# Electronvolt

meV, keV, MeV, GeV, TeV and PeV redirect here. For other uses, see MEV, KEV, GEV, TEV and PEV.

In physics, the electronvolt[1][2] (symbol eV; also written electron volt) is a unit of energy equal to approximately 160 zeptojoules (symbol zJ) or 1.6×1019 joules (symbol J). By definition, it is the amount of energy gained (or lost) by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, 1Lua error: Unmatched close-bracket at pattern character 67.) multiplied by the elementary charge (e, or 1.602176565(35)×1019 C). Therefore, one electron volt is equal to 1.602176565(35)×1019 Script error: No such module "convert"..[3] Historically, the electron volt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences because a particle with charge q has an energy E = qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the terminal bias in volts, one gets an energy in eV.

File:Light spectrum.svg
Photon frequency vs. energy per particle in electronvolts. The 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 rest mass.[4][5][6]

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. VF/ULF: Voice freq. Visible light UHF= Ultra high freq. SLF: Super low freq. NIR: Near Infrared VHF= Very high freq. ELF: Extremely low freq. Freq: Frequency

The electron volt is not an SI unit, and its definition is empirical (unlike the litre, the light year and other such non-SI units), thus its value in SI units must be obtained experimentally.[7] Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C2hα / μ0c0. It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). Thus meV stands for milli-electron volt.

In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion electron volts; it is equivalent to the GeV.

Measurement Unit SI value of unit
Energy eV 1.602176565(35)×1019Lua error: Unmatched close-bracket at pattern character 67.
Mass eV/c2 1.782662×1036Lua error: Unmatched close-bracket at pattern character 67.
Momentum eV/c 5.344286×1028Lua error: Unmatched close-bracket at pattern character 67.
Temperature eV/kB 11604.505(20)Lua error: Unmatched close-bracket at pattern character 67.
Time ħ/eV 6.582119×1016Lua error: Unmatched close-bracket at pattern character 67.
Distance ħc/eV 1.97327×107Lua error: Unmatched close-bracket at pattern character 67.

## Mass

By mass–energy equivalence, the electronvolt is also 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/c2, where c is the speed of light in vacuum (from E = mc2). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1.[8]

The mass equivalent of 1Lua error: Unmatched close-bracket at pattern character 67. is 1.783×1036Lua error: Unmatched close-bracket at pattern character 67..

For example, an electron and a positron, each with a mass of 0.511Lua error: Unmatched close-bracket at pattern character 67., can annihilate to yield 1.022Lua error: Unmatched close-bracket at pattern character 67. of energy. The proton has a mass of 0.938Lua error: Unmatched close-bracket at pattern character 67.. In general, the masses of all hadrons are of the order of 1Lua error: Unmatched close-bracket at pattern character 67., which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:

1Lua error: Unmatched close-bracket at pattern character 67. = 1.783×1027Lua error: Unmatched close-bracket at pattern character 67..

The atomic mass unit, 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:[3]

amu = 931.4941Lua error: Unmatched close-bracket at pattern character 67. = 0.9314941Lua error: Unmatched close-bracket at pattern character 67..

## Momentum

In high-energy physics, the electron volt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 1Lua error: Unmatched close-bracket at pattern character 67.). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.

The dimensions of momentum units are LMT−1. The dimensions of energy units are L2MT−2. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT−1), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c. Thus, dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.[9] [10]

The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 1Lua error: Unmatched close-bracket at pattern character 67., then the conversion to MKS can be achieved by:

$p = 1\; \text{GeV}/c = \frac{(1 \times 10^{9}) \cdot (1.60217646 \times 10^{-19} \; \text{C}) \cdot \text{V}}{(2.99792458 \times 10^{8}\; \text{m}/\text{s})} = 5.344286 \times 10^{-19}\; \text{kg}{\cdot}\text{m}/\text{s}.$

## Distance

In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced 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). In particular, particle scattering lengths 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:[3]

$\hbar = {{h}\over{2\pi}} = 1.054\ 571\ 726(47)\times 10^{-34}\ \mbox{J s} = 6.582\ 119\ 28(15)\times 10^{-16}\ \mbox{eV s}.$

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 Γ = ħ/τ. For example, the B0 meson has a lifetime of 1.530(9) picoseconds, mean decay length is = 459.7Lua error: Unmatched close-bracket at pattern character 67., or a decay width of (4.302±25)×104Lua error: Unmatched close-bracket at pattern character 67..

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

## Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to the Kelvin scale is defined by using kB, the Boltzmann constant:

${1 \over k_{\text{B}}} = {1.602\,176\,53(14) \times 10^{-19} \text{ J/eV} \over 1.380\,6505(24) \times 10^{-23} \text{ J/K}} = 11\,604.505(20) \text{ K/eV}.$

For example, a typical magnetic confinement fusion plasma is 15Lua error: Unmatched close-bracket at pattern character 67., or 170 megakelvin.

As an approximation: kBT is about 0.025Lua error: Unmatched close-bracket at pattern character 67. (≈ 290 K/11604 K/eV) at a temperature of 20Lua error: Unmatched close-bracket at pattern character 67..

