View source for Physics:Electronvolt

{{short description|Unit of energy}}
{{Hatnote|"meV", "keV", "MeV", "GeV", "TeV" and "PeV" redirect here. For other uses, see MEV, KEV, GEV, TEV and PEV.}}

In [[Physics:Physics|physics]], an '''electronvolt''' (symbol '''eV''', also written '''electron-volt''' and '''electron volt''') is the measure of an amount of [[Physics:Kinetic energy|kinetic energy]] gained by a single [[Physics:Electron|electron]] accelerating from rest through an [[Physics:Voltage|electric potential difference]] of one [[Volt|volt]] in [[Physics:Vacuum|vacuum]]. When used as a [[Units of energy|unit of energy]], the numerical value of 1 eV in [[Joule|joule]]s (symbol J) is equivalent to the numerical value of the [[Physics:Electric charge|charge]] of an electron in [[Coulomb|coulomb]]s (symbol C). Under the [[2019 redefinition of the SI base units|2019 redefinition of the SI base units]], this sets 1&nbsp;eV equal to the exact value {{physconst|eV|after=.}}

Historically, the electronvolt was devised as a standard unit of measure through its usefulness in [[Physics:Particle accelerator#Electrostatic particle accelerators|electrostatic particle accelerator]] sciences, because a particle with [[Physics:Electric charge|electric charge]] ''q'' gains an energy {{nowrap|1=''E'' = ''qV''}} after passing through a voltage of ''V.'' Since ''q'' must be an [[Integer|integer]] multiple of the [[Physics:Elementary charge|elementary charge]] ''e'' for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.

==Definition and use==
An electronvolt is the amount of kinetic energy gained or lost by a single [[Physics:Electron|electron]] accelerating from rest through an [[Physics:Voltage|electric potential difference]] of one [[Volt|volt]] in vacuum. Hence, it has a value of one [[Volt|volt]], {{val|1|u=J/C}}, multiplied by the [[Physics:Elementary charge|elementary charge]] {{physconst|e|symbol=yes|after=.}} Therefore, one electronvolt is equal to {{physconst|eV|after=.}}

The electronvolt (eV) is a unit of energy, but is not an SI unit. It is a common unit of energy within physics, widely used in [[Physics:Solid-state physics|solid state]], [[Physics:Atomic physics|atomic]], [[Physics:Nuclear physics|nuclear]], and [[Physics:Particle physics|particle physics]], and [[Astronomy:High-energy astronomy|high-energy astrophysics]]. It is commonly used with [[SI prefix]]es milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). The SI unit of energy is the joule (J).

In some older documents, and in the name [[Physics:Bevatron|Bevatron]], the symbol BeV is used, where the "B" stands for [[Billion|billion]]. The symbol BeV is therefore equivalent to the GeV.

== Relation to other physical properties and units ==
{| class="wikitable" style="float:right; margin:0 0 1em 1em;"
|-
! Measurement !! Unit || SI value of unit
|-
| [[Physics:Energy|Energy]] || eV || {{val|1.602176634|e=-19|u=J}}
|-
| [[Physics:Mass|Mass]] || eV/''c''<sup>2</sup> || {{val|1.78266192|e=-36|u=kg}}
|-
| [[Physics:Momentum|Momentum]] || eV/''c'' || {{val|5.34428599|e=-28|u=kg·m/s}}
|-
| [[Physics:Temperature|Temperature]] || eV/''k''<sub>B</sub> || {{val|1.160451812|e=4|u=K}}
|-
| [[Time]] || ''ħ''/eV || {{val|6.582119|e=-16|u=s}}
|-
| [[Distance]] || ''ħc''/eV || {{val|1.97327|e=-7|u=m}}
|}

