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Fix Matter see-also invoke

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{{Short description|Arrangement of electrons in an atom's orbitals}}

{{Quantum matter backlink|Atoms}}

An '''electron configuration''' describes how [[Physics:Quantum atoms/electron|electrons]] are distributed among the [[Physics:Quantum atoms/orbital|orbitals]] of an [[Physics:Quantum atoms/atom|atom]], molecule, or solid-state system.<ref name="IUPAC1">{{GoldBookRef|file=C01248|title=configuration (electronic)}}</ref> It determines many physical and chemical properties of the atom, including bonding, spectra, periodic trends, and reactivity.

<div style="float:right; border:1px solid #e0d890; background:#fff8cc; padding:6px; margin:0 0 1em 1em; width:450px;">
[[File:Electron_configuration-2.png|440px]]
<div style="font-size:90%;">Example of electron configuration showing how electrons occupy orbitals in an atom.</div>
</div>

== Description ==
In [[Physics:Quantum atoms/atom|atoms]], electron configuration gives the occupation of shells, subshells, and orbitals. For example, the electron configuration of neon is 1s2 2s2 2p6, meaning that the 1s, 2s, and 2p subshells contain two, two, and six electrons respectively.

Electron configurations describe electrons as occupying quantum states in an average field produced by the nucleus and the other electrons. In more formal quantum mechanics, configurations may be represented by Slater determinants or configuration state functions.

Electrons can move from one configuration to another by absorbing or emitting a quantum of energy, usually a photon. This connects electron configuration directly to [[Physics:Quantum atoms/energy level|energy levels]], spectroscopy, and atomic structure.

== Shells and subshells ==
An electron shell is a set of allowed quantum states sharing the same principal quantum number {{mvar|n}}. The maximum number of electrons in the {{mvar|n}}th shell is 2''n''2. Thus the first shell can hold two electrons, the second shell eight electrons, and the third shell eighteen electrons.

A subshell is defined by the azimuthal quantum number {{mvar|l}}. The values {{mvar|l}} = 0, 1, 2, and 3 correspond to the s, p, d, and f subshells. The maximum number of electrons in a subshell is 2(2{{mvar|l}} + 1), giving two electrons in an s subshell, six in a p subshell, and ten in a d subshell.

These limits follow from quantum mechanics and the Pauli exclusion principle, which states that no two electrons in the same atom can have the same set of four quantum numbers.<ref>{{GoldBookRef|file=PT07089|title=Pauli exclusion principle}}</ref> A detailed treatment of atomic spectra and structure is given by Cowan.<ref>{{Cite book |last=Cowan |first=Robert D. |title=The Theory of Atomic Structure and Spectra |date=2020 |publisher=University of California Press |isbn=9780520906150}}</ref>

== Notation ==
Electron configurations are written as a sequence of subshell labels with superscripts giving the number of electrons. Hydrogen is written as 1s1, lithium as 1s2 2s1, and phosphorus as 1s2 2s2 2p6 3s2 3p3.

The letters s, p, d, and f originated from early spectroscopic terms: sharp, principal, diffuse, and fundamental. Later labels continue alphabetically as g, h, i, and so on, although these orbitals are rarely needed in ordinary chemistry.<ref>{{cite web| url=http://scienceworld.wolfram.com/physics/ElectronOrbital.html|year=2007 |first=Eric W.|last= Weisstein|title=Electron Orbital|work=wolfram}}</ref><ref>{{cite book|title=General Chemistry
|first1=Darrell D. |last1=Ebbing|first2= Steven D. |last2=Gammon|url=https://books.google.com/books?id=_vRm5tiUJcsC&pg=PA284 |page=284|isbn=978-0-618-73879-3|date=2007-01-12|publisher=Cengage Learning }}</ref>

For larger atoms, noble-gas shorthand is often used. For example, phosphorus may be written as [Ne] 3s2 3p3. Empty subshells may be omitted or explicitly written with a superscript zero, depending on context.<ref>{{Cite book|last1=Rayner-Canham|first1=Geoff|title=Descriptive Inorganic Chemistry|last2=Overton|first2=Tina|publisher=Macmillan Education|year=2014|isbn=978-1-319-15411-0|edition=6|pages=13–15}}</ref>

== Filling rules ==
Electron configurations follow several important rules:

* the Pauli exclusion principle, which prevents two electrons in the same atom from sharing all four quantum numbers
* Hund’s rule, which favors parallel spins in degenerate orbitals
* the Aufbau principle, which fills lower-energy orbitals before higher-energy orbitals

