# Electronvolt

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Unit of energy

Several terms  redirect here. For other uses, see [MEV (disambiguation)](/source/MEV_(disambiguation)), [KEV (disambiguation)](/source/KEV_(disambiguation)), [GEV (disambiguation)](/source/GEV_(disambiguation)), [TEV (disambiguation)](/source/TEV_(disambiguation)), and [PEV (disambiguation)](/source/PEV_(disambiguation)).

electronvolt Unit system Non-SI accepted unit Unit of energy Symbol eV Conversions 1 eV in ... ... is equal to ... SI units 1.602176634×10−19 J‍[1] CGS units 1.602176634×10−12 erg kilowatt-hours 4.450490650×10−26 kWh kilocalories (thermochemical) 3.829294058×10−23 kcal BTUs 1.518570443×10−22 BTU

In [physics](/source/Physics), an **electronvolt** (symbol **eV**), also written as **electron-volt** and **electron volt**, is a [unit of measurement](/source/Unit_of_measurement) equivalent to the amount of [kinetic energy](/source/Kinetic_energy) gained by a single [electron](/source/Electron) accelerating through an [electric potential difference](/source/Voltage) of one [volt](/source/Volt) in a [vacuum](/source/Vacuum). When used as a [unit of energy](/source/Units_of_energy), the numerical value of 1 eV expressed in unit of [joules](/source/Joule) (symbol J) is equal to the numerical value of the [charge](/source/Electric_charge) of an electron in [coulombs](/source/Coulomb) (symbol C). Under the [2019 revision of the SI](/source/2019_revision_of_the_SI), this sets 1 eV equal to the exact value 1.602176634×10−19 J.[1] Historically, the electronvolt was devised as a standard unit of measure through its usefulness in [electrostatic particle accelerator](/source/Particle_accelerator#Electrostatic_particle_accelerators) sciences, because a particle with [electric charge](/source/Electric_charge) *q* gains an energy *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](/source/Electron) when it moves through an [electric potential difference](/source/Voltage) of one [volt](/source/Volt). Hence, it has a value of one [volt](/source/Volt), which is 1 J/C, multiplied by the [elementary charge](/source/Elementary_charge) *e* = 1.602176634×10−19 C.[2] Therefore, one electronvolt is equal to 1.602176634×10−19 J.[1]

The electronvolt (eV) is a unit of energy, but is not an [SI unit](/source/SI_unit). It is a commonly used [unit of energy](/source/Unit_of_energy) within physics, widely used in [solid state](/source/Solid-state_physics), [atomic](/source/Atomic_physics), [nuclear](/source/Nuclear_physics) and [particle](/source/Particle_physics) physics, and [high-energy astrophysics](/source/High-energy_astronomy). It is commonly used with [SI prefixes](/source/SI_prefix) *milli-* (10−3), *kilo-* (103), *mega-* (106), *giga-* (109), *tera-* (1012), *peta-* (1015), *exa-* (1018), *zetta-* (1021), *yotta-* (1024), *ronna-* (1027), or *quetta-* (1030), 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](/source/Bevatron)*, the symbol *BeV* is used, where the *B* stands for *[billion](/source/Billion)*. The symbol *BeV* is therefore equivalent to *GeV*, though neither is an SI unit.

## Relation to other physical properties and units

Quantity Unit SI value of unit energy eV 1.602176634×10−19 J‍[1] mass eV/c2 1.7826619216279×10−36 kg momentum eV/c 5.3442859926783×10−28 kg·m/s temperature eV/kB 11604.51812155 K time ħ/eV 6.5821195695091×10−16 s distance ħc/eV 1.973269804593×10−7 m

In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from it; products with fundamental constants of importance in the theory are often used.

### Mass

By [mass–energy equivalence](/source/Mass%E2%80%93energy_equivalence), the electronvolt corresponds to a unit of [mass](/source/Mass). It is common in [particle physics](/source/Particle_physics), where units of mass and energy are often interchanged, to express mass in units of eV/*c*2, where *c* is the [speed of light](/source/Speed_of_light) in vacuum (from [*E* = *mc*2](/source/Mass%E2%80%93energy_equivalence)). It is common to informally express mass in terms of eV as a [unit of mass](/source/Unit_of_mass), effectively using a system of [natural units](/source/Natural_units) with *c* set to 1.[3] The [kilogram](/source/Kilogram) equivalent of 1 eV/*c*2 is:

1 eV / c 2 = 1.602 176 634 × 10 − 19 kg ⋅ m 2 ⋅ s − 2 ( 299 792 458 m / s ) 2 = 1.782 661 92 × 10 − 36 kg . {\displaystyle 1\;{\text{eV}}/c^{2}={\frac {1.602\ 176\ 634\times 10^{-19}\,{\text{kg}}\cdot {\text{m}}^{2}\cdot {\text{s}}^{-2}}{(299\ 792\ 458\;\mathrm {m/s} )^{2}}}=1.782\ 661\ 92\times 10^{-36}\;{\text{kg}}.}

For example, an electron and a [positron](/source/Positron), each with a mass of 0.511 MeV/*c*2, can [annihilate](/source/Annihilation) to yield 1.022 MeV of energy. A [proton](/source/Proton) has a mass of 0.938 GeV/*c*2. In general, the masses of all [hadrons](/source/Hadron) are of the order of 1 GeV/*c*2, which makes the GeV/*c*2 a convenient unit of mass for particle physics:[4]

1 GeV/*c*2 = 1.78266192×10−27 kg.

The [atomic mass constant](/source/Atomic_mass_constant) (*m*u), 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:

*m*u = 1 Da = 931.4941 MeV/*c*2 = 0.9314941 GeV/*c*2.

### 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](/source/Momentum) in units of eV/*c*.[5] 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.

The [energy–momentum relation](/source/Energy%E2%80%93momentum_relation) in [natural units](/source/Natural_units),

          E

            2

        =

          p

            2

        +

          m

            0

            2

    {\displaystyle E^{2}=p^{2}+m_{0}^{2}}

, is a [Pythagorean equation](/source/Pythagorean_theorem) that can be visualized as a [right triangle](/source/Right_triangle) where the total [energy](/source/Energy)

        E

    {\displaystyle E}

 is the [hypotenuse](/source/Hypotenuse) and the [momentum](/source/Momentum)

        p

    {\displaystyle p}

 and [rest mass](/source/Invariant_mass)

          m

            0

    {\displaystyle m_{0}}

 are the two [legs](/source/Cathetus).

The [energy–momentum relation](/source/Energy%E2%80%93momentum_relation) E 2 = p 2 c 2 + m 0 2 c 4 {\displaystyle E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}} in natural units (with c = 1 {\displaystyle c=1} ) E 2 = p 2 + m 0 2 {\displaystyle E^{2}=p^{2}+m_{0}^{2}} is a [Pythagorean equation](/source/Pythagorean_equation). When a relatively high energy is applied to a particle with relatively low [rest mass](/source/Rest_mass), it can be approximated as E ≃ p {\displaystyle E\simeq p} in [high-energy physics](/source/Particle_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 eV/*c*.

The dimension of momentum is T−1LM. The dimension of energy is T−2L2M. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity (T−1L) facilitates the required conversion for using a unit of energy to quantify momentum.

For example, if the momentum *p* of an electron is 1 GeV/*c*, then the conversion to [MKS system of units](/source/MKS_system_of_units) can be achieved by: p = 1 GeV / c = 10 9 × ( 1.602 176 634 × 10 − 19 C ) × ( 1 V ) 2.99 792 458 × 10 8 m / s = 5.344 286 × 10 − 19 kg ⋅ m / s . {\displaystyle {\begin{aligned}p=1\;{\text{GeV}}/c&={\frac {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}}}}\\[1ex]&=5.344\ 286\times 10^{-19}\;{\text{kg}}{\cdot }{\text{m}}/{\text{s}}.\end{aligned}}}

### Distance

In [particle physics](/source/Particle_physics), a system of natural units in which the speed of light in vacuum *c* and the [reduced Planck constant](/source/Planck_constant) *ħ* are dimensionless and equal to unity is widely used: *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](/source/Mass%E2%80%93energy_equivalence)). In particular, particle [scattering lengths](/source/Scattering_length) 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: ℏ = 1.054 571 817 646 × 10 − 34 J ⋅ s = 6.582 119 569 509 × 10 − 16 e V ⋅ s . {\displaystyle \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} .}

The above relations also allow expressing the [mean lifetime](/source/Mean_lifetime) *τ* of an unstable particle (in seconds) in terms of its [decay width](/source/Decay_width) Γ (in eV) via Γ = *ħ*/*τ*. For example, the [B0 meson](/source/B_meson) has a lifetime of 1.530(9) [picoseconds](/source/Picosecond), mean decay length is *cτ* = 459.7 μm, or a decay width of 4.302(25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for [meson oscillations](/source/Neutral_particle_oscillation) 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: 1 eV h c = 1.602 176 634 × 10 − 19 J ( 6.62 607 015 × 10 − 34 J ⋅ s ) × ( 2.99 792 458 × 10 11 mm / s ) ≈ 806.55439 mm − 1 . {\displaystyle {\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}.}

### Temperature

In certain fields, such as [plasma physics](/source/Plasma_physics), it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the [Boltzmann constant](/source/Boltzmann_constant) to convert to the [Kelvin scale](/source/Kelvin_scale): 1 e V / k B = 1.602 176 634 × 10 − 19 J 1.380 649 × 10 − 23 J/K = 11 604.518 12 K , {\displaystyle {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}},} where *k*B is the [Boltzmann constant](/source/Boltzmann_constant).