===Mass===
By [[Mass–energy equivalence|mass–energy equivalence]], the electronvolt corresponds to a unit of [[Physics:Mass|mass]]. It is common in [[Physics:Particle physics|particle physics]], where units of mass and energy are often interchanged, to express mass in units of eV/''c''<sup>2</sup>, where ''c'' is the [[Physics:Speed of light|speed of light]] in vacuum (from [[Mass–energy equivalence|{{nowrap|1=''E'' = ''mc''<sup>2</sup>}}]]). It is common to informally express mass in terms of eV as a unit of mass, effectively using a system of [[Natural units|natural units]] with ''c'' set to 1.<ref>{{cite journal | bibcode=1983QJRAS..24...24B | title=Natural Units Before Planck | last1=Barrow | first1=J. D. | journal=Quarterly Journal of the Royal Astronomical Society | year=1983 | volume=24 | page=24 }}</ref> The [[Kilogram|kilogram]] equivalent of {{val|1|u=eV/c2}} is:

<math display="block">1\; \text{eV}/c^2 = \frac{(1.602\ 176\ 634 \times 10^{-19} \, \text{C}) \times 1 \, \text{V}}{(299\ 792\ 458\; \mathrm{m/s})^2} = 1.782\ 661\ 92 \times 10^{-36}\; \text{kg}.</math>

For example, an electron and a [[Physics:Positron|positron]], each with a mass of {{val|0.511|u=MeV/c2}}, can [[Physics:Annihilation|annihilate]] to yield {{val|1.022|u=MeV}} of energy. A [[Physics:Proton|proton]] has a mass of {{val|0.938|u=GeV/c2}}. In general, the masses of all [[Physics:Hadron|hadron]]s are of the order of {{val|1|u=GeV/c2}}, which makes the GeV/''c''<sup>2</sup> a convenient unit of mass for particle physics:<ref>{{cite web|url=https://indico.cern.ch/event/318730/contributions/737345/attachments/613347/843809/gevtypeunitshst14.pdf |title=Energy and momentum units in particle physics| author=Gron Tudor Jones| website=Indico.cern.ch| access-date=5 June 2022}}</ref>
{{block indent|em=1.2|text={{nowrap|1={{val|1|u=GeV/c2}} = {{val|1.78266192|e=-27|u=kg}}.}}}}

The [[Physics:Atomic mass constant|atomic mass constant]] (''m''<sub>u</sub>), one twelfth of the mass a carbon-12 atom, is close to the mass of a proton. To convert to electronvolt mass-equivalent, use the formula:
{{block indent|em=1.2|text={{nowrap|1=''m''<sub>u</sub> = 1 Da = {{val|931.4941|u=MeV/c2}} = {{val|0.9314941|u=GeV/c2}}.}}}}

===Momentum===
By dividing a particle's kinetic energy in electronvolts by the fundamental constant ''c'' (the speed of light), one can describe the particle's [[Physics:Momentum|momentum]] in units of eV/''c''.<ref name="FNALunits">{{cite web |url=http://quarknet.fnal.gov/toolkits/ati/whatgevs.html |title=Units in particle physics |publisher=Fermilab |date=22 March 2002 |work=Associate Teacher Institute Toolkit |access-date=13 February 2011 |url-status=live |archive-url=https://web.archive.org/web/20110514152552/http://quarknet.fnal.gov/toolkits/ati/whatgevs.html |archive-date=14 May 2011 }}</ref> In natural units in which the fundamental velocity constant ''c'' is numerically 1, the ''c'' may informally be omitted to express momentum as electronvolts. 
[[File:Einstein-triangle-in-natural-units.svg|thumb|The [[Physics:Energy–momentum relation|energy–momentum relation]] in [[Natural units|natural units]], <math>E^2 = p^2 + m_0^2</math>, is a [[Pythagorean theorem|Pythagorean equation]] that can be visualized as a [[Right triangle|right triangle]] where the total energy <math>E</math> is the [[Hypotenuse|hypotenuse]] and the momentum <math>p</math> and rest mass <math>m_0</math> are the two [[Cathetus|legs]].]]
The [[Physics:Energy–momentum relation|energy momentum relation]]

<math display="block">E^2 = p^2 c^2 + m_0^2 c^4</math>

in natural units (with <math>c=1</math>)

<math display="block">E^2 = p^2 + m_0^2</math>

is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as <math>E \simeq p</math> in [[Physics:Particle physics|high-energy physics]] such that an applied energy in units of eV conveniently results in an approximately equivalent change of momentum in units of eV/''c''.

