Editing Electronvolt

{{short description|Unit of energy}}
{{Redirect-several|MEV|KEV|GEV|TEV|PEV}}
{{Infobox unit
| name          = electronvolt
| image         = 
| caption       = 
| standard      = [[Non-SI units mentioned in the SI|Non-SI accepted unit]]
| quantity      = [[energy]]
| symbol        = eV
| units1        = [[joule]]s (SI)
| inunits1      = {{physconst|eV}}
}}

In [[physics]], an '''electronvolt''' (symbol '''eV'''), also written '''electron-volt''' and '''electron volt''', is the measure of an amount of [[kinetic energy]] gained by a single [[electron]] accelerating through an [[Voltage|electric potential difference]] of one [[volt]] in [[vacuum]]. When used as a [[Units of energy|unit of energy]], the numerical value of 1 eV in [[joule]]s (symbol J) is equal to the numerical value of the [[Electric charge|charge]] of an electron in [[coulomb]]s (symbol C). Under the [[2019 revision of the SI]], 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 [[Particle accelerator#Electrostatic particle accelerators|electrostatic particle accelerator]] sciences, because a particle with [[electric charge]] ''q'' gains an energy {{nowrap|1=''E'' = ''qV''}} after passing through a voltage of ''V''.

== Definition and use ==
An electronvolt is the amount of energy gained or lost by a single [[electron]] when it moves through an [[Voltage|electric potential difference]] of one [[volt]]. Hence, it has a value of one [[volt]], which is {{val|1|u=J/C}}, multiplied by the [[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 commonly used [[unit of energy]] within physics, widely used in [[Solid-state physics|solid state]], [[Atomic physics|atomic]], [[Nuclear physics|nuclear]] and [[particle physics|particle]] physics, and [[high-energy astronomy|high-energy astrophysics]]. It is commonly used with [[SI prefix]]es ''milli-'' (10<sup>−3</sup>), ''kilo-'' (10<sup>3</sup>), ''mega-'' (10<sup>6</sup>), ''giga-'' (10<sup>9</sup>), ''tera-'' (10<sup>12</sup>), ''peta-'' (10<sup>15</sup>), ''exa-'' (10<sup>18</sup>), ''zetta-'' (10<sup>21</sup>), ''yotta-'' (10<sup>24</sup>), ''ronna-'' (10<sup>27</sup>), or ''quetta-'' (10<sup>30</sup>), the respective symbols being meV, keV, MeV, GeV, TeV, PeV, EeV, ZeV, YeV, ReV, and QeV. The SI unit of energy is the joule (J).
 
In some older documents, and in the name ''[[Bevatron]]'', the symbol ''BeV'' is used, where the ''B'' stands for ''[[billion]]''. The symbol ''BeV'' is therefore equivalent to ''GeV'', though neither is an SI unit.

== Relation to other physical properties and units ==

{| class="wikitable" style="float:right; margin:0 0 1em 1em;"
|-
! Quantity !! Unit || SI value of unit
|-
| [[energy]] || eV || {{physconst|eV}}
|-
| [[mass]] || eV/''c''<sup>2</sup> || {{val|1.78266192|e=-36|u=kg}}
|-
| [[momentum]] || eV/''c'' || {{val|5.34428599|e=-28|u=kg·m/s}}
|-
| [[temperature]] || eV/''k''<sub>B</sub> || {{val|11604.51812|u=K}}
|-
| [[time]] || ''ħ''/eV || {{val|6.582119|e=-16|u=s}}
|-
| [[distance]] || ''ħc''/eV || {{val|1.97327|e=-7|u=m}}
|}
In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from the electronvolt as a product with fundamental constants of importance in the theory are often used.

=== Mass ===
By [[mass–energy equivalence]], the electronvolt corresponds to a unit of [[mass]]. It is common in [[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 [[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]] 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]] 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 [[positron]], each with a mass of {{val|0.511|u=MeV/c2}}, can [[Annihilation|annihilate]] to yield {{val|1.022|u=MeV}} of energy. A [[proton]] has a mass of {{val|0.938|u=GeV/c2}}. In general, the masses of all [[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 [[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 [[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 using the unit electronvolt.
[[File:Einstein-triangle-in-natural-units.svg|thumb|The [[energy–momentum relation]] in [[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]] where the total [[energy]] <math>E</math> is the [[hypotenuse]] and the [[momentum]] <math>p</math> and [[Invariant mass|rest mass]] <math>m_0</math> are the two [[Cathetus|legs]].]]
The [[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 [[Particle physics|high-energy physics]] such that an applied energy with expressed in the unit eV conveniently results in a numerically approximately equivalent change of momentum when expressed with the unit&nbsp;eV/''c''.

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

For example, if the momentum ''p'' of an electron is {{val|1|u=GeV/''c''}}, 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 [[particle physics]], a system of natural units in which the speed of light in vacuum ''c'' and the [[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]]). In particular, particle [[scattering length]]s are often presented using a unit of inverse particle mass.

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 [[B meson|{{Subatomic particle|B0}} meson]] has a lifetime of 1.530(9)&nbsp;[[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 [[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}}{(6.62\ 607\ 015 \times 10^{-34}\; \text{J} {\cdot} \text{s}) \times (2.99\ 792\ 458 \times 10^{11}\; \text{mm}/\text{s})} \thickapprox 806.55439 \; \text{mm}^{-1}.</math>

=== Temperature ===
In certain fields, such as [[plasma physics]], it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the [[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 [[Boltzmann constant]].

