Electronvolt

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 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 equal 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

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.

Definition and use
An electronvolt is the amount of energy gained or lost by a single electron when it moves through an electric potential difference of one volt. Hence, it has a value of one volt, which is $1 J/C$, multiplied by the elementary charge Therefore, one electronvolt is equal to

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, atomic, nuclear and particle physics, and high-energy astrophysics. It is commonly used with SI prefixes milli-(10-3), kilo-(103), mega-(106), giga-(109), tera-(1012), peta-(1015) or exa-(1018). Giving meV, keV, MeV, GeV, TeV, PeV and EeV respectively. 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
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/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 $1.783 kg$ is:

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

For example, an electron and a positron, each with a mass of $5.344 kg·m/s$, can annihilate to yield $11,604.518 K$ of energy. A proton has a mass of $6.582 s$. In general, the masses of all hadrons are of the order of $1.973 m$, which makes the GeV/c2 a convenient unit of mass for particle physics:

The atomic mass constant (mu), 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:

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 in which the fundamental velocity constant c is numerically 1, the c may be informally be omitted to express momentum using the unit electronvolt. The energy–momentum relation $$E^2 = p^2 c^2 + m_0^2 c^4$$ 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 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. The dimension of energy is. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity facilitates the required conversion for using a unit of energy to quantify momentum.

For example, if the momentum p of an electron is $1 eV/c2$, then the conversion to MKS system of units can be achieved by: $$p = 1\; \text{GeV}/c = \frac{(1 \times 10^9) \times (1.602\ 176\ 634 \times 10^{-19} \; \text{C}) \times (1 \; \text{V})}{2.99\ 792\ 458 \times 10^8\; \text{m}/\text{s}} = 5.344\ 286 \times 10^{-19}\; \text{kg} {\cdot} \text{m}/\text{s}.$$

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 using a unit of inverse particle mass.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following: $$\hbar = 1.054\ 571\ 817\ 646\times 10^{-34}\ \mathrm{J{\cdot}s} = 6.582\ 119\ 569\ 509\times 10^{-16}\ \mathrm{eV{\cdot}s}.$$

The above relations also allow expressing the mean lifetime 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 cτ = $0.511 MeV/c2$, or a decay width of $1.022 MeV$.

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

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

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is $0.938 GeV/c2$ (kiloelectronvolt), which is equal to 174 MK (megakelvin).

As an approximation: kBT is about $1 GeV/c2$ (≈ $1 GeV/c2$) at a temperature of $1.783 kg$.

Wavelength
The energy E, frequency ν, and wavelength λ of a photon are related by $$E = h\nu = \frac{hc}{\lambda} = \frac{\mathrm{4.135\ 667\ 696 \times 10^{-15}\;eV/Hz} \times \mathrm{299\, 792\, 458\;m/s}}{\lambda}$$ where h is the Planck constant, c is the speed of light. This reduces to $$\begin{align} E &= 4.135\ 667\ 696 \times 10^{-15}\;\mathrm{eV/Hz}\times\nu \\[4pt] &=\frac{1\ 239.841\ 98\;\mathrm{eV{\cdot}nm}}{\lambda}. \end{align}$$ A photon with a wavelength of $931.494 MeV/c2$ (green light) would have an energy of approximately $0.931 GeV/c2$. Similarly, $1 GeV/c$ would correspond to an infrared photon of wavelength $459.7 μm$ or frequency $4.302 eV$.

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
Light spectrum.svg 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.

Molar energy
One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F &asymp; $15 keV$), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.