The dimensions of momentum units are {{dimanalysis|length=1|mass=1|time=−1}}. The dimensions of energy units are {{dimanalysis|length=2|mass=1|time=−2}}. Dividing the units of energy (such as eV) by a fundamental constant (such as the speed of light) that has units of velocity ({{dimanalysis|length=1|time=−1}}) facilitates the required conversion for using energy units to describe momentum.

For example, if the momentum ''p'' of an electron is said to be {{val|1|u=GeV}}, then the conversion to [[MKS system of units]] can be achieved by:
<math display="block">p = 1\; \text{GeV}/c = \frac{(1 \times 10^9) \times (1.602\ 176\ 634 \times 10^{-19} \; \text{C}) \times (1 \; \text{V})}{2.99\ 792\ 458 \times 10^8\; \text{m}/\text{s}} = 5.344\ 286 \times 10^{-19}\; \text{kg} {\cdot} \text{m}/\text{s}.</math>

===Distance===
In [[Physics:Particle physics|particle physics]], a system of natural units in which the speed of light in vacuum ''c'' and the [[Physics:Planck constant|reduced Planck constant]] ''ħ'' are dimensionless and equal to unity is widely used: {{nowrap|1=''c'' = ''ħ'' = 1}}. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see [[Mass–energy equivalence|mass–energy equivalence]]). In particular, particle [[Physics:Scattering length|scattering length]]s are often presented in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:
<math display="block">\hbar = 1.054\ 571\ 817\ 646\times 10^{-34}\ \mathrm{J{\cdot}s} = 6.582\ 119\ 569\ 509\times 10^{-16}\ \mathrm{eV{\cdot}s}.</math>

The above relations also allow expressing the mean lifetime ''τ'' of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via {{nowrap|1=Γ = ''ħ''/''τ''}}. For example, the [[Physics:B meson|{{Subatomic particle|B0}} meson]] has a lifetime of 1.530(9)&nbsp;[[Picosecond|picosecond]]s, mean decay length is {{nowrap|1=''cτ'' = {{val|459.7|u=μm}}}}, or a decay width of {{val|4.302|25|e=-4|u=eV}}.

Conversely, the tiny meson mass differences responsible for [[Physics:Neutral particle oscillation|meson oscillations]] are often expressed in the more convenient inverse picoseconds.

Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy:
<math display="block">\frac{1\; \text{eV}}{hc} = \frac{1.602\ 176\ 634 \times 10^{-19} \; \text{J}}{(2.99\ 792\ 458 \times 10^{10}\; \text{cm}/\text{s}) \times (6.62\ 607\ 015 \times 10^{-34}\; \text{J} {\cdot} \text{s})} \thickapprox 8065.5439 \; \text{cm}^{-1}.</math>

===Temperature===
In certain fields, such as [[Physics:Plasma physics|plasma physics]], it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the [[Physics:Boltzmann constant|Boltzmann constant]] to convert to the Kelvin scale:
<math display="block">{1 \,\mathrm{eV} / k_{\text{B}}} = {1.602\ 176\ 634 \times 10^{-19} \text{ J} \over 1.380\ 649 \times 10^{-23} \text{ J/K}} = 11\ 604.518\ 12 \text{ K},</math>

where ''k''<sub>B</sub> is the [[Physics:Boltzmann constant|Boltzmann constant]].

The ''k''<sub>B</sub> is assumed when using the electronvolt to express temperature, for example, a typical [[Physics:Magnetic confinement fusion|magnetic confinement fusion]] plasma is {{val|15|u=keV}} (kiloelectronvolt), which is equal to 174&nbsp;MK (megakelvin).

