Editing Electron (section)

== Characteristics ==

=== Classification ===
[[File:Standard Model of Elementary Particles.svg|right|thumb|upright=1.25|alt=A table with four rows and four columns, with each cell containing a particle identifier|Standard Model of elementary particles. The electron (symbol e) is on the left.]]
In the [[Standard Model]] of particle physics, electrons belong to the group of subatomic particles called [[lepton]]s, which are believed to be fundamental or [[elementary particle]]s. Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the first [[generation (particle physics)|generation]] of fundamental particles.<ref>
{{cite journal
 | last1 = Frampton | first1 = P.H.
 | last2 = Hung | first2 = P.Q.
 | last3 = Sher | first3 = Marc
 | year = 2000
 | title = Quarks and Leptons Beyond the Third Generation
 | journal = [[Physics Reports]]
 | volume = 330 | issue = 5–6 | pages = 263–348
 | doi = 10.1016/S0370-1573(99)00095-2
 |arxiv = hep-ph/9903387 |bibcode = 2000PhR...330..263F
 | s2cid = 119481188
}}</ref> The second and third generation contain charged leptons, the [[muon]] and the [[tau (particle)|tau]], which are identical to the electron in charge, [[Spin (physics)|spin]] and [[fundamental interaction|interactions]], but are more massive. Leptons differ from the other basic constituent of matter, the [[quark]]s, by their lack of [[strong interaction]]. All members of the lepton group are fermions because they all have half-odd integer spin; the electron has spin {{sfrac|1|2}}.<ref name="raith">
{{cite book
 | last1 = Raith | first1 = W.
 | last2 = Mulvey | first2 = T.
 | year = 2001
 | title = Constituents of Matter: Atoms, Molecules, Nuclei and Particles
 | pages = 777–781
 | publisher = [[CRC Press]]
 | isbn = 978-0-8493-1202-1
}}</ref>

=== Fundamental properties ===
The [[invariant mass]] of an electron is approximately {{physconst|me|round=3|after=,}} or {{physconst|me_Da|round=3|after=.|ref=no}} Due to [[mass–energy equivalence]], this corresponds to a rest energy of {{physconst|mec2|round=2|ref=no}} ({{physconst|mec2_MeV|round=3|ref=no}}). The ratio between the mass of a [[proton]] and that of an electron is about 1836.<ref name=nist_codata_mu>
{{cite web
 | title = CODATA value: proton-electron mass ratio
 | url = https://physics.nist.gov/cgi-bin/cuu/Value?mpsme
 | work = 2006 CODATA recommended values
 | publisher = [[National Institute of Standards and Technology]]
 | access-date = 2009-07-18
 | df = dmy-all
 | archive-date = 2019-03-28
 | archive-url = https://web.archive.org/web/20190328001314/https://physics.nist.gov/cgi-bin/cuu/Value?mpsme
 | url-status = live
}}</ref><ref name=Zombeck2007>
{{cite book
 | last = Zombeck
 | first = M.V.
 | year = 2007
 | title = Handbook of Space Astronomy and Astrophysics
 | url = https://books.google.com/books?id=tp_G85jm6IAC&pg=PA14
 | edition = 3rd
 | page = 14
 | publisher = Cambridge University Press
 | isbn = 978-0-521-78242-5
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082414/https://books.google.com/books?id=tp_G85jm6IAC&pg=PA14
 | url-status = live
}}</ref> Astronomical measurements show that the [[proton-to-electron mass ratio]] has held the same value, as is predicted by the Standard Model, for at least half the [[age of the universe]].<ref>
{{cite journal
 | last = Murphy | first = M.T.
 | year = 2008
 | title = Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe
 | journal = [[Science (journal)|Science]]
 | volume = 320 | issue = 5883 | pages = 1611–1613
 | doi = 10.1126/science.1156352
 | pmid = 18566280
 |bibcode = 2008Sci...320.1611M |arxiv = 0806.3081 | s2cid = 2384708
 |display-authors=etal
}}</ref>

Electrons have an [[electric charge]] of {{val|-1.602176634|e=-19|ul=C}},<ref name="CODATA">The original source for CODATA is 
{{cite journal
 | last1 = Mohr | first1 = P.J.
 | last2 = Taylor | first2 = B.N.
 | last3 = Newell | first3 = D.B.
 | year = 2008
 | title = CODATA recommended values of the fundamental physical constants
 | journal = [[Reviews of Modern Physics]]
 | volume = 80 | pages = 633–730
 | doi = 10.1103/RevModPhys.80.633 | bibcode=2008RvMP...80..633M
 | issue = 2
 |arxiv = 0801.0028 | citeseerx = 10.1.1.150.1225
}}
: Individual physical constants from the CODATA are available at: 
{{cite web
 | url = https://physics.nist.gov/cuu/
 | title = The NIST Reference on Constants, Units and Uncertainty
 | publisher = [[National Institute of Standards and Technology]]
 | access-date = 2009-01-15
 | archive-date = 2009-01-16
 | archive-url = https://web.archive.org/web/20090116162522/http://physics.nist.gov/cuu/
 | url-status = live
}}</ref> which is used as a standard unit of charge for subatomic particles, and is also called the [[elementary charge]]. Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign.<ref>
{{cite journal
 | last1 = Zorn | first1 = J.C.
 | last2 = Chamberlain | first2 = G.E.
 | last3 = Hughes | first3 = V.W.
 | year = 1963
 | title = Experimental Limits for the Electron–Proton Charge Difference and for the Charge of the Neutron
 | journal = [[Physical Review]]
 | volume = 129 | issue = 6 | pages = 2566–2576
 | doi = 10.1103/PhysRev.129.2566
 |bibcode = 1963PhRv..129.2566Z
}}</ref> The electron is commonly symbolized by {{subatomicParticle|electron}}, and the positron is symbolized by {{subatomicParticle|positron}}.<ref name="raith" /><ref name="CODATA" />

The electron has an intrinsic [[angular momentum]] or spin of {{sfrac|''ħ''|2}}.<ref name="CODATA" /> This property is usually stated by referring to the electron as a [[spin-1/2]] particle.<ref name="raith" /> For such particles the spin magnitude is {{sfrac|''ħ''|2}},<ref name=Gupta2001 /> while the result of the measurement of a [[Projection (mathematics)|projection]] of the spin on any axis can only be ±{{sfrac|''ħ''|2}}. In addition to spin, the electron has an intrinsic [[Electron magnetic moment|magnetic moment]] along its spin axis.<ref name="CODATA" /> It is approximately equal to one [[Bohr magneton]],<ref name=Hanneke />{{efn|Bohr magneton:
: <math>\textstyle\mu_{\mathrm{B}}=\frac{e\hbar}{2m_{\mathrm{e}}}</math>}} which is a physical constant that is equal to {{physconst|muB|after=.}} The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as [[helicity (particle physics)|helicity]].<ref name="anastopoulos">
{{cite book
 | last = Anastopoulos
 | first = C.
 | year = 2008
 | title = Particle Or Wave: The Evolution of the Concept of Matter in Modern Physics
 | url = https://books.google.com/books?id=rDEvQZhpltEC&pg=PA261
 | publisher = Princeton University Press
 | pages = 261–262
 | isbn = 978-0-691-13512-0
 | access-date = 2020-08-25
 | archive-date = 2021-01-07
 | archive-url = https://web.archive.org/web/20210107160318/https://books.google.com/books?id=rDEvQZhpltEC&pg=PA261
 | url-status = live
}}</ref>