The Aufbau principle states that a maximum of two electrons are placed into orbitals in order of increasing orbital energy.<ref>{{GoldBookRef|file=AT06996|title=aufbau principle}}</ref> In the Madelung rule, subshells are filled by increasing {{mvar|n}} + {{mvar|l}}; if two subshells have the same value, the one with lower {{mvar|n}} is filled first.<ref name="Madelung">{{cite book | last = Madelung | first = Erwin | author-link = Erwin Madelung | title = Mathematische Hilfsmittel des Physikers | location = Berlin | publisher = Springer | year = 1936}}</ref><ref>{{cite journal | title = Theoretical justification of Madelung's rule | journal = Journal of Chemical Education | last = Wong | first = D. Pan | year = 1979 | issue = 11 | pages = 714–18 | volume = 56 | doi = 10.1021/ed056p714|bibcode = 1979JChEd..56..714W }}</ref>

The common filling sequence begins:

:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

== Ground and excited states ==
The configuration with the lowest electronic energy is the ground-state configuration. Any higher-energy configuration is an excited state. For example, sodium has the ground-state configuration 1s2 2s2 2p6 3s1. If the 3s electron is promoted to 3p, the atom enters an excited configuration.

Atoms can return from excited states to lower states by emitting photons. This is why electron configuration is essential for understanding emission spectra, absorption spectra, lasers, and atomic lamps.

== History ==
The concept of electron arrangement developed from early atomic theory and spectroscopy. Irving Langmuir proposed a shell-like arrangement of electrons in 1919.<ref>{{cite journal |last1=Langmuir |first1=Irving |author1-link=Irving Langmuir |date=June 1919 |title=The Arrangement of Electrons in Atoms and Molecules |journal=Journal of the American Chemical Society |volume=41 |issue=6 |pages=868–934 |doi=10.1021/ja02227a002|bibcode=1919JAChS..41..868L |url=https://zenodo.org/record/1429026 }}</ref> Niels Bohr later connected electron shells with periodicity in the elements.<ref name="Bohr">{{cite journal | last = Bohr | first = Niels | s2cid = 123582460 | author-link = Niels Bohr | title = Über die Anwendung der Quantumtheorie auf den Atombau. I | journal = Zeitschrift für Physik| year = 1923 | volume = 13 | issue = 1 | page = 117|bibcode = 1923ZPhy...13..117B |doi = 10.1007/BF01328209 }}</ref>

Richard Abegg described valence electrons in 1904.<ref>{{cite journal
| doi = 10.1002/zaac.19040390125
| volume = 39
| issue = 1
| pages = 330–380
| last = Abegg
| first = R.
| title = Die Valenz und das periodische System. Versuch einer Theorie der Molekularverbindungen
| trans-title = Valency and the periodic system. Attempt at a theory of molecular compounds
| journal = Zeitschrift für Anorganische Chemie
| year = 1904
| url = https://zenodo.org/record/1428102
}}</ref> E. C. Stoner improved the shell model by incorporating an additional quantum number.<ref>{{cite journal | doi = 10.1080/14786442408634535 | last = Stoner | first = E.C. | author-link = Edmund Clifton Stoner | title = The distribution of electrons among atomic levels | journal = Philosophical Magazine |series=6th Series| volume = 48 | year = 1924 | pages = 719–36 | issue = 286}}</ref> Wolfgang Pauli introduced the exclusion principle in 1925, providing the key rule for shell and subshell occupation.<ref>{{cite journal | last = Pauli | first = Wolfgang | s2cid = 122477612 | author-link=Wolfgang Pauli | title = Über den Einfluss der Geschwindigkeitsabhändigkeit der elektronmasse auf den Zeemaneffekt | journal = Zeitschrift für Physik| year = 1925 | volume = 31 | issue = 1 | pages = 373 | doi = 10.1007/BF02980592|bibcode = 1925ZPhy...31..373P }} English translation from {{cite journal | last = Scerri | first = Eric R. | url = http://www.chem.ucla.edu/dept/Faculty/scerri/pdf/BJPS.pdf | title = The Electron Configuration Model, Quantum Mechanics and Reduction | journal = The British Journal for the Philosophy of Science| year = 1991 | volume = 42 | issue = 3 | pages = 309–25 | doi = 10.1093/bjps/42.3.309}}</ref>

The Schrödinger equation, published in 1926, supplied the modern quantum-mechanical basis for atomic orbitals and quantum numbers.

== Periodic table ==
The structure of the periodic table is closely related to electron configuration. Elements in the same group often have similar valence-shell configurations and therefore similar chemical properties.

The s, p, d, and f blocks of the periodic table correspond to the filling of s, p, d, and f subshells. Valence electrons largely determine bonding behavior, ionization energy, and chemical reactivity.

== Exceptions and limitations ==
The Aufbau principle is approximate. Electron energies depend on the nuclear charge, electron-electron interactions, and the occupation of other orbitals. Transition metals and heavier elements often show exceptions to simple Madelung filling.