## Properties

File:EV to nm vis.png
Graph of wavelength (nm) to energy (eV)

The energy E, frequency v, and wavelength λ of a photon are related by

$E=h\nu=\frac{hc}{\lambda}$ $=\frac{(4.13566\,7516\times 10^{-15}\,\mbox{eV}\,\mbox{s})(299\,792\,458\,\mbox{m/s})}{\lambda}$

where h is the Planck constant, c is the speed of light. This reduces to

$E\mbox{(eV)}=4.13566\,7516\,\mbox{feVs}\cdot\nu\ \mbox{(PHz)}$ $=\frac{1\,239.84193\,\mbox{eV}\,\mbox{nm}}{\lambda\ \mbox{(nm)}}.$[11]

A photon with a wavelength of 532Lua error: Unmatched close-bracket at pattern character 67. (green light) would have an energy of approximately 2.33Lua error: Unmatched close-bracket at pattern character 67.. Similarly, 1Lua error: Unmatched close-bracket at pattern character 67. would correspond to an infrared photon of wavelength 1240Lua error: Unmatched close-bracket at pattern character 67. or frequency 241.8Lua error: Unmatched close-bracket at pattern character 67..

## 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 light. For example, the yield of a 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

• 5.25×1032Lua error: Unmatched close-bracket at pattern character 67.: total energy released from a 20 kt nuclear fission device
• 1.22×1028Lua error: Unmatched close-bracket at pattern character 67.: the energy at the Planck scale
• 1×1025Lua error: Unmatched close-bracket at pattern character 67.: the approximate grand unification energy
• ~624 EeV (6.24×1020Lua error: Unmatched close-bracket at pattern character 67.): energy consumed by a single 100-watt light bulb in one second (100Lua error: Unmatched close-bracket at pattern character 67. = 100Lua error: Unmatched close-bracket at pattern character 67.6.24×1020Lua error: Unmatched close-bracket at pattern character 67.)
• 300 EeV (3×1020Lua error: Unmatched close-bracket at pattern character 67. = ~50 Script error: No such module "convert".):[12] the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed)
• 2Lua error: Unmatched close-bracket at pattern character 67.: two petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica[13]
• 14Lua error: Unmatched close-bracket at pattern character 67.: the designed proton collision energy at the Large Hadron Collider (which has operated at about half of this energy since 30 March 2010)
• 1Lua error: Unmatched close-bracket at pattern character 67.: a trillion electronvolts, or 1.602×107Lua error: Unmatched close-bracket at pattern character 67., about the kinetic energy of a flying mosquito[14]
• 125.1±0.2 GeV: the energy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma[15]
• 210Lua error: Unmatched close-bracket at pattern character 67.: the average energy released in fission of one Pu-239 atom
• 200Lua error: Unmatched close-bracket at pattern character 67.: the average energy released in nuclear fission of one U-235 atom
• 17.6Lua error: Unmatched close-bracket at pattern character 67.: the average energy released in the fusion of deuterium and tritium to form He-4; this is 0.41Lua error: Unmatched close-bracket at pattern character 67. per kilogram of product produced
• 1Lua error: Unmatched close-bracket at pattern character 67. (1.602×1013Lua error: Unmatched close-bracket at pattern character 67.): about twice the rest energy of an electron
• 13.6Lua error: Unmatched close-bracket at pattern character 67.: the energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1Lua error: Unmatched close-bracket at pattern character 67. to 10Lua error: Unmatched close-bracket at pattern character 67. per bond
• 1.6Lua error: Unmatched close-bracket at pattern character 67. to 3.4Lua error: Unmatched close-bracket at pattern character 67.: the photon energy of visible light
• 25Lua error: Unmatched close-bracket at pattern character 67.: the thermal energy kBT at room temperature; one air molecule has an average kinetic energy 38Lua error: Unmatched close-bracket at pattern character 67.
• 230Lua error: Unmatched close-bracket at pattern character 67.: the thermal energy kBT of the cosmic microwave background

## Notes and references

1. ^ IUPAC Gold Book, p. 75
2. ^ SI brochure, Sec. 4.1 Table 7
3. ^ a b c
4. ^ What is Light?UC Davis lecture slides
5. ^ Elert, Glenn. "The Electromagnetic Spectrum, The Physics Hypertextbook". Hypertextbook.com. Retrieved 2010-10-16.
6. ^ "Definition of frequency bands on". Vlf.it. Retrieved 2010-10-16.
7. ^
8. ^ Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24.
9. ^ "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Retrieved 13 February 2011.
10. ^ "Special Relativity". Virtual Visitor Center. SLAC. 15 June 2009. Retrieved 13 February 2011.
11. ^ "CODATA Value: Planck constant in eV s". Retrieved 30 March 2015.
12. ^ Open Questions in Physics. German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
13. ^
14. ^ Glossary - CMS Collaboration, CERN
15. ^ ATLAS; CMS (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". arXiv:1503.07589.