The electron has no known [[preon|substructure]].<ref name="prl50">
{{cite journal
 | last1 = Eichten | first1 = E.J.
 | last2 = Peskin | first2 = M.E.
 | last3 = Peskin | first3 = M.
 | year = 1983
 | title = New Tests for Quark and Lepton Substructure
 | journal = [[Physical Review Letters]]
 | volume = 50 | pages = 811–814 | issue = 11
 | doi = 10.1103/PhysRevLett.50.811 | bibcode=1983PhRvL..50..811E
 | osti = 1446807
 | s2cid = 119918703
}}</ref><ref>
{{cite journal
 | last = Gabrielse | first = G.
 | year = 2006
 | title = New Determination of the Fine Structure Constant from the Electron ''g'' Value and QED
 | journal = [[Physical Review Letters]]
 | volume = 97 | pages = 030802(1–4)
 | doi = 10.1103/PhysRevLett.97.030802
 | pmid = 16907491
 | bibcode=2006PhRvL..97c0802G
 | issue = 3
 | s2cid = 763602
 |display-authors=etal
}}</ref> Nevertheless, in [[condensed matter physics]], [[spin–charge separation]] can occur in some materials. In such cases, electrons 'split' into three independent particles, the [[spinon]], the [[orbiton]] and the [[Holon (physics)|holon]] (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can behave as independent [[quasiparticles]].<ref name=bbc>{{cite web |url=https://news.bbc.co.uk/1/hi/england/8227861.stm |title=UK {{pipe}} England {{pipe}} Physicists 'make electrons split' |work=BBC News |date=2009-08-28 |access-date=2016-07-11 |archive-date=2017-08-31 |archive-url=https://web.archive.org/web/20170831102806/http://news.bbc.co.uk/1/hi/england/8227861.stm |url-status=live }}</ref><ref>[https://www.sciencedaily.com/releases/2009/07/090730141607.htm Discovery About Behavior Of Building Block Of Nature Could Lead To Computer Revolution] {{Webarchive|url=https://web.archive.org/web/20190404130054/https://www.sciencedaily.com/releases/2009/07/090730141607.htm |date=2019-04-04 }}. ''Science Daily'' (July 31, 2009)</ref><ref name=gov>{{cite web |last=Yarris |first=Lynn |url=https://www.lbl.gov/Science-Articles/Archive/ALS-spinons-holons.html |title=First Direct Observations of Spinons and Holons |publisher=Lbl.gov |date=2006-07-13 |access-date=2016-07-11 |archive-date=2022-02-24 |archive-url=https://web.archive.org/web/20220224105553/https://www2.lbl.gov/Science-Articles/Archive/ALS-spinons-holons.html |url-status=live }}</ref>

The issue of the radius of the electron is a challenging problem of modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the [[self-energy]] of the electron tending to infinity.<ref>[[Eduard Shpolsky]], Atomic physics (Atomnaia fizika), second edition, 1951</ref> Observation of a single electron in a [[Penning trap]] suggests the upper limit of the particle's radius to be 10<sup>−22</sup>&nbsp;meters.<ref>
{{cite journal
 | last = Dehmelt | first = H.
 | year = 1988
 | title = A Single Atomic Particle Forever Floating at Rest in Free Space: New Value for Electron Radius
 | journal = [[Physica Scripta]]
 | volume = T22 | pages = 102–110
 | doi = 10.1088/0031-8949/1988/T22/016
 |bibcode = 1988PhST...22..102D | s2cid = 250760629
}}</ref>
The upper bound of the electron radius of 10<sup>−18</sup>&nbsp;meters<ref>{{cite web |author-link=Gerald Gabrielse |first=Gerald |last=Gabrielse |url=https://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html |title=Electron Substructure |department=Physics |publisher=Harvard University |access-date=2016-06-21 |archive-date=2019-04-10 |archive-url=https://web.archive.org/web/20190410164332/https://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html |url-status=dead }}</ref> can be derived using the [[uncertainty relation]] in energy. There ''is'' also a physical constant called the "[[classical electron radius]]", with the much larger value of {{val|2.8179|e=-15|u=m}}, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects of [[quantum mechanics]]; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.<ref>
{{cite book
 | last = Meschede
 | first = D.
 | year = 2004
 | title = Optics, light and lasers: The Practical Approach to Modern Aspects of Photonics and Laser Physics
 | url = https://books.google.com/books?id=PLISLfBLcmgC&pg=PA168
 | publisher = [[Wiley-VCH]]
 | page = 168
 | isbn = 978-3-527-40364-6
 | access-date = 2020-08-25
 | archive-date = 2014-08-21
 | archive-url = https://web.archive.org/web/20140821185221/http://books.google.com/books?id=PLISLfBLcmgC&pg=PA168
 | url-status = live
}}</ref><ref name=HakenWolfBrewer2005 /><ref group="lower-alpha">The classical electron radius is derived as follows. Assume that the electron's charge is spread uniformly throughout a spherical volume. Since one part of the sphere would repel the other parts, the sphere contains electrostatic potential energy. This energy is assumed to equal the electron's [[Invariant mass#Rest energy|rest energy]], defined by [[special relativity]] (''E''&nbsp;=&nbsp;''mc''<sup>2</sup>).<br />
From [[electrostatics]] theory, the [[potential energy]] of a sphere with radius ''r'' and charge ''e'' is given by:
: <math>E_{\mathrm p} = \frac{e^2}{8\pi \varepsilon_0 r},</math>
where ''ε''<sub>0</sub> is the [[vacuum permittivity]]. For an electron with rest mass ''m''<sub>0</sub>, the rest energy is equal to:
: <math>\textstyle E_{\mathrm p} = m_0 c^2,</math>
where ''c'' is the speed of light in vacuum. Setting them equal and solving for ''r'' gives the classical electron radius.<br />
See: Haken, Wolf, & Brewer (2005).</ref>

There are [[elementary particle]]s that spontaneously [[Particle decay|decay]] into less massive particles. An example is the [[muon]], with a [[Exponential decay#Mean lifetime|mean lifetime]] of {{val|2.2|e=-6}}&nbsp;seconds, which decays into an electron, a muon [[neutrino]] and an electron [[neutrino#Antineutrinos|antineutrino]]. The electron, on the other hand, is thought to be stable on theoretical grounds: the electron is the least massive particle with non-zero electric charge, so its decay would violate [[charge conservation]].<ref>
{{cite journal
 | last = Steinberg | first = R.I.
 | year = 1999
 | title = Experimental test of charge conservation and the stability of the electron
 | journal = [[Physical Review D]]
 | volume = 61 | issue = 2 | pages = 2582–2586
 | doi = 10.1103/PhysRevD.12.2582
 |bibcode = 1975PhRvD..12.2582S |display-authors=etal
}}</ref> The experimental lower bound for the electron's mean lifetime is {{val|6.6|e=28}} years, at a 90% [[confidence interval|confidence level]].<ref name=bx2015 /><ref>
{{cite journal
 |last            = Beringer |first=J.
 |display-authors = etal
 |collaboration   = Particle Data Group
 |year            = 2012
 |title           = Review of Particle Physics: [electron properties]
 |journal         = [[Physical Review D]]
 |volume          = 86
 |issue           = 1
 |pages           = 010001
 |doi             = 10.1103/PhysRevD.86.010001
 |bibcode         = 2012PhRvD..86a0001B
 |url             = https://pdg.lbl.gov/2012/listings/rpp2012-list-electron.pdf
 |doi-access      = free
 |access-date     = 2022-02-24
 |archive-date    = 2022-01-15
 |archive-url     = https://web.archive.org/web/20220115063155/https://pdg.lbl.gov/2012/listings/rpp2012-list-electron.pdf
 |url-status      = live
}}</ref><ref>
{{cite journal
 | last1 =  Back | first1 = H.O. |display-authors=etal
 | year = 2002
 | title = Search for electron decay mode e → γ + ν with prototype of Borexino detector
 | journal = [[Physics Letters B]]
 | volume = 525 | issue = 1–2 | pages = 29–40
 | doi = 10.1016/S0370-2693(01)01440-X | doi-access = free
 | bibcode = 2002PhLB..525...29B
}}</ref>