The *k*B is assumed when using the electronvolt to express temperature, for example, a typical [magnetic confinement fusion](/source/Magnetic_confinement_fusion) plasma is 15 keV (kiloelectronvolt), which corresponds to 174 MK (megakelvin).

As an approximation: at a temperature of *T* = 20 °C, *k*B*T* is about 0.025 eV (≈ ⁠290 K/11604 K/eV⁠).

### Wavelength

Energy of photons in the visible spectrum in eV

Graph of wavelength (nm) to energy (eV)

The energy *E*, frequency *ν*, and wavelength *λ* of a photon are related by E = h ν = h c λ = 4.135 667 696 × 10 − 15 e V / H z × 299 792 458 m / s λ {\displaystyle 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 }}} where *h* is the [Planck constant](/source/Planck_constant), *c* is the [speed of light](/source/Speed_of_light). This reduces to[6] E = 4.135 667 696 × 10 − 15 e V / H z × ν = 1 239.841 98 e V ⋅ n m λ . {\displaystyle {\begin{aligned}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{aligned}}} A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm or frequency 241.8 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](/source/Scintillation_(physics)) light. For example, the yield of a [phototube](/source/Phototube) is measured in phe/keVee ([photoelectrons](/source/Photoelectron) 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

**Photon frequency vs. energy particle in electronvolts**. The [energy of a photon](/source/Photon_energy) 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](/source/Rest_mass).[7][8][9]

Legend γ: gamma rays MIR: mid-infrared HF: high freq. HX: hard X-rays FIR: far infrared MF: medium freq. SX: soft X-rays radio waves LF: low freq. EUV: extreme ultraviolet EHF: extremely high freq. VLF: very low freq. NUV: near ultraviolet SHF: super high freq. ULF: ultra-low freq. visible light UHF: ultra high freq. SLF: super low freq. NIR: near infrared VHF: very high freq. ELF: extremely low freq.

Energy Source 10 YeV approximate grand unification energy 120 PeV the highest-energy neutrino detected by the KM3NeT neutrino telescope[10] 14 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) 125.1±0.2 GeV rest mass energy of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma[11] 105.7 MeV rest mass energy of a muon 0.511 MeV rest mass energy of an electron 13.6 eV energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond 1.65 to 3.26 eV range of photon energy ( h c λ ) {\displaystyle ({\tfrac {hc}{\lambda }})} of visible spectrum from red to violet 38 meV average kinetic energy, ⁠3/2⁠kBT, of one gas molecule at room temperature 230 μeV thermal energy, kBT, at the cosmic microwave background radiation temperature of ~2.7 kelvin

### Molar energy

One [mole](/source/Mole_(unit)) of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to the [Faraday constant](/source/Faraday_constant) (*F* ≈ 96485 C⋅mol−1), 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)](/source/Orders_of_magnitude_(energy))

## References

1. ^ [***a***](#cite_ref-physconst-eV_1-0) [***b***](#cite_ref-physconst-eV_1-1) [***c***](#cite_ref-physconst-eV_1-2) [***d***](#cite_ref-physconst-eV_1-3) ["2022 CODATA Value: electron volt"](https://physics.nist.gov/cgi-bin/cuu/Value?evj). *The NIST Reference on Constants, Units, and Uncertainty*. [NIST](/source/National_Institute_of_Standards_and_Technology). May 2024. Retrieved 2024-05-18.

1. **[^](#cite_ref-physconst-e_2-0)** ["2022 CODATA Value: elementary charge"](https://physics.nist.gov/cgi-bin/cuu/Value?e). *The NIST Reference on Constants, Units, and Uncertainty*. [NIST](/source/National_Institute_of_Standards_and_Technology). May 2024. Retrieved 2024-05-18.

1. **[^](#cite_ref-3)** Barrow, J. D. (1983). "Natural Units Before Planck". *Quarterly Journal of the Royal Astronomical Society*. **24**: 24. [Bibcode](/source/Bibcode_(identifier)):[1983QJRAS..24...24B](https://ui.adsabs.harvard.edu/abs/1983QJRAS..24...24B).

