Physics:Quantum atoms/energy level - Revision history

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	== Energy level transitions ==		== Energy level transitions ==
	~~[[File:Atomic Absorption (hv corrected).svg\|thumb\|right\|Absorption of a photon causing an electron transition to a higher energy level.]]~~

	[[File:Schematic diagram of atomic line spontaneous emission (hv corrected).png\|thumb\|left\|Emission of a photon during a transition to a lower energy level.]]		[[File:Schematic diagram of atomic line spontaneous emission (hv corrected).png\|thumb\|left\|Emission of a photon during a transition to a lower energy level.]]

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	An approximate expression becomes:		An approximate expression becomes:

	:~~contentReference[oaicite:3]~~{~~index=3~~}		:<math>E_{n\ell} \approx -\frac{13.6\,\mathrm{eV}\, Z_{\mathrm{eff}}^2}{n^2}</math>

	These effects help determine electron configurations and atomic structure.		These effects help determine electron configurations and atomic structure.
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	The interaction energy is:		The interaction energy is:

	:~~contentReference[oaicite:4]{index~~=4}		:<math>\Delta E = m_\ell \mu_B B</math>

	This splitting produces the '''Zeeman effect'''.		This splitting produces the '''Zeeman effect'''.
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	The total molecular energy may be written as:		The total molecular energy may be written as:

	:~~contentReference[oaicite:5]~~{~~index~~=5}		:<math>E_{\mathrm{mol}} = E_{\mathrm{electronic}} + E_{\mathrm{vibrational}} + E_{\mathrm{rotational}}</math>

	Different molecular orbitals may be bonding, antibonding, or non-bonding.<ref name="chemguide">[http://www.chemguide.co.uk/analysis/uvvisible/theory.html#top UV-Visible Absorption Spectra]</ref>		Different molecular orbitals may be bonding, antibonding, or non-bonding.<ref name="chemguide">[http://www.chemguide.co.uk/analysis/uvvisible/theory.html#top UV-Visible Absorption Spectra]</ref>
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	Electrons may transition between energy levels by absorbing or emitting photons. The photon energy equals the difference between the initial and final states:		Electrons may transition between energy levels by absorbing or emitting photons. The photon energy equals the difference between the initial and final states:

	:~~contentReference[oaicite:6]~~{~~index=6~~}		:<math>\Delta E = h f = \frac{h c}{\lambda}</math>

	where {{math\|''h''}} is the Planck constant, {{mvar\|f}} is frequency, and {{mvar\|λ}} is wavelength.		where {{math\|''h''}} is the Planck constant, {{mvar\|f}} is frequency, and {{mvar\|λ}} is wavelength.

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	Each shell can contain only a limited number of electrons. The maximum number is approximately given by:		Each shell can contain only a limited number of electrons. The maximum number is approximately given by:

	:~~contentReference[oaicite:0]{index=0}~~		:<math>2n^2</math>

	Thus the first shell holds two electrons, the second eight, and the third eighteen.<ref name="madsci">[http://www.madsci.org/posts/archives/1999-03/921736624.Ch.r.html Re: Why do electron shells have set limits ?] madsci.org, 17 March 1999, Dan Berger, Faculty Chemistry/Science, Bluffton College</ref>		Thus the first shell holds two electrons, the second eight, and the third eighteen.<ref name="madsci">[http://www.madsci.org/posts/archives/1999-03/921736624.Ch.r.html Re: Why do electron shells have set limits ?] madsci.org, 17 March 1999, Dan Berger, Faculty Chemistry/Science, Bluffton College</ref>
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	For hydrogen-like atoms containing one electron, the energy levels are approximately given by:		For hydrogen-like atoms containing one electron, the energy levels are approximately given by:

	:~~contentReference[oaicite:1]~~{~~index=1~~}		:<math>E_n = -\frac{13.6\,\mathrm{eV}\, Z^2}{n^2}</math>

	where {{math\|''R''<sub>∞</sub>}} is the Rydberg constant, {{mvar\|Z}} is the atomic number, and {{mvar\|n}} is the principal quantum number.		where {{math\|''R''<sub>∞</sub>}} is the Rydberg constant, {{mvar\|Z}} is the atomic number, and {{mvar\|n}} is the principal quantum number.
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	The related Rydberg formula for emitted or absorbed wavelengths is:		The related Rydberg formula for emitted or absorbed wavelengths is:

	:~~contentReference[oaicite:~~2]{~~index=~~2}		:<math>\frac{1}{\lambda} = R_\infty Z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)</math>

	These relations successfully explain the spectral lines of hydrogen and hydrogen-like ions.		These relations successfully explain the spectral lines of hydrogen and hydrogen-like ions.