=== Quantum properties ===
As with all particles, electrons can act as waves. This is called the [[wave–particle duality]] and can be demonstrated using the [[double-slit experiment]].

The wave-like nature of the electron allows it to pass through two parallel slits simultaneously, rather than just one slit as would be the case for a classical particle. In quantum mechanics, the wave-like property of one particle can be described mathematically as a [[complex number|complex]]-valued function, the [[wave function]], commonly denoted by the [[Greek alphabet|Greek letter]] [[Psi (Greek)|psi]] (''ψ''). When the [[Absolute value#Complex numbers|absolute value]] of this function is [[square (algebra)|squared]], it gives the probability that a particle will be observed near a location—a [[probability density function|probability density]].<ref name="munowitz">
{{cite book
 | last = Munowitz | first = M.
 | year = 2005
 | title = Knowing the Nature of Physical Law
 | url = https://archive.org/details/knowingnatureofp0000muno
 | url-access = registration | page = [https://archive.org/details/knowingnatureofp0000muno/page/162 162] | publisher = Oxford University Press
 | isbn = 978-0-19-516737-5
}}</ref>{{rp|162–218}}

[[File:Asymmetricwave2.png|right|thumb|alt=A three dimensional projection of a two dimensional plot. There are symmetric hills along one axis and symmetric valleys along the other, roughly giving a saddle-shape|Example of an antisymmetric wave function for a quantum state of [[Particle in a box|two identical fermions in a one-dimensional box]], with each horizontal axis corresponding to the position of one particle. If the particles swap position, the wave function inverts its sign.]]
Electrons are [[identical particles]] because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, {{nowrap|''ψ''(''r''<sub>1</sub>, ''r''<sub>2</sub>) {{=}} −''ψ''(''r''<sub>2</sub>, ''r''<sub>1</sub>)}}, where the variables ''r''<sub>1</sub> and ''r''<sub>2</sub> correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. [[Boson]]s, such as the photon, have symmetric wave functions instead.<ref name="munowitz" />{{rp|162–218}}

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a [[zero probability]] that each pair will occupy the same location or state. This is responsible for the [[Pauli exclusion principle]], which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different [[atomic orbital|orbitals]] in an atom, rather than all overlapping each other in the same orbit.<ref name="munowitz" />{{rp|162–218}}

=== Virtual particles ===
{{Main|Virtual particle}}
In a simplified picture, which often tends to give the wrong idea but may serve to illustrate some aspects, every photon spends some time as a combination of a virtual electron plus its antiparticle, the virtual positron, which rapidly [[Annihilation|annihilate]] each other shortly thereafter.<ref>
{{cite magazine
 | last = Kane | first = G.
 | date = October 9, 2006
 | url = https://www.sciam.com/article.cfm?id=are-virtual-particles-rea&topicID=13
 | title = Are virtual particles really constantly popping in and out of existence? Or are they merely a mathematical bookkeeping device for quantum mechanics?
 | magazine = [[Scientific American]]
 | access-date = 2008-09-19 |df=dmy-all
}}</ref> The combination of the energy variation needed to create these particles, and the time during which they exist, fall under the threshold of detectability expressed by the [[Uncertainty principle|Heisenberg uncertainty relation]], Δ''E''&nbsp;·&nbsp;Δ''t''&nbsp;≥&nbsp;''ħ''. In effect, the energy needed to create these virtual particles, Δ''E'', can be "borrowed" from the [[Vacuum state|vacuum]] for a period of time, Δ''t'', so that their product is no more than the [[reduced Planck constant]], {{nowrap|''ħ'' ≈ {{val|6.6|e=-16|u=eV·s}}}}. Thus, for a virtual electron, Δ''t'' is at most {{val|1.3|e=-21|u=s}}.<ref name="taylor">
{{cite book
 | last = Taylor
 | first = J.
 | year = 1989
 | chapter = Gauge Theories in Particle Physics
 | chapter-url = https://books.google.com/books?id=akb2FpZSGnMC&pg=PA464
 | editor = Davies, Paul
 | title = The New Physics
 | page = 464
 | publisher = [[Cambridge University Press]]
 | isbn = 978-0-521-43831-5
 | access-date = 2020-08-25
 | archive-date = 2014-09-21
 | archive-url = https://web.archive.org/web/20140921171834/http://books.google.com/books?id=akb2FpZSGnMC&pg=PA464
 | url-status = live
}}</ref>

[[File:Virtual pairs near electron.png|right|thumb|alt=A sphere with a minus sign at lower left symbolizes the electron, while pairs of spheres with plus and minus signs show the virtual particles|A schematic depiction of virtual electron–positron pairs appearing at random near an electron (at lower left)]]
While an electron–positron virtual pair is in existence, the [[Coulomb's law|Coulomb force]] from the ambient [[electric field]] surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes what is called [[vacuum polarization]]. In effect, the vacuum behaves like a medium having a [[Relative permittivity|dielectric permittivity]] more than [[1|unity]]. Thus the effective charge of an electron is actually smaller than its true value, and the charge decreases with increasing distance from the electron.<ref name="genz">
{{cite book
 | last = Genz | first = H.
 | year = 2001
 | title = Nothingness: The Science of Empty Space
 | pages = 241–243, 245–247
 | publisher = [[Da Capo Press]]
 | isbn = 978-0-7382-0610-3
}}</ref><ref>
{{cite news
 | last = Gribbin
 | first = J.
 | date = January 25, 1997
 | title = More to electrons than meets the eye
 | magazine = [[New Scientist]]
 | url = https://www.newscientist.com/article/mg15320662.300-science--more-to-electrons-than-meets-the-eye.html
 | access-date = 2008-09-17
 | df = dmy-all
 | archive-date = 2015-02-11
 | archive-url = https://web.archive.org/web/20150211085433/http://www.newscientist.com/article/mg15320662.300-science--more-to-electrons-than-meets-the-eye.html
 | url-status = live
}}</ref> This polarization was confirmed experimentally in 1997 using the Japanese [[KEKB (accelerator)|TRISTAN]] particle accelerator.<ref>
{{cite journal
 | last1 = Levine | first1 = I. |display-authors=etal
 | year = 1997
 | title = Measurement of the Electromagnetic Coupling at Large Momentum Transfer
 | journal = [[Physical Review Letters]]
 | volume = 78 | issue = 3 | pages = 424–427
 | doi = 10.1103/PhysRevLett.78.424
 | bibcode=1997PhRvL..78..424L
}}</ref> Virtual particles cause a comparable [[shielding effect]] for the mass of the electron.<ref>
{{cite conference
 | last = Murayama | first = H.
 | date =10–17 March 2006
 | title = Supersymmetry Breaking Made Easy, Viable and Generic
 | conference = Proceedings of the XLIInd Rencontres de Moriond on Electroweak Interactions and Unified Theories
 | place = La Thuile, Italy
 | arxiv = 0709.3041
 | bibcode = 2007arXiv0709.3041M
}} – lists a 9% mass difference for an electron that is the size of the [[Planck length|Planck distance]].</ref>

