-4AE1-92D8-34D41DE987F6","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":6216,\"id\":\"P6216\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P6216\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P6216\">Urheberrechtsstatus<\/a>"}},"text\/plain":{"de":{"":"Urheberrechtsstatus"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":50423863,\"id\":\"Q50423863\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"P6216":"<a target=\"_blank\" title=\"d:Special:EntityPage\/Q50423863\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q50423863\">urheberrechtlich gesch\u00fctzt<\/a>"}},"text\/plain":{"de":{"P6216":"urheberrechtlich gesch\u00fctzt"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P6216 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P6216" href="https://www.wikidata.org/wiki/Special:EntityPage/P6216">Urheberrechtsstatus</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M11272751$C23063C8-F325-4AE1-92D8-34D41DE987F6" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q50423863" href="https://www.wikidata.org/wiki/Special:EntityPage/Q50423863">urheberrechtlich geschützt</a></bdi></h4></div></div></div></div></div></div></div></div><div id="P275" data-property="P275" data-statements="[{"mainsnak":{"snaktype":"value","property":"P275","hash":"4315b8c41a664bcb36dc3783262461e54b0ddf16","datavalue":{"value":{"entity-type":"item","numeric-id":50829104,"id":"Q50829104"},"type":"wikibase-entityid"}},"type":"statement","id":"M11272751$DE7D13CD-A1E0-4EBA-95CC-6A29082DF597","rank":"normal"},{"mainsnak":{"snaktype":"value","property":"P275","hash":"a35b4558d66c92eacbe2f569697ffb1934e0316e","datavalue":{"value":{"entity-type":"item","numeric-id":14946043,"id":"Q14946043"},"type":"wikibase-entityid"}},"type":"statement","id":"M11272751$C4801879-96C4-4B98-8517-63D3A0DD3C31","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":275,\"id\":\"P275\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P275\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P275\">Lizenz<\/a>"}},"text\/plain":{"de":{"":"Lizenz"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":50829104,\"id\":\"Q50829104\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"P275":"<a target=\"_blank\" title=\"d:Special:EntityPage\/Q50829104\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q50829104\">GNU-Lizenz f\u00fcr freie Dokumentation Version 1.2 oder sp\u00e4ter<\/a>"}},"text\/plain":{"de":{"P275":"GNU-Lizenz f\u00fcr freie Dokumentation Version 1.2 oder sp\u00e4ter"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":14946043,\"id\":\"Q14946043\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"P275":"<a target=\"_blank\" title=\"d:Special:EntityPage\/Q14946043\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q14946043\">Creative Commons Namensnennung \u2013 Weitergabe unter gleichen Bedingungen 3.0 Generisch<\/a>"}},"text\/plain":{"de":{"P275":"Creative 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Version 1.2 oder später</a></bdi></h4></div></div></div></div></div><div class="wbmi-item wbmi-item-read"><div data-guid="M11272751$C4801879-96C4-4B98-8517-63D3A0DD3C31" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q14946043" href="https://www.wikidata.org/wiki/Special:EntityPage/Q14946043">Creative Commons Namensnennung – Weitergabe unter gleichen Bedingungen 3.0 Generisch</a></bdi></h4></div></div></div></div></div></div></div></div><div id="P7482" data-property="P7482" data-statements="[{"mainsnak":{"snaktype":"value","property":"P7482","hash":"83568a288a8b8b4714a68e7239d8406833762864","datavalue":{"value":{"entity-type":"item","numeric-id":66458942,"id":"Q66458942"},"type":"wikibase-entityid"}},"type":"statement","id":"M11272751$F8AF9869-BAF9-4D08-9633-2A32BE0DC70D","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":7482,\"id\":\"P7482\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P7482\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P7482\">Quelle der Datei<\/a>"}},"text\/plain":{"de":{"":"Quelle der Datei"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"P7482":"<a target=\"_blank\" title=\"d:Special:EntityPage\/Q66458942\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q66458942\">durch Hochlader erstelltes Original<\/a>"}},"text\/plain":{"de":{"P7482":"durch Hochlader erstelltes Original"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P7482 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><div class="wbmi-statements-widget"><div class="wbmi-statement-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/P7482" href="https://www.wikidata.org/wiki/Special:EntityPage/P7482">Quelle der Datei</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M11272751$F8AF9869-BAF9-4D08-9633-2A32BE0DC70D" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q66458942" href="https://www.wikidata.org/wiki/Special:EntityPage/Q66458942">durch Hochlader erstelltes Original</a></bdi></h4></div></div></div></div></div></div></div></div><div