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

As an approximation: at a temperature of {{nowrap|1=''T'' = {{val|20|u=degC}}}}, ''k''<sub>B</sub>''T'' is about {{val|0.025|u=eV}} (≈ {{sfrac|290 K|11604 K/eV}}).

=== 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 ''ν'', and wavelength ''λ'' of a photon are related by
<math display="block">E = h\nu = \frac{hc}{\lambda}
= \frac{\mathrm{4.135\ 667\ 696 \times 10^{-15}\;eV/Hz} \times \mathrm{299\, 792\, 458\;m/s}}{\lambda}</math>
where ''h'' is the [[Planck constant]], ''c'' is the [[speed of light]]. This reduces to{{physconst|h_eV/Hz|ref=only}}
<math display="block">\begin{align}
E
&= 4.135\ 667\ 696 \times 10^{-15}\;\mathrm{eV/Hz}\times\nu \\[4pt]
&=\frac{1\ 239.841\ 98\;\mathrm{eV{\cdot}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 [[Scintillation (physics)|scintillation]] light. For example, the yield of a [[phototube]] is measured in phe/keVee ([[photoelectron]]s 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 [[photon energy|energy of a photon]] varies only with the frequency of the photon, related by the speed of light. This contrasts with a massive particle of which the energy depends on its velocity and [[rest mass]].<ref>{{Cite web |last=Molinaro |first=Marco |date=9 January 2006 |title="What is Light?" |url=http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf |url-status=dead |archive-url=https://web.archive.org/web/20071129084926id_/http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf |archive-date=29 November 2007 |access-date=7 February 2014 |website=[[University of California, Davis]] |series=IST 8A (Shedding Light on Life) - W06}}</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>
{| border="0"
!colpan=3| Legend
|-
| γ: [[gamma ray]]s || MIR: mid-infrared || HF: [[High frequency|high freq.]]
|-
| HX: hard [[X-ray]]s || FIR: far infrared || MF: [[Medium frequency|medium freq.]]
|-
| SX: soft X-rays || [[radio waves]] || LF: [[Low frequency|low freq.]]
|-
| EUV: extreme [[ultraviolet]] || EHF: [[Extremely high frequency|extremely high freq.]] || VLF: [[Very low frequency|very low freq.]]
|-
| NUV: [[near ultraviolet]] || SHF: [[Super high frequency|super high freq.]] || ULF: [[Ultra low frequency|ultra-low freq.]]
|-
| [[visible light]] || UHF: [[Ultra high frequency|ultra high freq.]] ||SLF: [[Super low frequency|super low freq.]]
|-
| NIR: near [[infrared]]||VHF: [[Very high frequency|very high freq.]] ||ELF: [[Extremely low frequency|extremely low freq.]]
|-
|}]]

{| class="wikitable sortable"
! Energy || Source
|-
| {{val|10|u=[[yotta-|Y]]<nowiki/>eV}} || approximate [[grand unification energy]]
|-
| {{val|2|u=[[peta-|P]]<nowiki/>eV}} || 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 [[Large Hadron Collider]] (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
|-
| {{val|125.1|0.2|u=GeV}} || [[rest mass energy]] of the [[Higgs boson]], as measured by two separate detectors at the [[Large Hadron Collider|LHC]] to a certainty better than [[Standard deviation|5 sigma]]<ref>{{Cite journal|last1=ATLAS |last2=CMS |author-link1=ATLAS experiment|author-link2=Compact Muon Solenoid|arxiv=1503.07589 |title= Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments|journal=Physical Review Letters |volume=114 |issue=19 |pages=191803 |date=26 March 2015 |doi=10.1103/PhysRevLett.114.191803 |doi-access=free |pmid=26024162 |bibcode=2015PhRvL.114s1803A }}</ref>
|-
| {{val|105.7|u=MeV}} || [[rest mass energy]] of a [[muon]]
|-
| {{val|0.511|u=MeV}} || [[rest mass energy]] of an electron
|-
| {{val|13.6|u=eV}} || energy required to [[ion]]ize [[hydrogen atom|atomic hydrogen]]; [[Molecular bond|molecular]] [[bond energy|bond energies]] are on the [[orders of magnitude|order]] of {{val|1|u=eV}} to {{val|10|u=eV}} per bond
|-
| {{val|1.65|to|3.26|u=eV}} || range of [[photon energy]] <math>(\tfrac{hc}{\lambda})</math> of [[visible spectrum]] from [[red]] to [[Violet (color)|violet]]
|-
|{{val|38|u=meV}}
|[[Kinetic theory of gases|average kinetic energy]], {{math|{{sfrac|3|2}}}}[[kT (energy)|{{math|''k''<sub>B</sub>''T''}}]], of one gas molecule at [[room temperature]]
|-
| {{val|230|u=μeV}} || [[thermal energy]], [[kT (energy)|{{math|''k''<sub>B</sub>''T''}}]], at the [[cosmic microwave background]] radiation temperature of ~2.7&nbsp;[[kelvin]]
|-
|}

=== Molar energy ===
One mole of particles given 1&nbsp;eV of energy each has approximately 96.5&nbsp;kJ of energy – this corresponds to the [[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''&nbsp;eV is equal to ''E''·''F''·''n''.

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

== References ==
{{reflist}}

== External links ==
* [https://physics.nist.gov/cuu/Constants/ Fundamental Physical Constants from NIST]

{{SI units}}

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