The interaction with virtual particles also explains the small (about 0.1%) deviation of the intrinsic magnetic moment of the electron from the Bohr magneton (the [[Anomalous magnetic dipole moment|anomalous magnetic moment]]).<ref name=Hanneke>
{{cite journal
 | last1 = Odom | first1 = B. |display-authors=etal
 | year = 2006
 | title = New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron
 | journal = [[Physical Review Letters]]
 | volume = 97 | issue=3 | pages = 030801
 | doi = 10.1103/PhysRevLett.97.030801
 | pmid=16907490 | bibcode=2006PhRvL..97c0801O
}}</ref><ref>
{{cite journal
 | last = Schwinger | first = J.
 | year = 1948
 | title = On Quantum-Electrodynamics and the Magnetic Moment of the Electron
 | journal = [[Physical Review]]
 | volume = 73 | issue = 4 | pages = 416–417
 | doi = 10.1103/PhysRev.73.416 | doi-access = free
 | bibcode = 1948PhRv...73..416S
}}</ref> The extraordinarily precise agreement of this predicted difference with the experimentally determined value is viewed as one of the great achievements of [[quantum electrodynamics]].<ref>
{{cite book
 | last = Huang
 | first = K.
 | year = 2007
 | title = Fundamental Forces of Nature: The Story of Gauge Fields
 | url = https://books.google.com/books?id=q-CIFHpHxfEC&pg=PA123
 | pages = 123–125
 | publisher = [[World Scientific]]
 | isbn = 978-981-270-645-4
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204071144/https://books.google.com/books?id=q-CIFHpHxfEC&pg=PA123
 | url-status = live
}}</ref>

The apparent paradox in [[classical physics]] of a point particle electron having intrinsic angular momentum and magnetic moment can be explained by the formation of [[Virtual particle|virtual photons]] in the electric field generated by the electron. These photons can heuristically be thought of as causing the electron to shift about in a jittery fashion (known as [[zitterbewegung]]), which results in a net circular motion with [[precession]].<ref>
{{cite journal
 | last1 = Foldy | first1 = L.L.
 | last2 = Wouthuysen | first2 = S.
 | year = 1950
 | title = On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
 | journal = [[Physical Review]]
 | volume = 78 | issue = 1 | pages = 29–36
 | doi = 10.1103/PhysRev.78.29
 |bibcode = 1950PhRv...78...29F
}}</ref> This motion produces both the spin and the magnetic moment of the electron.<ref name="curtis74" /> In atoms, this creation of virtual photons explains the [[Lamb shift]] observed in [[spectral line]]s.<ref name="genz" /> The Compton Wavelength shows that near elementary particles such as the electron, the uncertainty of the energy allows for the creation of virtual particles near the electron. This wavelength explains the "static" of virtual particles around elementary particles at a close distance.

=== Interaction ===
An electron generates an electric field that exerts an attractive force on a particle with a positive charge, such as the proton, and a repulsive force on a particle with a negative charge. The strength of this force in nonrelativistic approximation is determined by [[Coulomb's law|Coulomb's inverse square law]].<ref name=Griffiths1998>
{{cite book
 |last=Griffiths |first=David J.
 |title=Introduction to Electrodynamics |edition=3rd
 |publisher=Prentice Hall |year=1998
 |isbn=978-0-13-805326-0
 |url=https://archive.org/details/introductiontoel00grif_0
}}</ref>{{rp|pages=58–61}} When an electron is in motion, it generates a [[magnetic field]].<ref name="munowitz" />{{rp|page=140}} The [[Ampère's circuital law|Ampère–Maxwell law]] relates the magnetic field to the mass motion of electrons (the [[electric current|current]]) with respect to an observer. This property of induction supplies the magnetic field that drives an [[electric motor]].<ref>
{{cite book
 |last=Crowell
 |first=B.
 |title=Electricity and Magnetism
 |url=https://books.google.com/books?id=s9QWZNfnz1oC&pg=PT129
 |pages=129–152
 |publisher=Light and Matter
 |year=2000
 |isbn=978-0-9704670-4-1
 |access-date=2020-08-25
 |archive-date=2022-02-04
 |archive-url=https://web.archive.org/web/20220204083733/https://books.google.com/books?id=s9QWZNfnz1oC&pg=PT129
 |url-status=live
}}</ref> The electromagnetic field of an arbitrary moving charged particle is expressed by the [[Liénard–Wiechert potential]]s, which are valid even when the particle's speed is close to that of light ([[special relativity|relativistic]]).<ref name=Griffiths1998 />{{rp|pages=429–434}}

[[File:Lorentz force.svg|right|thumb|alt=A graph with arcs showing the motion of charged particles|A particle with charge ''q'' (at left) is moving with velocity ''v'' through a magnetic field ''B'' that is oriented toward the viewer. For an electron, ''q'' is negative, so it follows a curved trajectory toward the top.]]
When an electron is moving through a magnetic field, it is subject to the [[Lorentz force]] that acts perpendicularly to the plane defined by the magnetic field and the electron velocity. This [[centripetal force]] causes the electron to follow a [[Helix|helical]] trajectory through the field at a radius called the [[gyroradius]]. The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation.<ref>
{{cite journal
 |last1 = Mahadevan |first1 = R.
 |last2 = Narayan |first2 = R.
 |last3 = Yi |first3 = I.
 |year = 1996
 |title = Harmony in Electrons: Cyclotron and Synchrotron Emission by Thermal Electrons in a Magnetic Field
 |journal = [[The Astrophysical Journal]]
 |volume = 465 | pages = 327–337
 |arxiv = astro-ph/9601073
 |doi = 10.1086/177422 |bibcode=1996ApJ...465..327M
 |s2cid = 16324613
}}</ref>{{efn|Radiation from non-relativistic electrons is sometimes termed [[cyclotron radiation]].}}<ref name=munowitz />{{rp|page=160}} The energy emission in turn causes a recoil of the electron, known as the [[Abraham–Lorentz force#Abraham–Lorentz–Dirac Force|Abraham–Lorentz–Dirac Force]], which creates a friction that slows the electron. This force is caused by a [[back-reaction]] of the electron's own field upon itself.<ref>
{{cite journal
 |last = Rohrlich |first = F.
 |year = 1999
 |title = The Self-Force and Radiation Reaction
 |journal = [[American Journal of Physics]]
 |volume = 68 |issue = 12 |pages = 1109–1112
 |doi = 10.1119/1.1286430
 |bibcode = 2000AmJPh..68.1109R
}}</ref>