As an approximation: ''k''<sub>B</sub>''T'' is about {{val|0.025|u=eV}} (≈ {{sfrac|290 K|11604 K/eV}}) at a temperature of {{val|20|u=degC}}.

===Wavelength===
[[File:Colors in eV.svg|thumb|Energy of photons in the visible spectrum in eV|239x239px]]
[[File:EV_to_nm_vis-en.svg|thumb|Graph of wavelength (nm) to energy (eV)]]
The energy ''E'', frequency ''v'', and wavelength ''λ'' of a photon are related by

<math display="block">E = h\nu = \frac{hc}{\lambda}
= \frac{4.135\, 667\, 516 \times 10^{-15}\,\mathrm{eV{\cdot}s} \times 299\, 792\, 458\,\mathrm{m/s}}{\lambda}</math>

where ''h'' is the [[Physics:Planck constant|Planck constant]], ''c'' is the [[Physics:Speed of light|speed of light]]. This reduces to<ref name=":0">{{cite web | title=CODATA Value: Planck constant in eV s | url=http://physics.nist.gov/cgi-bin/cuu/Value?hev|access-date=30 March 2015| url-status=live| archive-url=https://web.archive.org/web/20150122120538/http://physics.nist.gov/cgi-bin/cuu/Value?hev| archive-date=22 January 2015}}</ref>
<math display="block">\begin{align}
E\mathrm{(eV)}
&=4.135\, 667\, 516 \times 10^{-15}\,\mathrm{eV{\cdot}s}\times\nu \\[4pt]
&=\frac{1\ 239.841\ 93\,\text{eV}{\cdot}\text{nm}}{\lambda}.
\end{align}</math>
A photon with a wavelength of {{val|532|u=nm}} (green light) would have an energy of approximately {{val|2.33|u=eV}}. Similarly, {{val|1|u=eV}} would correspond to an infrared photon of wavelength {{val|1240|u=nm}} or frequency {{val|241.8|u=THz}}.

==Scattering experiments==
In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by [[Physics:Scintillation|scintillation]] light. For example, the yield of a [[Physics:Phototube|phototube]] is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.

==Energy comparisons==
[[File:Light spectrum.svg|right|frame|'''Photon frequency vs. energy particle in electronvolts'''. The [[Physics:Photon energy|energy of a photon]] varies only with the frequency of the photon, related by speed of light constant. This contrasts with a massive particle of which the energy depends on its velocity and [[Physics:Rest mass|rest mass]].<ref>[http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf What is Light?] {{webarchive |url=https://web.archive.org/web/20131205005843/http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf |date=December 5, 2013 }} – UC Davis lecture slides</ref><ref>{{cite web |author=Elert, Glenn |url=http://physics.info/em-spectrum/ |title=Electromagnetic Spectrum, The Physics Hypertextbook |publisher=hypertextbook.com |access-date=2016-07-30 |url-status=live |archive-url=https://web.archive.org/web/20160729235315/http://physics.info/em-spectrum/ |archive-date=2016-07-29 }}</ref><ref>{{cite web |url=http://www.vlf.it/frequency/bands.html |title=Definition of frequency bands on |publisher=Vlf.it |access-date=2010-10-16 |url-status=live |archive-url=https://web.archive.org/web/20100430012219/http://www.vlf.it/frequency/bands.html |archive-date=2010-04-30 }}</ref>

