# Electronvolt

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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 from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value 1.602176634×10−19 J.

Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q gains an energy E = qV after passing through a voltage of V. Since q must be an integer multiple of the elementary charge e for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.

It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics, and high-energy astrophysics. 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). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (109) electronvolts; it is equivalent to the GeV.

Measurement Unit SI value of unit
Energy eV 1.602176634×10−19 J
Mass eV/c2 1.782662×10−36 kg
Momentum eV/c 5.344286×10−28 kg·m/s
Temperature eV/kB 1.160451812×104 K
Time ħ/eV 6.582119×10−16 s
Distance ħc/eV 1.97327×10−7 m

## Definition

An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the electron's elementary charge e, 1.602176634×10−19 C. Therefore, one electronvolt is equal to 1.602176634×10−19 J.

The electronvolt, as opposed to the volt, is not an SI unit. The electronvolt (eV) is a unit of energy whereas the volt (V) is the derived SI unit of electric potential. The SI unit for energy is the joule (J).

## 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/c2, where c is the speed of light in vacuum (from E = mc2). 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. The kilogram equivalent of 1 eV/c2 is:

$1\;{\text{eV}}/c^{2}={\frac {(1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\cdot 1\,{\text{V}}}{(2.99\ 792\ 458\times 10^{8}\;\mathrm {m/s} )^{2}}}=1.782\ 661\ 92\times 10^{-36}\;{\text{kg}}.$ For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the gigaelectronvolt a convenient unit of mass for particle physics:

1 GeV/c2 = 1.78266192×10−27 kg.

The unified atomic mass unit (u), almost exactly 1 gram divided by the Avogadro number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to electron volts, use the formula:

1 u = 931.4941 MeV/c2 = 0.9314941 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. In natural units where the fundamental velocity constant c is 1, the c may informally be omitted to express momentum as electronvolts. The energy–momentum relation in natural units, $E^{2}=p^{2}+m_{0}^{2}$ , is a Pythagorean equation that can be visualized as a right triangle where the total energy $E$ is the hypotenuse and the momentum $p$ and rest mass $m_{0}$ are the two legs.

$E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}$ in natural units (with $c=1$ )

$E^{2}=p^{2}+m_{0}^{2}$ is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as $E\simeq p$ in 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 T−1LM. The dimensions of energy units are T−2L2M. Dividing the units of energy (such as eV) by a fundamental constant (such as the speed of light) that has units of velocity (T−1L) facilitates the required conversion for using energy units to describe momentum.

For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS system of units can be achieved by:

$p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\cdot (1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\cdot (1\;{\text{V}})}{2.99\ 792\ 458\times 10^{8}\;{\text{m}}/{\text{s}}}}=5.344\ 286\times 10^{-19}\;{\text{kg}}\cdot {\text{m}}/{\text{s}}.$ ## 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:

$\hbar ={\frac {h}{2\pi }}=1.054\ 571\ 817\ 646\times 10^{-34}\ {\mbox{J s}}=6.582\ 119\ 569\ 509\times 10^{-16}\ {\mbox{eV s}}.$ 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 = 459.7 μm, or a decay width of (4.302±25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for 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:

${\frac {1\;{\text{eV}}}{hc}}={\frac {1.602\ 176\ 634\times 10^{-19}\;{\text{J}}}{(2.99\ 792\ 458\times 10^{10}\;{\text{cm}}/{\text{s}})\cdot (6.62\ 607\ 015\times 10^{-34}\;{\text{J}}\cdot {\text{s}})}}\thickapprox 8065.5439\;{\text{cm}}^{-1}.$ ## 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:

${1eV \over k_{\text{B}}}={1.602\ 176\ 634\times 10^{-19}{\text{ J}} \over 1.380\ 649\times 10^{-23}{\text{ J/K}}}=11\ 604.518\ 12{\text{ K}}.$ Where kB is the Boltzmann constant, K is Kelvin, J is Joules, eV is electronvolts.

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kilo-electronvolts), which is equal to 174 MK (million Kelvin).

As an approximation: kBT is about 0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 20 °C.

## Properties

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

$E=h\nu ={\frac {hc}{\lambda }}={\frac {(4.135\ 667\ 516\times 10^{-15}\,\mathrm {eV\,s} )(299\,792\,458\,\mathrm {m/s} )}{\lambda }}$ where h is the Planck constant, c is the speed of light. This reduces to

{\begin{aligned}E\mathrm {(eV)} &=4.135\ 667\ 516\,{\mbox{feVs}}\cdot \nu \ {\mbox{(PHz)}}\\[4pt]&={\frac {1\ 239.841\ 93\,{\mbox{eV}}\,{\mbox{nm}}}{\lambda \ {\mbox{(nm)}}}}.\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 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 Photon frequency vs. energy 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. 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
Energy Source
5.25×1032 eV total energy released from a 20 kt nuclear fission device
1.22×1028 eV the Planck energy
10 YeV (1×1025 eV) approximate grand unification energy
~624 EeV (6.24×1020 eV) energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/s6.24×1020 eV/s)
300 EeV (3×1020 eV = ~50 J) The first ultra-high-energy cosmic ray particle observed, the so-called Oh-My-God particle.
2 PeV two petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica
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)
1 TeV a trillion electronvolts, or 1.602×10−7 J, about the kinetic energy of a flying mosquito
172 GeV rest energy of top quark, the heaviest measured elementary particle
125.1±0.2 GeV 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
210 MeV average energy released in fission of one Pu-239 atom
200 MeV approximate average energy released in nuclear fission fission fragments of one U-235 atom.
105.7 MeV rest energy of a muon
17.6 MeV average energy released in the nuclear fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced
2 MeV approximate average energy released in a nuclear fission neutron released from one U-235 atom.
1.9 MeV rest energy of up quark, the lowest mass quark.
1 MeV (1.602×10−13 J) about twice the rest energy of an electron
1 to 10 keV approximate thermal temperature, $k_{B}T$ , in nuclear fusion systems, like the core of the sun, magnetically confined plasma, inertial confinement and nuclear weapons
13.6 eV the energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond
1.6 eV to 3.4 eV the photon energy of visible light
1.1 eV energy $E_{g}$ required to break a covalent bond in silicon
720 meV energy $E_{g}$ required to break a covalent bond in germanium
< 120 meV approximate rest energy of neutrinos (sum of 3 flavors)
25 meV thermal energy, $k_{B}T$ , at room temperature; one air molecule has an average kinetic energy 38 meV
230 μeV thermal energy, $k_{B}T$ , of the cosmic microwave background

### Per mole

One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F96485 C mol−1), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.