[[File:Bremsstrahlung.svg|thumb|left|upright|alt=A curve shows the motion of the electron, a red dot shows the nucleus, and a wiggly line the emitted photon|Here, [[Bremsstrahlung]] is produced by an electron ''e'' deflected by the electric field of an atomic nucleus. The energy change ''E''<sub>2</sub>&nbsp;−&nbsp;''E''<sub>1</sub> determines the frequency ''f'' of the emitted photon.]]
Photons mediate electromagnetic interactions between particles in [[quantum electrodynamics]]. An isolated electron at a constant velocity cannot emit or absorb a real photon; doing so would violate [[conservation of energy]] and [[momentum]]. Instead, virtual photons can transfer momentum between two charged particles. This exchange of virtual photons, for example, generates the Coulomb force.<ref>
{{cite book
 |last=Georgi
 |first=H.
 |chapter=Grand Unified Theories
 |page=427
 |editor=Davies, Paul
 |title=The New Physics
 |chapter-url=https://books.google.com/books?id=akb2FpZSGnMC&pg=PA427
 |publisher=Cambridge University Press
 |year=1989
 |isbn=978-0-521-43831-5
 |access-date=2020-08-25
 |archive-date=2014-09-21
 |archive-url=https://web.archive.org/web/20140921171123/http://books.google.com/books?id=akb2FpZSGnMC&pg=PA427
 |url-status=live
}}</ref> Energy emission can occur when a moving electron is deflected by a charged particle, such as a proton. The deceleration of the electron results in the emission of [[Bremsstrahlung]] radiation.<ref>
{{cite journal
 |last1=Blumenthal |first1= G.J.
 |last2=Gould |first2=R.
 |year=1970
 |title=Bremsstrahlung, Synchrotron Radiation, and Compton Scattering of High-Energy Electrons Traversing Dilute Gases
 |journal=[[Reviews of Modern Physics]]
 |volume=42 |issue=2 |pages=237–270
 |doi=10.1103/RevModPhys.42.237 |bibcode=1970RvMP...42..237B
}}</ref>

An inelastic collision between a photon (light) and a solitary (free) electron is called [[Compton scattering]]. This collision results in a transfer of momentum and energy between the particles, which modifies the wavelength of the photon by an amount called the [[Compton scattering|Compton shift]].{{efn|The change in wavelength, Δ''λ'', depends on the angle of the recoil, ''θ'', as follows,
: <math>\textstyle \Delta \lambda = \frac{h}{m_{\mathrm{e}}c} (1 - \cos \theta),</math>
where ''c'' is the speed of light in vacuum and ''m''<sub>e</sub> is the electron mass. See Zombeck (2007).<ref name=Zombeck2007 />{{rp|page=393, 396}} }} The maximum magnitude of this wavelength shift is ''h''/''m''<sub>e</sub>''c'', which is known as the [[Compton wavelength]].<ref>
{{cite web
 |title=The Nobel Prize in Physics 1927
 |publisher=[[Nobel Foundation|The Nobel Foundation]]
 |year=2008
 |url=https://nobelprize.org/nobel_prizes/physics/laureates/1927/
 |access-date=2008-09-28
 |df=dmy-all
 |archive-date=2008-10-24
 |archive-url=https://web.archive.org/web/20081024124054/http://nobelprize.org/nobel_prizes/physics/laureates/1927/
 |url-status=live
}}</ref> For an electron, it has a value of {{val|2.43|e=-12|u=m}}.<ref name="CODATA" /> When the wavelength of the light is long (for instance, the wavelength of the [[Light|visible light]] is 0.4–0.7&nbsp;μm) the wavelength shift becomes negligible. Such interaction between the light and free electrons is called [[Thomson scattering]] or linear Thomson scattering.<ref name="Chen1998">
{{cite journal
 |last1=Chen |first1=S.-Y.
 |last2=Maksimchuk |first2=A.
 |last3=Umstadter |first3=D.
 |year=1998
 |title=Experimental observation of relativistic nonlinear Thomson scattering
 |journal=[[Nature (journal)|Nature]]
 |volume=396 |issue=6712 |pages=653–655
 |doi=10.1038/25303 |arxiv=physics/9810036
 |bibcode=1998Natur.396..653C|s2cid=16080209
}}</ref>

The relative strength of the electromagnetic interaction between two charged particles, such as an electron and a proton, is given by the [[fine-structure constant]]. This value is a dimensionless quantity formed by the ratio of two energies: the electrostatic energy of attraction (or repulsion) at a separation of one Compton wavelength, and the rest energy of the charge. It is given by {{physconst|alpha|symbol=yes|round=9|after=,}} which is approximately equal to {{sfrac|1|137}}.

When electrons and positrons collide, they [[Electron–positron annihilation|annihilate]] each other, giving rise to two or more gamma ray photons. If the electron and positron have negligible momentum, a [[Positronium|positronium atom]] can form before annihilation results in two or three gamma ray photons whose energies total 1.022&nbsp;MeV.<ref>
{{cite journal
 | last1 = Beringer | first1 = R.
 | last2 = Montgomery | first2 = C.G.
 | year = 1942
 | title = The Angular Distribution of Positron Annihilation Radiation
 | journal = [[Physical Review]]
 | volume = 61 | issue = 5–6 | pages = 222–224
 | doi = 10.1103/PhysRev.61.222
 | bibcode = 1942PhRv...61..222B }}</ref><ref>{{cite book
 | last = Buffa | first = A.
 | title = College Physics
 | publisher = Prentice Hall | edition = 4th | year = 2000
 | isbn = 978-0-13-082444-8
 | url = https://archive.org/details/collegephysicsvo00jerr/page/888
 | page =888
}}</ref> On the other hand, a high-energy photon can transform into an electron and a positron by a process called [[pair production]], but only in the presence of a nearby charged particle, such as a nucleus.<ref>
{{cite journal
 | last = Eichler | first = J.
 | year = 2005
 | title = Electron–positron pair production in relativistic ion–atom collisions
 | journal = [[Physics Letters A]]
 | volume = 347 | issue = 1–3 | pages = 67–72
 | doi = 10.1016/j.physleta.2005.06.105
 | bibcode = 2005PhLA..347...67E
}}</ref><ref>
{{cite journal
 | last = Hubbell
 | first = J.H.
 | year = 2006
 | title = Electron positron pair production by photons: A historical overview
 | journal = {{ill|Radiation Physics and Chemistry|fr}}
 | volume = 75
 | issue = 6
 | pages = 614–623
 | bibcode = 2006RaPC...75..614H
 | doi = 10.1016/j.radphyschem.2005.10.008
 | url = https://zenodo.org/record/1259327
 | access-date = 2019-06-21
 | archive-date = 2019-06-21
 | archive-url = https://web.archive.org/web/20190621192329/https://zenodo.org/record/1259327
 | url-status = live
}}</ref>