1. **[^](#cite_ref-4)** Gron Tudor Jones. ["Energy and momentum units in particle physics"](https://indico.cern.ch/event/318730/contributions/737345/attachments/613347/843809/gevtypeunitshst14.pdf) (PDF). *Indico.cern.ch*. Retrieved 5 June 2022.

1. **[^](#cite_ref-FNALunits_5-0)** ["Units in particle physics"](http://quarknet.fnal.gov/toolkits/ati/whatgevs.html). *Associate Teacher Institute Toolkit*. Fermilab. 22 March 2002. [Archived](https://web.archive.org/web/20110514152552/http://quarknet.fnal.gov/toolkits/ati/whatgevs.html) from the original on 14 May 2011. Retrieved 13 February 2011.

1. **[^](#cite_ref-physconst-heV_6-0)** ["2022 CODATA Value: Planck constant in eV/Hz"](https://physics.nist.gov/cgi-bin/cuu/Value?hev). *The NIST Reference on Constants, Units, and Uncertainty*. [NIST](/source/National_Institute_of_Standards_and_Technology). May 2024. Retrieved 2024-05-18.

1. **[^](#cite_ref-7)** Molinaro, Marco (9 January 2006). [""What is Light?""](https://web.archive.org/web/20071129084926id_/http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf) (PDF). *[University of California, Davis](/source/University_of_California%2C_Davis)*. IST 8A (Shedding Light on Life) - W06. Archived from [the original](http://cbst.ucdavis.edu/education/courses/winter-2006-IST8A/ist8a_2006_01_09light.pdf) (PDF) on 29 November 2007. Retrieved 7 February 2014.

1. **[^](#cite_ref-8)** Elert, Glenn. ["Electromagnetic Spectrum, The Physics Hypertextbook"](http://physics.info/em-spectrum/). hypertextbook.com. [Archived](https://web.archive.org/web/20160729235315/http://physics.info/em-spectrum/) from the original on 2016-07-29. Retrieved 2016-07-30.

1. **[^](#cite_ref-9)** ["Definition of frequency bands on"](http://www.vlf.it/frequency/bands.html). Vlf.it. [Archived](https://web.archive.org/web/20100430012219/http://www.vlf.it/frequency/bands.html) from the original on 2010-04-30. Retrieved 2010-10-16.

1. **[^](#cite_ref-10)** KM3NeT Collaboration (21 May 2014). ["A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino"](http://icecube.wisc.edu/news/view/227). *Nature*. **638** (8050): 376–382. [doi](/source/Doi_(identifier)):[10.1038/s41586-024-08543-1](https://doi.org/10.1038%2Fs41586-024-08543-1). [PMC](/source/PMC_(identifier)) [11821517](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11821517). [PMID](/source/PMID_(identifier)) [39939793](https://pubmed.ncbi.nlm.nih.gov/39939793).{{[cite journal](https://en.wikipedia.org/wiki/Template:Cite_journal)}}: CS1 maint: numeric names: authors list ([link](https://en.wikipedia.org/wiki/Category:CS1_maint:_numeric_names:_authors_list))

1. **[^](#cite_ref-11)** [ATLAS](/source/ATLAS_experiment); [CMS](/source/Compact_Muon_Solenoid) (26 March 2015). ["Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments"](https://doi.org/10.1103%2FPhysRevLett.114.191803). *Physical Review Letters*. **114** (19) 191803. [arXiv](/source/ArXiv_(identifier)):[1503.07589](https://arxiv.org/abs/1503.07589). [Bibcode](/source/Bibcode_(identifier)):[2015PhRvL.114s1803A](https://ui.adsabs.harvard.edu/abs/2015PhRvL.114s1803A). [doi](/source/Doi_(identifier)):[10.1103/PhysRevLett.114.191803](https://doi.org/10.1103%2FPhysRevLett.114.191803). [PMID](/source/PMID_(identifier)) [26024162](https://pubmed.ncbi.nlm.nih.gov/26024162).

## External links

- [Fundamental Physical Constants from NIST](https://physics.nist.gov/cuu/Constants/)

v t e SI units Base units ampere candela kelvin kilogram metre mole second Derived units with special names becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber See also International System of Units Historical definitions of the SI base units 2019 revision of the SI Metric prefixes Conversion of units System of units of measurement Category

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Adapted from the Wikipedia article [Electronvolt](https://en.wikipedia.org/wiki/Electronvolt) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Electronvolt?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.