Legend
{| border="0"
|-
|γ: [[Physics:Gamma ray|Gamma ray]]s|||MIR: Mid infrared|||HF: [[Physics:High frequency|High freq.]]
|-
|HX: Hard [[Physics:X-ray|X-ray]]s ||FIR: Far infrared||MF: [[Physics:Medium frequency|Medium freq.]]
|-
|SX: Soft X-rays||Radio waves||LF: [[Physics:Low frequency|Low freq.]]
|-
|EUV: Extreme [[Physics:Ultraviolet|ultraviolet]]||EHF: [[Physics:Extremely high frequency|Extremely high freq.]]||VLF: [[Physics:Very low frequency|Very low freq.]]
|-
|NUV: Near ultraviolet||SHF: [[Physics:Super high frequency|Super high freq.]]||VF/ULF: Voice freq.
|-
|[[Physics:Visible light|Visible light]]||UHF: [[Physics:Ultra high frequency|Ultra high freq.]]||SLF: [[Physics:Super low frequency|Super low freq.]]
|-
|NIR: Near [[Physics:Infrared|Infrared]]||VHF: [[Engineering:Very high frequency|Very high freq.]]||ELF: [[Physics:Extremely low frequency|Extremely low freq.]]
|-
| || ||Freq: [[Physics:Frequency|Frequency]]
|}]]