In the theory of [[electroweak interaction]], the [[Chirality (physics)|left-handed]] component of electron's wavefunction forms a [[weak isospin]] doublet with the [[Neutrino|electron neutrino]]. This means that during [[weak interaction]]s, electron neutrinos behave like electrons. Either member of this doublet can undergo a [[charged current]] interaction by emitting or absorbing a {{SubatomicParticle|W boson|link=yes}} and be converted into the other member. Charge is conserved during this reaction because the W&nbsp;boson also carries a charge, canceling out any net change during the transmutation. Charged current interactions are responsible for the phenomenon of [[beta decay]] in a [[Radioactive decay|radioactive]] atom. Both the electron and electron neutrino can undergo a [[neutral current]] interaction via a {{SubatomicParticle|Z boson0|link=yes}} exchange, and this is responsible for neutrino–electron [[elastic scattering]].<ref name="quigg">
{{cite conference
 |last=Quigg |first=C.
 |title=The Electroweak Theory |page=80
 |conference=TASI 2000: Flavor Physics for the Millennium
 |date=4–30 June 2000
 |place=Boulder, Colorado
 |arxiv=hep-ph/0204104 |bibcode = 2002hep.ph....4104Q
}}</ref>
{{clear}}

=== Atoms and molecules ===
{{Main|Atom}}
[[File:Hydrogen Density Plots.png|right|thumb|upright=1.25|alt=A table of five rows and five columns, with each cell portraying a color-coded probability density|Probability densities for the first few hydrogen atom orbitals, seen in cross-section. The energy level of a bound electron determines the orbital it occupies, and the color reflects the probability of finding the electron at a given position.]]
An electron can be ''bound'' to the nucleus of an atom by the attractive Coulomb force. A system of one or more electrons bound to a nucleus is called an atom. If the number of electrons is different from the nucleus's electrical charge, such an atom is called an [[ion]]. The wave-like behavior of a bound electron is described by a function called an [[atomic orbital]]. Each orbital has its own set of quantum numbers such as energy, angular momentum and projection of angular momentum, and only a discrete set of these orbitals exist around the nucleus. According to the Pauli exclusion principle each orbital can be occupied by up to two electrons, which must differ in their [[spin quantum number]].

Electrons can transfer between different orbitals by the emission or absorption of photons with an energy that matches the difference in potential.<ref name=Tipler2003 />{{rp|159–160}} Other methods of orbital transfer include collisions with particles, such as electrons, and the [[Auger effect]].<ref>
{{cite book
 | last = Burhop | first = E.H.S.
 | author-link = Eric Burhop
 | year = 1952
 | title = The Auger Effect and Other Radiationless Transitions
 | publisher = Cambridge University Press
 | pages = 2–3
 | isbn = 978-0-88275-966-1
}}</ref> To escape the atom, the energy of the electron must be increased above its [[Ionization energy|binding energy]] to the atom. This occurs, for example, with the [[photoelectric effect]], where an incident photon exceeding the atom's [[ionization energy]] is absorbed by the electron.<ref name=Tipler2003>
{{cite book
 | last1=Tipler | first1=Paul
 | last2=Llewellyn | first2=Ralph
 | title = Modern Physics
 | publisher=Macmillan | year=2003 | edition=illustrated
 | isbn=978-0-7167-4345-3
}}</ref>{{rp|127–132}}

The orbital angular momentum of electrons is [[Angular momentum operator#Quantization|quantized]]. Because the electron is charged, it produces an orbital magnetic moment that is proportional to the angular momentum. The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus. The magnetic moment of the nucleus is negligible compared with that of the electrons. The magnetic moments of the electrons that occupy the same orbital, called paired electrons, cancel each other out.<ref>
{{cite book
 | last = Jiles
 | first = D.
 | title = Introduction to Magnetism and Magnetic Materials
 | url = https://books.google.com/books?id=axyWXjsdorMC&pg=PA280
 | pages = 280–287
 | publisher = [[CRC Press]]
 | year = 1998
 | isbn = 978-0-412-79860-3
 | access-date = 2020-08-25
 | archive-date = 2021-01-26
 | archive-url = https://web.archive.org/web/20210126003325/https://books.google.com/books?id=axyWXjsdorMC&pg=PA280
 | url-status = live
}}</ref>

The [[chemical bond]] between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics.<ref>
{{cite book
 |last1        = Löwdin
 |first1       = P.O.
 |last2        = Erkki Brändas
 |first2       = E.
 |last3        = Kryachko
 |first3       = E.S.
 |title        = Fundamental World of Quantum Chemistry: A Tribute to the Memory of Per-Olov Löwdin
 |url          = https://books.google.com/books?id=8QiR8lCX_qcC&pg=PA393
 |pages        = 393–394
 |publisher    = Springer Science+Business Media
 |year         = 2003
 |isbn         = 978-1-4020-1290-7
 |access-date  = 2020-08-25
 |archive-date = 2022-02-04
 |archive-url  = https://web.archive.org/web/20220204071147/https://books.google.com/books?id=8QiR8lCX_qcC&pg=PA393
 |url-status   = live
}}</ref> The strongest bonds are formed by the [[Covalent bond|sharing]] or [[Electron transfer|transfer]] of electrons between atoms, allowing the formation of [[molecule]]s.<ref name=Pauling>
{{cite book
 | last = Pauling | first = L.C.
 | title = The Nature of the Chemical Bond and the Structure of Molecules and Crystals: an introduction to modern structural chemistry
 | url = https://archive.org/details/natureofchemical0000paul_3ed/page/4
 | url-access = registration | pages =4–10
 | publisher = Cornell University Press | edition = 3rd | year = 1960
 | isbn = 978-0-8014-0333-0
}}</ref> Within a molecule, electrons move under the influence of several nuclei, and occupy [[molecular orbital]]s; much as they can occupy atomic orbitals in isolated atoms.<ref>
{{cite book
 | last1 = McQuarrie
 | first1 = D.A.
 | last2 = Simon
 | first2 = J.D.
 | title = Physical Chemistry: A Molecular Approach
 | url = https://books.google.com/books?id=f-bje0-DEYUC&pg=PA325
 | publisher = University Science Books
 | year = 1997
 | pages = 325–361
 | isbn = 978-0-935702-99-6
 | access-date = 2020-08-25
 | archive-date = 2021-01-07
 | archive-url = https://web.archive.org/web/20210107160307/https://books.google.com/books?id=f-bje0-DEYUC&pg=PA325
 | url-status = live
}}</ref> A fundamental factor in these molecular structures is the existence of [[electron pair]]s. These are electrons with opposed spins, allowing them to occupy the same molecular orbital without violating the Pauli exclusion principle (much like in atoms). Different molecular orbitals have different spatial distribution of the electron density. For instance, in bonded pairs (i.e. in the pairs that actually bind atoms together) electrons can be found with the maximal probability in a relatively small volume between the nuclei. By contrast, in non-bonded pairs electrons are distributed in a large volume around nuclei.<ref
>{{cite journal
 |last=Daudel |first=R.
 |year=1974
 |title=The Electron Pair in Chemistry
 |journal=[[Canadian Journal of Chemistry]]
 |volume=52 |issue=8 |pages=1310–1320
 |doi=10.1139/v74-201
 |display-authors=etal
 |doi-access=free
}}</ref>

