Editing Atomic orbital (section)

{{Short description|Function describing an electron in an atom}}
{{Redirect|Orbital shell|the collection of spaceflight orbits|Satellite constellation{{!}}Orbital shell (spaceflight)}}
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[[File:Neon orbitals.png|right|thumb|upright=2|The shapes of the first five atomic orbitals are 1s, 2s, 2p<sub>x</sub>, 2p<sub>y</sub>, and 2p<sub>z</sub>. The two colors show the phase or sign of the wave function in each region. Each picture is [[domain coloring]] of a {{math|ψ(''x'', ''y'', ''z'')}}<!--Please don't italicize a bracket. --> function which depends on the coordinates of one electron. To see the elongated shape of {{math|ψ(''x'', ''y'', ''z'')<sup>2</sup>}} functions that show [[probability density]] more directly, see pictures of d-orbitals below.]]

In [[quantum mechanics]], an '''atomic orbital''' ({{IPAc-en|ˈ|ɔːr|b|ɪ|t|ə|l|audio=LL-Q1860 (eng)-Flame, not lame-Atomic orbital.wav}}) is a [[Function (mathematics)|function]] describing the location and [[Matter wave|wave-like behavior]] of an [[electron]] in an [[atom]].<ref>{{cite book|first1= Milton|last1= Orchin|first2=Roger S.|last2=Macomber|first3=Allan|last3=Pinhas|first4=R. Marshall|last4= Wilson|year=2005|chapter-url=http://media.wiley.com/product_data/excerpt/81/04716802/0471680281.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://media.wiley.com/product_data/excerpt/81/04716802/0471680281.pdf |archive-date=9 October 2022 |url-status=live|title= The Vocabulary and Concepts of Organic Chemistry |edition= 2nd |publisher=Wiley|chapter=1. Atomic Orbital Theory}}</ref> This function describes an electron's [[Charge density|charge distribution]] around the [[Atomic nucleus|atom's nucleus]], and can be used to calculate the [[probability]] of finding an electron in a specific region around the nucleus.<ref>{{cite book |last=Daintith |first=J. |url=https://archive.org/details/dictionaryofchem0000unse_r3p4/page/408/mode/2up?view=theater |title=Oxford Dictionary of Chemistry |publisher=Oxford University Press |year=2004 |isbn=978-0-19-860918-6 |location=New York |pages=407–409}}</ref>

Each orbital in an atom is characterized by a set of values of three [[quantum number]]s {{mvar|n}}, {{mvar|ℓ}}, and {{mvar|m<sub>ℓ</sub>}}, which respectively correspond to  electron's energy, its [[angular momentum|orbital angular momentum]], and its orbital angular momentum projected along a chosen axis ([[magnetic quantum number]]). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of {{mvar|m<sub>ℓ</sub>}} and {{mvar|−m<sub>ℓ</sub>}} orbitals, and are often labeled using  associated [[Spherical harmonics#Harmonic polynomial representation|harmonic polynomials]] (e.g., ''xy'', {{nowrap|''x''<sup>2</sup> − ''y''<sup>2</sup>}}) which describe their angular structure.

An orbital can be occupied by a maximum of two electrons, each with its own [[spin quantum number|projection of spin]] <math>m_s</math>. The simple names '''s orbital''', '''p orbital''', '''d orbital''', and '''f orbital''' refer to orbitals with angular momentum quantum number {{math|1=''ℓ'' = 0, 1, 2,}} and {{math|3}} respectively. These names, together with  their n values, are used to describe  [[electron configuration]]s of atoms. They are derived from  description by early spectroscopists of certain series of [[alkali metal]] [[Spectral line|spectroscopic lines]] as [[Sharp series|sharp]], [[Principal series (spectroscopy)|principal]], [[Diffuse series|diffuse]], and [[Fundamental series|fundamental]]. Orbitals for {{math|''ℓ'' > 3}} continue alphabetically (g, h, i, k, ...),<ref>{{cite book|first=David|last=Griffiths|year=1995|title=Introduction to Quantum Mechanics|pages=190–191|publisher=Prentice Hall|isbn=978-0-13-124405-4}}</ref> omitting&nbsp;j<ref>{{cite book|first=Ira|last=Levine|year=2000|title=Quantum Chemistry|edition=5|pages=[https://archive.org/details/quantumchemistry00levi_0/page/144 144–145]|publisher=Prentice Hall|isbn=978-0-13-685512-5|url=https://archive.org/details/quantumchemistry00levi_0/page/144}}</ref><ref>{{cite book|first1=Keith J.|last1=Laidler|first2=John H.|last2=Meiser|year=1982|title=Physical Chemistry|page=488|publisher=Benjamin/Cummings|isbn=978-0-8053-5682-3}}</ref> because some languages do not distinguish between letters "i" and "j".<ref>{{Cite book|url=https://books.google.com/books?id=QbQJAgAAQBAJ&pg=PA106|title=Quanta, Matter, and Change: A Molecular Approach to Physical Chemistry|publisher=Oxford University Press|isbn=978-0-19-920606-3|year=2009|page=106|first1=Peter |last1=Atkins |first2=Julio |last2=de Paula |first3=Ronald |last3=Friedman}}</ref>

Atomic orbitals are  basic building blocks of the '''atomic orbital model''' (or electron cloud or wave mechanics model), a modern framework for visualizing  submicroscopic behavior of electrons in matter. In this model, the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler [[hydrogen atom|hydrogen-like]] atomic orbitals. The repeating ''periodicity'' of blocks of 2, 6, 10, and 14 [[Chemical element|elements]] within sections of  [[periodic table]] arises naturally from  total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number {{mvar|n}}, particularly when the atom bears a positive charge, energies of certain sub-shells become very similar and so, the [[Aufbau principle|order]] in which they are said to be populated by electrons (e.g., [[Chromium|Cr]] = [Ar]4s<sup>1</sup>3d<sup>5</sup> and Cr<sup>2+</sup> = [Ar]3d<sup>4</sup>) can be rationalized only somewhat arbitrarily.

[[File:Hydrogen Density Plots.png|thumb|upright=1.5|Cross-sections of atomic orbitals of the electron in a hydrogen atom at different energy levels.  The probability of finding the electron is given by the color, as shown in the key at upper right.]]