Chromium, copper, niobium, palladium, platinum, and other elements have configurations that differ from the simplest filling sequence. Explanations involving half-filled or filled subshells are useful but incomplete.<ref name=mustdie>{{cite journal |last1=Scerri |first1=Eric |date=2019 |title=Five ideas in chemical education that must die |journal=Foundations of Chemistry |volume=21 |pages=61–69 |doi=10.1007/s10698-018-09327-y|s2cid=104311030 }}</ref> Orbital energies may shift with ionization, bonding, and chemical environment.<ref>{{cite journal | last = Melrose | first = Melvyn P. |author2=Scerri, Eric R. | title = Why the 4s Orbital is Occupied before the 3d | journal = Journal of Chemical Education | volume = 73 | issue = 6 | pages = 498–503 | year = 1996 | doi = 10.1021/ed073p498|bibcode = 1996JChEd..73..498M }}</ref><ref>{{cite magazine |last=Scerri |first=Eric |author-link=Eric Scerri |date=7 November 2013 |title=The trouble with the aufbau principle |url=https://eic.rsc.org/feature/the-trouble-with-the-aufbau-principle/2000133.article |url-status=live |magazine=[[Education in Chemistry]] |volume=50 |issue=6 |pages=24–26 |publisher=[[Royal Society of Chemistry]] |archive-url=https://web.archive.org/web/20180121061346/https://eic.rsc.org/feature/the-trouble-with-the-aufbau-principle/2000133.article |archive-date=21 January 2018 |access-date=12 June 2018}}</ref>

Chemical environments can also change the effective configuration. For example, thorium ions and thorium compounds may show different orbital occupations.<ref>{{cite journal |first1=Ryan R. |last1=Langeslay |first2=Megan E. |last2=Fieser |first3=Joseph W. |last3=Ziller |first4=Philip |last4=Furche |first5=William J. |last5=Evans |title=Synthesis, structure, and reactivity of crystalline molecular complexes of the {[C5H3(SiMe3)2]3Th}1− anion containing thorium in the formal +2 oxidation state |journal=Chem. Sci. |year=2015 |volume=6 |pages=517–521 |doi=10.1039/C4SC03033H|pmc=5811171 |pmid=29560172 |issue=1 }}</ref><ref>{{cite book|last1 = Wickleder|first1 = Mathias S.|first2 = Blandine|last2 = Fourest|first3 = Peter K.|last3 = Dorhout|ref = Wickleder et al.|contribution = Thorium|title = The Chemistry of the Actinide and Transactinide Elements|editor1-first = Lester R.|editor1-last = Morss|editor2-first = Norman M.|editor2-last = Edelstein|editor3-first = Jean|editor3-last = Fuger|edition = 3rd|date = 2006|volume = 3|publisher = Springer|location = Dordrecht, the Netherlands|pages = 52–160|url = http://radchem.nevada.edu/classes/rdch710/files/thorium.pdf|doi = 10.1007/1-4020-3598-5_3| isbn=978-1-4020-3555-5 |url-status = dead|archive-url = https://web.archive.org/web/20160307160941/http://radchem.nevada.edu/classes/rdch710/files/Thorium.pdf|archive-date = 2016-03-07}}</ref> In metals and compounds, configurations may be better described as mixtures or superpositions of several configurations.<ref>{{Cite journal|doi = 10.26434/chemrxiv.11860941|title = The Chemical Bond Across the Periodic Table: Part 1 – First Row and Simple Metals|last1 = Ferrão|first1 = Luiz|last2 = Machado|first2 = Francisco Bolivar Correto|last3 = Cunha|first3 = Leonardo dos Anjos|last4 = Fernandes|first4 = Gabriel Freire Sanzovo|url = https://figshare.com/articles/The_Chemical_Bond_Across_the_Periodic_Table_Part_1_First_Row_and_Simple_Metals/11860941|journal =[[ChemRxiv]] | s2cid=226121612 |access-date = 23 August 2020|archive-date = 1 December 2020|archive-url = https://web.archive.org/web/20201201001121/https://figshare.com/articles/The_Chemical_Bond_Across_the_Periodic_Table_Part_1_First_Row_and_Simple_Metals/11860941|url-status = dead|url-access = subscription|doi-access = free}}</ref>