=== Conductivity ===
[[File:Lightning over Oradea Romania cropped.jpg|right|thumb|alt=Four bolts of lightning strike the ground|A [[lightning]] discharge consists primarily of a flow of electrons.<ref>
{{cite book
 | last1 = Rakov
 | first1 = V.A.
 | last2 = Uman
 | first2 = M.A.
 | title = Lightning: Physics and Effects
 | url = https://books.google.com/books?id=TuMa5lAa3RAC&pg=PA4
 | page = 4
 | publisher = Cambridge University Press
 | year = 2007
 | isbn = 978-0-521-03541-5
 | access-date = 2020-08-25
 | archive-date = 2021-01-26
 | archive-url = https://web.archive.org/web/20210126003319/https://books.google.com/books?id=TuMa5lAa3RAC&pg=PA4
 | url-status = live
}}</ref> The electric potential needed for lightning can be generated by a triboelectric effect.<ref>
{{cite journal
 | last1 = Freeman | first1 = G.R.
 | last2 = March | first2 = N.H.
 | year = 1999
 | title = Triboelectricity and some associated phenomena
 | journal = Materials Science and Technology
 | volume = 15 | issue = 12 | pages = 1454–1458
 | doi = 10.1179/026708399101505464
 | bibcode = 1999MatST..15.1454F
}}</ref><ref>
{{cite journal
 | last1 = Forward | first1 = K.M.
 | last2 = Lacks | first2 = D.J.
 | last3 = Sankaran | first3 = R.M.
 | year = 2009
 | title = Methodology for studying particle–particle triboelectrification in granular materials
 | journal = {{ill|Journal of Electrostatics|tr}}
 | volume = 67 | issue = 2–3 | pages = 178–183
 | doi = 10.1016/j.elstat.2008.12.002
}}</ref>]]
If a body has more or fewer electrons than are required to balance the positive charge of the nuclei, then that object has a net electric charge. When there is an excess of electrons, the object is said to be negatively charged. When there are fewer electrons than the number of protons in nuclei, the object is said to be positively charged. When the number of electrons and the number of protons are equal, their charges cancel each other and the object is said to be electrically neutral. A macroscopic body can develop an electric charge through rubbing, by the [[triboelectric effect]].<ref>
{{cite book
 | last = Weinberg | first = S.
 | title = The Discovery of Subatomic Particles
 | url = https://archive.org/details/discoveryofsubat00wein_0/page/15
 | url-access = registration | pages =15–16
 | publisher = Cambridge University Press | year = 2003
 | isbn = 978-0-521-82351-7
}}</ref>

Independent electrons moving in vacuum are termed ''free'' electrons. Electrons in metals also behave as if they were free. In reality the particles that are commonly termed electrons in metals and other solids are quasi-electrons—[[quasiparticle]]s, which have the same electrical charge, spin, and magnetic moment as real electrons but might have a different mass.<ref name="Liang-fu Lou">
{{cite book
 | last = Lou
 | first = L.-F.
 | title = Introduction to phonons and electrons
 | url = https://books.google.com/books?id=XMv-vfsoRF8C&pg=PA162
 | pages = 162, 164
 | publisher = [[World Scientific]]
 | year = 2003
 | isbn = 978-981-238-461-4
 | bibcode = 2003ipe..book.....L
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204071149/https://books.google.com/books?id=XMv-vfsoRF8C&pg=PA162
 | url-status = live
}}</ref> When free electrons – both in vacuum and metals – move, they produce a [[Flow network|net flow]] of charge called an [[electric current]], which generates a magnetic field. Likewise a current can be created by a changing magnetic field. These interactions are described mathematically by [[Maxwell's equations]].<ref>
{{cite book
 | last1 = Guru
 | first1 = B.S.
 | last2 = Hızıroğlu
 | first2 = H.R.
 | title = Electromagnetic Field Theory Fundamentals
 | url = https://archive.org/details/electromagneticf0000bhag
 | pages = 138, 276
 | publisher = Cambridge University Press
 | year = 2004
 | isbn = 978-0-521-83016-4
 | url-access=registration
}}</ref>

At a given temperature, each material has an [[Electrical resistivity and conductivity|electrical conductivity]] that determines the value of electric current when an [[electric potential]] is applied. Examples of good conductors include metals such as copper and gold, whereas glass and [[Polytetrafluoroethylene|Teflon]] are poor conductors. In any [[dielectric]] material, the electrons remain bound to their respective atoms and the material behaves as an [[Insulator (electricity)|insulator]]. Most [[semiconductor]]s have a variable level of conductivity that lies between the extremes of conduction and insulation.<ref>
{{cite book
 | last1 = Achuthan
 | first1 = M.K.
 | last2 = Bhat
 | first2 = K.N.
 | title = Fundamentals of Semiconductor Devices
 | url = https://books.google.com/books?id=REQkwBF4cVoC&pg=PA49
 | pages = 49–67
 | publisher = [[Tata McGraw-Hill]]
 | year = 2007
 | isbn = 978-0-07-061220-4
 | access-date = 2020-08-25
 | archive-date = 2021-01-07
 | archive-url = https://web.archive.org/web/20210107160319/https://books.google.com/books?id=REQkwBF4cVoC&pg=PA49
 | url-status = live
}}</ref> On the other hand, [[metallic bond|metals]] have an [[electronic band structure]] containing partially filled electronic bands. The presence of such bands allows electrons in metals to behave as if they were free or [[delocalized electron]]s. These electrons are not associated with specific atoms, so when an electric field is applied, they are free to move like a gas (called [[Fermi gas]])<ref name="ziman">
{{cite book
 | last = Ziman
 | first = J.M.
 | title = Electrons and Phonons: The Theory of Transport Phenomena in Solids
 | url = https://books.google.com/books?id=UtEy63pjngsC&pg=PA260
 | publisher = Oxford University Press
 | year = 2001
 | page = 260
 | isbn = 978-0-19-850779-6
 | access-date = 2020-08-25
 | archive-date = 2022-02-24
 | archive-url = https://web.archive.org/web/20220224105543/https://books.google.com/books?id=UtEy63pjngsC&pg=PA260
 | url-status = live
}}</ref> through the material much like free electrons.

Because of collisions between electrons and atoms, the [[drift velocity]] of electrons in a conductor is on the order of millimeters per second. However, the speed at which a change of current at one point in the material causes changes in currents in other parts of the material, the [[Wave propagation speed|velocity of propagation]], is typically about 75% of light speed.<ref>
{{cite journal
 | last = Main
 | first = P.
 | date = June 12, 1993
 | title = When electrons go with the flow: Remove the obstacles that create electrical resistance, and you get ballistic electrons and a quantum surprise
 | journal = [[New Scientist]]
 | volume = 1887
 | page = 30
 | url = https://www.newscientist.com/article/mg13818774.500-when-electrons-go-with-the-flow-remove-the-obstacles-thatcreate-electrical-resistance-and-you-get-ballistic-electrons-and-a-quantumsurprise.html
 | access-date = 2008-10-09
 | df = dmy-all
 | archive-date = 2015-02-11
 | archive-url = https://web.archive.org/web/20150211085229/http://www.newscientist.com/article/mg13818774.500-when-electrons-go-with-the-flow-remove-the-obstacles-thatcreate-electrical-resistance-and-you-get-ballistic-electrons-and-a-quantumsurprise.html
 | url-status = live
}}</ref> This occurs because electrical signals propagate as a wave, with the velocity dependent on the [[Relative permittivity|dielectric constant]] of the material.<ref>
{{cite book
 | last = Blackwell
 | first = G.R.
 | title = The Electronic Packaging Handbook
 | url = https://books.google.com/books?id=D0PBG53PQlUC&pg=SA6-PA39
 | pages = 6.39–6.40
 | publisher = [[CRC Press]]
 | year = 2000
 | isbn = 978-0-8493-8591-9
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204083743/https://books.google.com/books?id=D0PBG53PQlUC&pg=SA6-PA39
 | url-status = live
}}</ref>