id="P571" data-property="P571" data-statements="[{"mainsnak":{"snaktype":"value","property":"P571","hash":"9837f9a3def3f43f9933ffdd10525728bd2d75f3","datavalue":{"value":{"time":"+2010-08-01T00:00:00Z","timezone":0,"before":0,"after":0,"precision":10,"calendarmodel":"http:\/\/www.wikidata.org\/entity\/Q1985727"},"type":"time"}},"type":"statement","id":"M11272751$47F3483E-A7D3-43F2-9094-83DB92C6CB6B","rank":"normal"}]" data-formatvalue="{"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":571,\"id\":\"P571\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"de":{"":"<a target=\"_blank\" title=\"d:Special:EntityPage\/P571\" href=\"https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/P571\">Datum der Gr\u00fcndung, Erstellung, Entstehung, Erbauung<\/a>"}},"text\/plain":{"de":{"":"Datum der Gr\u00fcndung, Erstellung, Entstehung, 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class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi>August 2010</bdi></h4></div></div></div></div></div></div></div></div></mediainfoviewstatements></mediainfoview>    </div></div> <h2 id="filehistory">Dateiversionen</h2> <div id="mw-imagepage-section-filehistory"> <p>Klicke auf einen Zeitpunkt, um diese Version zu laden. </p> <table class="wikitable filehistory"> <tr><th></th><th>Version vom</th><th>Vorschaubild</th><th>Maße</th><th>Benutzer</th><th>Kommentar</th></tr> <tr><td>aktuell</td><td class="filehistory-selected" style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/0/07/Hydrogen_eigenstate_n2_l1_m-1.png">17:02, 25. Aug. 2010</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/0/07/Hydrogen_eigenstate_n2_l1_m-1.png"><img alt="Vorschaubild der Version vom 17:02, 25. Aug. 2010" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Hydrogen_eigenstate_n2_l1_m-1.png/120px-Hydrogen_eigenstate_n2_l1_m-1.png" decoding="async" loading="lazy" width="120" height="120" data-file-width="2560" data-file-height="2560" /></a></td><td>2.560 × 2.560 <span style="white-space: nowrap;">(392 KB)</span></td><td><a href="/wiki/Benutzer:Geek3" class="mw-userlink" title="Benutzer:Geek3"><bdi>Geek3</bdi></a></td><td dir="ltr">bigger scale</td></tr> <tr><td></td><td style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/archive/0/07/20100825160200%21Hydrogen_eigenstate_n2_l1_m-1.png">22:37, 24. Aug. 2010</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/archive/0/07/20100825160200%21Hydrogen_eigenstate_n2_l1_m-1.png"><img alt="Vorschaubild der Version vom 22:37, 24. Aug. 2010" src="//upload.wikimedia.org/wikipedia/commons/thumb/archive/0/07/20100825160200%21Hydrogen_eigenstate_n2_l1_m-1.png/120px-Hydrogen_eigenstate_n2_l1_m-1.png" decoding="async" loading="lazy" width="120" height="120" data-file-width="2560" data-file-height="2560" /></a></td><td>2.560 × 2.560 <span style="white-space: nowrap;">(234 KB)</span></td><td><a href="/wiki/Benutzer:Geek3" class="mw-userlink" title="Benutzer:Geek3"><bdi>Geek3</bdi></a></td><td dir="ltr">selfmade</td></tr> </table> </div> <h2 id="filelinks">Dateiverwendung</h2> <div id='mw-imagepage-section-linkstoimage'> <p>Die folgende Seite verwendet diese Datei: </p><ul class="mw-imagepage-linkstoimage"> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Atomorbital" title="Atomorbital">Atomorbital</a></li> </ul> </div> <h2 id="globalusage">Globale Dateiverwendung</h2> <div id="mw-imagepage-section-globalusage"><p>Die nachfolgenden anderen Wikis verwenden diese Datei: </p><ul> <li class='mw-gu-onwiki-en_wikibooks_org'>Verwendung auf en.wikibooks.org <ul> <li><a class="external" href="https://en.wikibooks.org/wiki/General_Chemistry/The_Quantum_Atom">General Chemistry/The Quantum Atom</a></li> <li><a class="external" href="https://en.wikibooks.org/wiki/General_Chemistry/Print_version">General Chemistry/Print version</a></li> </ul></li> <li class='mw-gu-onwiki-fr_wikipedia_org'>Verwendung auf fr.wikipedia.org <ul> <li><a class="external" href="https://fr.wikipedia.org/wiki/Orbitale_atomique">Orbitale atomique</a></li> </ul></li> </ul> </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Abgerufen von „<a dir="ltr" href="https://de.wikipedia.org/wiki/Datei:Hydrogen_eigenstate_n2_l1_m-1.png">https://de.wikipedia.org/wiki/Datei:Hydrogen_eigenstate_n2_l1_m-1.png</a>“</div></div> <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div> </div> </div> <div id="mw-navigation"> <h2>Navigationsmenü</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Meine Werkzeuge</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="Benutzerseite der IP-Adresse, von der aus du Änderungen durchführst">Nicht angemeldet</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spezial:Meine_Diskussionsseite" title="Diskussion über Änderungen von dieser IP-Adresse [n]" accesskey="n"><span>Diskussionsseite</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spezial:Meine_Beitr%C3%A4ge" title="Eine Liste der Bearbeitungen, die von dieser IP-Adresse gemacht wurden [y]" accesskey="y"><span>Beiträge</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Spezial:Benutzerkonto_anlegen&returnto=Datei%3AHydrogen+eigenstate+n2+l1+m-1.png" title="Wir ermutigen dich dazu, ein Benutzerkonto zu erstellen und dich anzumelden. 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