In physics, an electronvolt (symbol eV), also called electron-volt, is a unit used to measure energy. It equals the energy gained by an electron when it moves through a voltage of one volt in a vacuum. When converted to joules (symbol J), 1 eV is equal to the charge of an electron in coulombs (symbol C). According to the 2019 revision of the International System of Units (SI), 1 eV is exactly equal to 1.602 176 634 × 10⁻¹⁹ joules. Historically, the electronvolt was created to help measure energy in early studies of particles moving through electric fields, as a charged particle gains energy equal to E = qV when 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. This equals 1 volt, which is 1 joule per coulomb (1 J/C), multiplied by the elementary charge, which is 1.602 176 634 × 10^-19 coulombs. Therefore, one electronvolt equals 1.602 176 634 × 10^-19 joules.
The electronvolt (eV) is a unit of energy but is not an SI unit. It is widely used in physics, especially in solid state, atomic, nuclear, and particle physics, as well as in high-energy astrophysics. It is often combined with SI prefixes such as milli- (10^-3), kilo- (10^3), mega- (10^6), giga- (10^9), tera- (10^12), peta- (10^15), exa- (10^18), zetta- (10^21), yotta- (10^24), ronna- (10^27), or quetta- (10^30). The corresponding symbols are 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, the symbol BeV is used. Here, the "B" stands for billion (10^9), making BeV equivalent to GeV. However, neither BeV nor GeV is an SI unit.
Relation to other physical properties and units
In physics, the electronvolt (eV) is used to measure energy. Other quantities in these fields are often measured using units based on the electronvolt. These units are created by combining the electronvolt with important numbers in physics.
Through the principle of mass-energy equivalence, the electronvolt can also represent a unit of mass. In particle physics, where energy and mass are often used interchangeably, mass is frequently expressed in units of eV/c², where c is the speed of light in a vacuum. Sometimes, mass is informally written in eV by assuming the speed of light is 1. The mass equivalent of 1 eV/c² is approximately 1.78 x 10⁻³⁶ kilograms.
For example, an electron and a positron, each with a mass of 0.511 MeV/c², can combine to produce 1.022 MeV of energy. A proton has a mass of 0.938 GeV/c². Most hadrons, a type of particle, have masses around 1 GeV/c², making GeV/c² a useful unit for measuring mass in particle physics.
The atomic mass constant (mₐ), which is one twelfth the mass of a carbon-12 atom, is close to the mass of a proton. To convert this mass into electronvolts, a specific formula is used.
To find a particle's momentum in units of eV/c, divide its kinetic energy in electronvolts by the speed of light. In natural units where the speed of light is treated as 1, the speed of light can be omitted, and momentum is expressed in eV.
The energy-momentum relationship, E² = p²c² + m₀²c⁴, becomes E² = p² + m₀² in natural units. This is a Pythagorean equation. When a particle with low rest mass is given high energy, its energy can be approximated as E ≈ p. In this case, energy measured in eV can be used to estimate momentum in eV/c.
The dimensions of energy and momentum are the same: T L M (time, length, mass). Dividing energy (like eV) by the speed of light (a velocity with dimensions T L) allows energy to be used to measure momentum.
For example, if an electron has a momentum of 1 GeV/c, its value in the MKS system is approximately 5.34 x 10⁻¹⁹ kg·m/s.
In particle physics, a system of natural units is used where the speed of light (c) and the reduced Planck constant (ħ) are both equal to 1. In this system, distances and times are expressed in inverse energy units. Energy and mass are measured in the same units, as shown by mass-energy equivalence. Particle scattering lengths are often described using inverse particle mass units.
Outside this system, the conversion between electronvolts, seconds, and nanometers involves specific constants. For instance, ħ (the reduced Planck constant) is approximately 6.58 x 10⁻¹⁶ eV·s.
The mean lifetime (τ) of an unstable particle in seconds can be calculated using its decay width (Γ) in eV via Γ = ħ / τ. For example, the B meson has a lifetime of 1.530(9) picoseconds and a decay width of 4.302(25) x 10⁻¹² eV.
Small differences in meson mass, which cause meson oscillations, are often expressed in inverse picoseconds for convenience.
Energy in electronvolts can be related to the wavelength of light. For example, 1 eV corresponds to a wavelength of approximately 806.55 mm⁻¹.
In plasma physics, the electronvolt is used to describe temperature. To convert eV to Kelvin, divide by the Boltzmann constant (kₐ). For example, 1 eV/kₐ is about 11,604.5 K. A typical magnetic confinement fusion plasma at 15 keV corresponds to 174 million Kelvin.
At room temperature (20°C), the product of the Boltzmann constant and temperature (kₐT) is approximately 0.025 eV.
The energy (E), frequency (ν), and wavelength (λ) of a photon are related by E = hν = hc/λ, where h is the Planck constant and c is the speed of light. This simplifies to E = 4.136 x 10⁻¹⁵ eV/Hz × ν or E = 1239.84 eV·nm / λ. A photon with a wavelength of 532 nm (green light) has an energy of about 2.33 eV. A photon with 1 eV of energy has a wavelength of approximately 1240 nm or a frequency of 241.8 THz.
Scattering experiments
In low-energy nuclear scattering experiments, scientists often use units like eVr and keVr to measure nuclear recoil energy. This helps tell apart nuclear recoil energy from electron equivalent recoil energy, which is measured using scintillation light and has units like eVee and keVee. For example, the output of a phototube is measured in phe/keVee (photoelectrons per keV of electron-equivalent energy). The connection between eV, eVr, and eVee depends on the material where the scattering occurs. This connection must be determined through experiments for each material.
Energy comparisons
One mole of particles, each given 1 eV of energy, has about 96.5 kJ of energy. This amount is connected to the Faraday constant (F ≈ 96,485 C/mol), which shows that the energy in joules for n moles of particles, each with energy E eV, is equal to E multiplied by F multiplied by n.