In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from it; products 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 Mass–energy equivalence|). 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 is: 1\; \text{eV}/c^2 = \frac{1.602\ 176\ 634 \times 10^{-19} \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}}{(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 , can
annihilate to yield of energy. A
proton has a mass of . In general, the masses of all
hadrons are of the order of , 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 informally be omitted to express momentum using the unit electronvolt. 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. 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 , then the conversion to
MKS system of units can be achieved by: \begin{align} p = 1\; \text{GeV}/c &= \frac{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}} \\[1ex] &= 5.344\ 286 \times 10^{-19}\; \text{kg} {\cdot} \text{m}/\text{s}. \end{align}
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: . 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 . For example, the
meson has a lifetime of 1.530(9)
picoseconds, mean decay length is , or a decay width of . 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}}{(6.62\ 607\ 015 \times 10^{-34}\; \text{J} {\cdot} \text{s}) \times (2.99\ 792\ 458 \times 10^{11}\; \text{mm}/\text{s})} \thickapprox 806.55439 \; \text{mm}^{-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 (kiloelectronvolt), which corresponds to 174 MK (megakelvin). As an approximation: at a temperature of ,
kB
T is about (≈ ).
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 (green light) would have an energy of approximately . Similarly, would correspond to an infrared photon of wavelength or frequency . == Scattering experiments ==