Relativistic effects become important for heavy elements and can shift orbital energies, especially for s and p orbitals.<ref>{{GoldBookRef|file=RT07093|title=relativistic effects}}</ref><ref>{{cite journal | first = Pekka | last = Pyykkö | title = Relativistic effects in structural chemistry | journal = [[Chemical Reviews]] |year = 1988 | volume = 88 | pages = 563–94 | doi = 10.1021/cr00085a006 | issue = 3}}</ref> Superheavy-element configurations are therefore partly predicted rather than experimentally verified.<ref>{{cite journal |last1=Umemoto |first1=Koichiro |last2=Saito |first2=Susumu |date=1996 |title=Electronic Configurations of Superheavy Elements |url=https://journals.jps.jp/doi/pdf/10.1143/JPSJ.65.3175 |journal=Journal of the Physical Society of Japan |volume=65 |issue=10 |pages=3175–9 |doi=10.1143/JPSJ.65.3175 |bibcode=1996JPSJ...65.3175U |access-date=31 January 2021|url-access=subscription }}</ref><ref name=Haire>{{cite book| title=The Chemistry of the Actinide and Transactinide Elements| editor1-last=Morss|editor2-first=Norman M.| editor2-last=Edelstein| editor3-last=Fuger|editor3-first=Jean| last1=Hoffman|first1=Darleane C. |last2=Lee |first2=Diana M. |last3=Pershina |first3=Valeria |chapter=Transactinides and the future elements| publisher= [[Springer Science+Business Media]]| year=2006| isbn=978-1-4020-3555-5| location=Dordrecht, The Netherlands| edition=3rd}}</ref><ref>{{cite conference |url=https://www.epj-conferences.org/articles/epjconf/pdf/2016/26/epjconf-NS160-01001.pdf |title=Is the Periodic Table all right ("PT OK")? |last1=Pyykkö |first1=Pekka |date=2016 |conference=Nobel Symposium NS160 – Chemistry and Physics of Heavy and Superheavy Elements}}</ref>

== Open and closed shells ==
An '''open shell''' is a valence shell that is not completely filled, or that contains unpaired electrons. A '''closed shell''' is a filled shell or subshell and is usually especially stable.<ref>{{cite web|url=http://www.newi.ac.uk/buckleyc/periodic.htm|title=Periodic table|access-date=2007-11-01|archive-url=https://web.archive.org/web/20071103074338/http://www.newi.ac.uk/buckleyc/periodic.htm|archive-date=2007-11-03|url-status=dead}}</ref>

In molecules, open-shell systems contain unpaired electrons and often require special quantum-chemical treatment such as restricted open-shell or unrestricted Hartree–Fock methods.<ref>{{cite book|chapter-url=http://www.semichem.com/ampacmanual/ci.html |url=http://www.semichem.com/ampacmanual/ |publisher=Semichem, Inc. |chapter=Chapter 11. Configuration Interaction|title=AMPAC™ 10 User Guide}}</ref> Open-shell molecules are often more difficult to model computationally.<ref>{{cite web|url=http://iopenshell.usc.edu/|title=Laboratory for Theoretical Studies of Electronic Structure and Spectroscopy of Open-Shell and Electronically Excited Species – iOpenShell|website=iopenshell.usc.edu}}</ref>

== Noble gas configuration ==
A noble gas configuration is a filled-shell electron configuration like those of helium, neon, argon, krypton, xenon, and radon. Main-group atoms often react in ways that move them toward a noble-gas-like valence shell. This is the basis of the octet rule for many simple compounds.

== Molecules and solids ==
Electron configuration in molecules is more complex than in atoms because molecular orbitals extend over more than one nucleus. Molecular orbitals are labeled by symmetry rather than by atomic s, p, d, and f labels. The configuration of dioxygen, for example, explains its paramagnetism and was an important success of molecular orbital theory.<ref>Levine I.N. ''Quantum Chemistry'' (4th ed., Prentice Hall 1991) p.376 {{ISBN|0-205-12770-3}}</ref><ref>Miessler G.L. and Tarr D.A. ''Inorganic Chemistry'' (2nd ed., Prentice Hall 1999) p.118 {{ISBN|0-13-841891-8}}</ref>

In solids, the number of electron states becomes very large and the states form energy bands. In that context, the language of electron configuration gives way to band theory.

== Applications ==
Electron configurations are used to understand:

* the structure of the periodic table
* chemical bonding and valence
* atomic and molecular spectra
* magnetic properties
* lasers and semiconductors
* computational chemistry and molecular orbital theory

In computational chemistry, configurations are often combined with molecular orbital theory and basis-set methods. Density functional theory uses a different framework but still connects electronic structure to observable properties.

== Properties ==

* distribution over [[Physics:Quantum atoms/energy level|energy levels]]
* arrangement within [[Physics:Quantum atoms/orbital|orbitals]]
* linked to [[Physics:Quantum atoms/spin|spin]] and quantum numbers
* determines valence behavior and periodic trends
* important for spectroscopy and chemical bonding

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}
{{Sourceattribution|Physics:Quantum atoms/electron configuration|1}}

Physics:Quantum atoms/electron configuration - Revision history

imported>WikiHarold: Fix Matter see-also invoke

imported>WikiHarold: Fix Matter see-also invoke