Harold: /* History */

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History

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	== History ==		== History ==
	The first evidence for quantized atomic energy levels came from the observation of spectral lines in sunlight by Joseph von Fraunhofer and William Hyde Wollaston.		The first evidence for quantized atomic energy levels came from the observation of spectral lines in sunlight by [[Biography:Joseph von Fraunhofer\|Joseph von Fraunhofer]] and [[Biography:William Hyde Wollaston\|William Hyde Wollaston]].

	In 1913, [[Biography:Niels Bohr\|Niels Bohr]] proposed quantized electron orbits in the Bohr model of the atom. Modern quantum mechanical explanations based on the Schrödinger equation were developed in the 1920s by [[Biography:Erwin Schrödinger\|Erwin Schrödinger]] and [[Biography:Werner Heisenberg\|Werner Heisenberg]].<ref name=Ruedenberg_Schwarz_2013>{{cite book \| chapter=Three Millennia of Atoms and Molecules \| first1=Klaus \| last1=Ruedenberg \| first2=W. H. Eugen \| last2=Schwarz \| title=Pioneers of Quantum Chemistry \| pages=1–45 \| series=ACS Symposium Series \| volume=1122 \| isbn=9780841227163 \| date=February 13, 2013 \| publisher=American Chemical Society \| doi=10.1021/bk-2013-1122.ch001 }}</ref>		In 1913, [[Biography:Niels Bohr\|Niels Bohr]] proposed quantized electron orbits in the Bohr model of the atom. Modern quantum mechanical explanations based on the Schrödinger equation were developed in the 1920s by [[Biography:Erwin Schrödinger\|Erwin Schrödinger]] and [[Biography:Werner Heisenberg\|Werner Heisenberg]].<ref name=Ruedenberg_Schwarz_2013>{{cite book \| chapter=Three Millennia of Atoms and Molecules \| first1=Klaus \| last1=Ruedenberg \| first2=W. H. Eugen \| last2=Schwarz \| title=Pioneers of Quantum Chemistry \| pages=1–45 \| series=ACS Symposium Series \| volume=1122 \| isbn=9780841227163 \| date=February 13, 2013 \| publisher=American Chemical Society \| doi=10.1021/bk-2013-1122.ch001 }}</ref>

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	These transitions form the basis of atomic and molecular spectroscopy. Depending on the energy involved, transitions may emit or absorb radio waves, infrared radiation, visible light, ultraviolet radiation, or X-rays.		These transitions form the basis of atomic and molecular spectroscopy. Depending on the energy involved, transitions may emit or absorb radio waves, infrared radiation, visible light, ultraviolet radiation, or X-rays.

			== Historical names ==
			* [[Biography:Niels Bohr\|Niels Bohr]] introduced quantized atomic energy levels in his 1913 model of hydrogen.
			* [[Biography:Johann Balmer\|Johann Balmer]] and [[Biography:Johannes Rydberg\|Johannes Rydberg]] found spectral regularities that helped reveal atomic level structure.
			* [[Biography:Erwin Schrödinger\|Erwin Schrödinger]] and [[Biography:Werner Heisenberg\|Werner Heisenberg]] gave the modern quantum-mechanical framework for energy eigenstates.

	== History ==		== History ==

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	~~{{Quantum article nav\|previous=Physics:Quantum atoms/electron\|previous label=Atoms/electron\|next=Physics:Quantum atoms/electron configuration\|next label=Atoms/electron configuration}}~~



	{{Short description\|Discrete energy state of an electron in an atom}}		{{Short description\|Discrete energy state of an electron in an atom}}
	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}
			{{Quantum article nav\|previous=Physics:Quantum atoms/electron\|previous label=Atoms/electron\|next=Physics:Quantum atoms/electron configuration\|next label=Atoms/electron configuration}}
	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

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	{{Short description\|Discrete energy state of an electron in an atom}}I		{{Short description\|Discrete energy state of an electron in an atom}}

	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}

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	{{Short description\|Discrete energy state of an electron in an atom}}~~Book II~~		{{Short description\|Discrete energy state of an electron in an atom}}I

	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}

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	{{Short description\|Discrete energy state of an electron in an atom}}		{{Short description\|Discrete energy state of an electron in an atom}}Book II

	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}

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	{{Short description\|Discrete energy state of an electron in an atom}}		{{Short description\|Discrete energy state of an electron in an atom}}Book II

	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}