Historically, the electronvolt 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.
Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C√2hα / 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). 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.
An electronvolt is the amount of energy gained (or lost) by the charge of a single electron moving across an electric potential difference of one volt. Hence, it has a value of one volt, 7000100000000000000♠1 J/C, multiplied by the electron's elementary chargee, 6981160217662079999♠1.6021766208(98)×10−19 C. Therefore, one electronvolt is equal to 6981160217662079999♠1.6021766208(98)×10−19 J. The electronvolt is not an SI unit, and its definition is empirical (unlike the litre, the light-year and other such non-SI units), where its value in SI units must be obtained experimentally.
For example, an electron and a positron, each with a mass of 6999511000000000000♠0.511 MeV/c2, can annihilate to yield 6987163742436971400♠1.022 MeV of energy. The proton has a mass of 6999938000000000000♠0.938 GeV/c2. In general, the masses of all hadrons are of the order of 7000100000000000000♠1 GeV/c2, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:
7000100000000000000♠1 GeV/c2 = 6973178300000000000♠1.783×10−27 kg.
1 u = 7002931494100000000♠931.4941 MeV/c2 = 6999931494100000000♠0.9314941 GeV/c2.
In high-energy physics, the electronvolt 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., 6981160217648700000♠1 eV). 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.
By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.
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 6990160217648700000♠1 GeV, then the conversion to MKS can be achieved by:
In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constantħ 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:
The above relations also allow expressing the mean lifetimeτ of an unstable particle (in seconds) in terms of its decay widthΓ (in eV) via Γ = ħ/τ. For example, the B0 meson has a lifetime of 1.530(9) picoseconds, mean decay length is cτ = 6996459699999999999♠459.7 μm, or a decay width of 6977689256324707400♠(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: 1 eV = 8065.544005(49) cm−1.
A photon with a wavelength of 6993532000000000000♠532 nm (green light) would have an energy of approximately 6981373307121471000♠2.33 eV. Similarly, 6981160217648700000♠1 eV would correspond to an infrared photon of wavelength 6994124000000000000♠1240 nm or frequency 7014241800000000000♠241.8 THz.
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.
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
~624 EeV (7001999758127888000♠6.24×1020 eV): energy consumed by a single 100-watt light bulb in one second (7002100000000000000♠100 W = 7002100000000000000♠100 J/s ≈ 7001999758127888000♠6.24×1020 eV/s)
300 EeV (7001480652946100000♠3×1020 eV = ~7001500000000000000♠50 J): the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed)
6996320435297400000♠2 PeV: two petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica
6994224304708180000♠14 TeV: the designed proton collision energy at the Large Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
6993160217648700000♠1 TeV: a trillion electronvolts, or 6993160200000000000♠1.602×10−7 J, about the kinetic energy of a flying mosquito
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
6989336457062270000♠210 MeV: the average energy released in fission of one Pu-239 atom
One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F ≈ 7004964850000000000♠96485 C mol−1) where the energy in joules of N moles of particles each with energy X eV is X·F·N.