{| class="wikitable sortable"
! Energy || Source
|-
| {{val|5.25|e=32|u=eV}} || total energy released from a 20&nbsp;[[Physics:TNT equivalent|kt]] nuclear fission device
|-
| 12.2 R<nowiki/>eV ({{val|1.22|e=28|u=eV}}) || the [[Physics:Planck energy|Planck energy]]
|-
| 10 [[Yotta-|Y]]<nowiki/>eV ({{val|1|e=25|u=eV}}) || approximate [[Physics:Grand unification energy|grand unification energy]]
|-
| ~624 [[Exa-|E]]<nowiki/>eV ({{val|6.24|e=20|u=eV}}) || energy consumed by a single 100-watt light bulb in one second ({{val|100|u=W}} = {{val|100|u=J/s}} ≈ {{val|6.24|e=20|u=eV/s}})
|-
| 300 [[Exa-|E]]<nowiki/>eV ({{val|3|e=20|u=eV}} = ~{{val|50|ul=J}}) || The first [[Astronomy:Ultra-high-energy cosmic ray|ultra-high-energy cosmic ray]] particle observed, the so-called [[Physics:Oh-My-God particle|Oh-My-God particle]].<ref>[http://www.desy.de/user/projects/Physics/General/open_questions.html Open Questions in Physics.] {{webarchive|url=https://web.archive.org/web/20140808124758/http://www.desy.de/user/projects/Physics/General/open_questions.html|date=2014-08-08}} German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.</ref>
|-
| {{val|2|u=PeV}} || two petaelectronvolts, the highest-energy neutrino detected by the IceCube neutrino telescope in Antarctica<ref>{{cite web|url=http://icecube.wisc.edu/news/view/227|title=A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino|date=21 May 2014 |url-status=live|archive-url=https://web.archive.org/web/20150319072501/http://icecube.wisc.edu/news/view/227|archive-date=2015-03-19}}</ref>
|-
| {{val|14|u=TeV}} || designed proton center-of-mass collision energy at the [[Physics:Large Hadron Collider|Large Hadron Collider]] (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
|-
| {{val|1|u=TeV}} || a trillion electronvolts, or {{val|1.602|e=-7|u=J}}, about the kinetic energy of a flying [[Biology:Mosquito|mosquito]]<ref>[http://cms.web.cern.ch/content/glossary Glossary] {{webarchive|url=https://web.archive.org/web/20140915005403/http://cms.web.cern.ch/content/glossary |date=2014-09-15 }} - CMS Collaboration, CERN</ref>
|-
|172 GeV
|rest energy of [[Physics:Top quark|top quark]], the heaviest measured [[Physics:Elementary particle|elementary particle]]
|-
|-
| {{val|210|u=MeV}}|| average energy released in fission of one [[Physics:Plutonium-239|Pu-239]] atom
|-
| {{val|200|u=MeV}}|| approximate average energy released in [[Physics:Nuclear fission|nuclear fission]] fission fragments of one U-235 atom.
|-
|105.7 MeV
|rest energy of a [[Physics:Muon|muon]]
|-
|{{val|17.6|u=MeV}}|| average energy released in the [[Physics:Nuclear fusion|nuclear fusion]] of [[Physics:Deuterium|deuterium]] and [[Physics:Tritium|tritium]] to form He-4; this is {{val|0.41|u=PJ}} per kilogram of product produced
|-
|2 MeV
|approximate average energy released in a [[Physics:Nuclear fission|nuclear fission]] neutron released from one U-235 atom. 
|-
|1.9 MeV
|rest energy of [[Physics:Up quark|up quark]], the lowest mass quark.
|-
| {{val|1|u=MeV}} ({{val|1.602|e=-13|u=J}}) || about twice the rest energy of an electron
|-
|1 to 10 keV
|approximate thermal temperature, <math>k_\text{B}T</math>, in [[Physics:Nuclear fusion|nuclear fusion]] systems, like the core of the [[Astronomy:Sun|sun]], [[Physics:Magnetic confinement fusion|magnetically confined plasma]], [[Physics:Inertial confinement fusion|inertial confinement]] and [[Engineering:Nuclear weapon|nuclear weapon]]s
|-
| {{val|13.6|u=eV}} || the energy required to [[Physics:Ion|ion]]ize [[Physics:Hydrogen atom|atomic hydrogen]]; molecular [[Physics:Bond energy|bond energies]] are on the order of {{val|1|u=eV}} to {{val|10|u=eV}} per bond
|-
| {{val|1.6|u=eV}} to {{val|3.4|u=eV}} || the [[Physics:Photon energy|photon energy]] of visible light
|-
| {{val|1.1|u=eV}}|| energy <math>E_g</math> required to break a [[Chemistry:Covalent|covalent]] bond in [[Chemistry:Silicon|silicon]]
|-
| {{val|720|u=meV}}|| energy <math>E_g</math> required to break a [[Chemistry:Covalent|covalent]] bond in [[Chemistry:Germanium|germanium]]
|-
|< {{val|120|u=meV}}
|approximate rest energy of [[Physics:Neutrino|neutrino]]s (sum of 3 flavors)<ref name="Mertens">
 {{cite journal
  |arxiv=1605.01579
  |bibcode=2016JPhCS.718b2013M
  |doi=10.1088/1742-6596/718/2/022013
  |title=Direct neutrino mass experiments
  |journal=Journal of Physics: Conference Series
  |volume=718 |issue=2 |page=022013 |year=2016
  |first1=Susanne |last1=Mertens
 |s2cid=56355240
 }}</ref>
|-
| {{val|25|u=meV}}||[[Physics:Thermal energy|thermal energy]], <math>k_\text{B}T</math>, at room temperature; one air molecule has an [[Physics:Kinetic theory of gases|average kinetic energy]] {{val|38|u=meV}}
|-
|{{val|230|u=μeV}}|| thermal energy, <math>k_\text{B}T</math>, of the [[Astronomy:Cosmic microwave background|cosmic microwave background]]
|}

===Per mole===
One mole of particles given 1&nbsp;eV of energy each has approximately 96.5&nbsp;kJ of energy – this corresponds to the [[Physics:Faraday constant|Faraday constant]] (''F'' &asymp; {{val|96485|u=C⋅mol<sup>−1</sup>}}), where the energy in joules of ''n'' moles of particles each with energy ''E'' eV is equal to ''E''·''F''·''n''.

==See also==
*[[Orders of magnitude (energy)]]

== References ==
{{Reflist}}

==External links==
*[http://physics.nist.gov/cuu/Constants physical constants reference; CODATA data]

{{SI units}}

{{DEFAULTSORT:Electron Volt}}
[[Category:Particle physics]]
[[Category:Units of chemical measurement]]
[[Category:Units of energy]]
[[Category:Voltage]]
[[Category:Electron]]

{{Sourceattribution|Electronvolt}}