Metals make relatively good conductors of heat, primarily because the delocalized electrons are free to transport thermal energy between atoms. However, unlike electrical conductivity, the thermal conductivity of a metal is nearly independent of temperature. This is expressed mathematically by the [[Wiedemann–Franz law]],<ref name="ziman" /> which states that the ratio of [[thermal conductivity]] to the electrical conductivity is proportional to the temperature. The thermal disorder in the metallic lattice increases the electrical [[Electrical resistivity and conductivity|resistivity]] of the material, producing a temperature dependence for electric current.<ref name="durrant">
{{cite book
 | last = Durrant
 | first = A.
 | title = Quantum Physics of Matter: The Physical World
 | url = https://books.google.com/books?id=F0JmHRkJHiUC&pg=PA43
 | pages = 43, 71–78
 | publisher = CRC Press
 | year = 2000
 | isbn = 978-0-7503-0721-5
 | access-date = 2015-10-16
 | archive-date = 2016-05-27
 | archive-url = https://web.archive.org/web/20160527150628/https://books.google.com/books?id=F0JmHRkJHiUC&pg=PA43
 | url-status = live
}}</ref>

When cooled below a point called the [[Critical point (thermodynamics)|critical temperature]], materials can undergo a phase transition in which they lose all resistivity to electric current, in a process known as [[superconductivity]]. In [[BCS theory]], pairs of electrons called [[Cooper pair]]s have their motion coupled to nearby matter via lattice vibrations called [[phonon]]s, thereby avoiding the collisions with atoms that normally create electrical resistance.<ref>
{{cite web
 | title = The Nobel Prize in Physics 1972
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | year = 2008
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1972/
 | access-date = 2008-10-13
 | df = dmy-all
 | archive-date = 2008-10-11
 | archive-url = https://web.archive.org/web/20081011050516/http://nobelprize.org/nobel_prizes/physics/laureates/1972/
 | url-status = live
}}</ref> (Cooper pairs have a radius of roughly 100&nbsp;nm, so they can overlap each other.)<ref>
{{cite journal
 | last = Kadin | first = A.M.
 | title = Spatial Structure of the Cooper Pair
 | journal = {{ill|Journal of Superconductivity and Novel Magnetism|tr}}
 | year = 2007
 | volume = 20 | issue = 4 | pages = 285–292
 | arxiv = cond-mat/0510279
 | doi =10.1007/s10948-006-0198-z
 | s2cid = 54948290
}}</ref> However, the mechanism by which [[unconventional superconductor|higher temperature superconductors]] operate remains uncertain.

Electrons inside conducting solids, which are quasi-particles themselves, when tightly confined at temperatures close to [[absolute zero]], behave as though they had split into three other [[quasiparticle]]s: [[spinon]]s, [[orbiton]]s and [[holon (physics)|holons]].<ref>
{{cite web
 | title = Discovery about behavior of building block of nature could lead to computer revolution
 | date = July 31, 2009
 | website = [[Science Daily|ScienceDaily]]
 | url = https://www.sciencedaily.com/releases/2009/07/090730141607.htm
 | access-date = 2009-08-01
 | df = dmy-all
 | archive-date = 2019-04-04
 | archive-url = https://web.archive.org/web/20190404130054/https://www.sciencedaily.com/releases/2009/07/090730141607.htm
 | url-status = live
}}</ref><ref>
{{cite journal
 | last1 = Jompol | first1 = Y.  |display-authors=etal
 | year = 2009
 | title = Probing Spin-Charge Separation in a Tomonaga-Luttinger Liquid
 | journal = [[Science (journal)|Science]]
 | volume = 325 | issue = 5940 | pages = 597–601
 | doi =10.1126/science.1171769
 | pmid =19644117 | bibcode = 2009Sci...325..597J |arxiv = 1002.2782
 | s2cid = 206193
}}</ref> The former carries spin and magnetic moment, the next carries its orbital location while the latter electrical charge.

=== Motion and energy ===
According to [[Albert Einstein|Einstein's]] theory of [[special relativity]], as an electron's speed approaches the [[speed of light]], from an observer's point of view its [[Mass in special relativity|relativistic mass]] increases, thereby making it more and more difficult to accelerate it from within the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in vacuum, ''c''. However, when relativistic electrons—that is, electrons moving at a speed close to ''c''—are injected into a dielectric medium such as water, where the local speed of light is significantly less than ''c'', the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called [[Cherenkov radiation]].<ref>
{{cite web
 | title = The Nobel Prize in Physics 1958, for the discovery and the interpretation of the Cherenkov effect
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | year = 2008
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1958/
 | access-date = 2008-09-25
 | df = dmy-all
 | archive-date = 2008-10-18
 | archive-url = https://web.archive.org/web/20081018162638/http://nobelprize.org/nobel_prizes/physics/laureates/1958/
 | url-status = live
}}</ref>

[[File:Lorentz factor.svg|thumb|right|alt=The plot starts at zero and curves sharply upward toward the right|Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as ''v'' approaches ''c''.]]
The effects of special relativity are based on a quantity known as the [[Lorentz factor]], defined as <math>\textstyle \gamma=1/ \sqrt{ 1-{v^2}/{c^2} }</math>, where ''v'' is the speed of the particle. The kinetic energy ''K''<sub>e</sub> of an electron moving with velocity ''v'' is:
: <math>\displaystyle K_{\mathrm{e}} = (\gamma - 1)m_{\mathrm{e}} c^2,</math>
where ''m''<sub>e</sub> is the mass of electron. For example, the [[SLAC National Accelerator Laboratory|Stanford linear accelerator]] can [[Acceleration|accelerate]] an electron to roughly 51&nbsp;GeV.<ref>
{{cite web
 | date = August 26, 2008
 | title = Special Relativity
 | publisher = [[SLAC National Accelerator Laboratory|Stanford Linear Accelerator Center]]
 | url = https://www2.slac.stanford.edu/vvc/theory/relativity.html
 | access-date = 2008-09-25
 | df = dmy-all
 | archive-date = 2008-08-28
 | archive-url = https://web.archive.org/web/20080828113927/http://www2.slac.stanford.edu/VVC/theory/relativity.html
 | url-status = live
}}</ref>
Since an electron behaves as a wave, at a given velocity it has a characteristic [[Matter wave|de Broglie wavelength]]. This is given by ''λ''<sub>e</sub>&nbsp;=&nbsp;''h''/''p'' where ''h'' is the [[Planck constant]] and ''p'' is the momentum.<ref name="de_broglie" /> For the 51&nbsp;GeV electron above, the wavelength is about {{val|2.4|e=-17|u=m}}, small enough to explore structures well below the size of an atomic nucleus.<ref>
{{cite book
 | last = Adams
 | first = S.
 | title = Frontiers: Twentieth Century Physics
 | url = https://books.google.com/books?id=yIsMaQblCisC&pg=PA215
 | page = 215
 | publisher = [[CRC Press]]
 | year = 2000
 | isbn = 978-0-7484-0840-5
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204071142/https://books.google.com/books?id=yIsMaQblCisC&pg=PA215
 | url-status = live
}}</ref>