Electronvolt

The electronvolt, symbol eV, is a unit of energy defined as the kinetic energy gained by an electron when it is accelerated through an electric potential difference of one volt in vacuum. It is a non-SI unit accepted for use with the International System of Units (SI). One electronvolt equals exactly 1.602176634 × 10⁻¹⁹ joules. Its small size makes it convenient for describing the energies of individual particles and microscopic processes. (nist.gov)

Definition and physical meaning

The definition connects electrical work with particle energy. A particle carrying electric charge $q$, moving between initial and final electrostatic potentials, undergoes a change in potential energy:

If no other process removes energy, its kinetic-energy change is $\Delta K=-\Delta U$. For an electron, whose charge is $-e$, motion toward a potential one volt higher therefore produces an energy gain of one electronvolt. Here $e$ is the positive magnitude of the elementary charge, not the electron’s signed charge. The dimensional relation is $1\ \mathrm{C}\times1\ \mathrm{V}=1\ \mathrm{J}$, where C denotes the coulomb. (nist.gov)

The name does not restrict the unit to electrons or electrical acceleration. It can express any energy, including a photon’s energy or an atom’s ionization energy. A particle with charge magnitude $ze$, accelerated through a potential difference of magnitude $V$ in the energy-gaining direction, gains $zV$ electronvolts when $V$ is expressed numerically in volts. Thus, a doubly charged ion accelerated through 100 V gains 200 eV under ideal, loss-free conditions. These are consequences of the charge–potential definition. (nist.gov)

Exact value and SI status

Since the revised SI took effect on 20 May 2019, the elementary charge has had the exact value

Consequently, the electronvolt-to-joule conversion is exact, rather than an experimentally determined approximation. Earlier reference tables assigned it a measurement uncertainty because the elementary charge was then measured rather than fixed by definition. The change did not make the electronvolt an SI unit; it remains an accepted non-SI unit. (bipm.org)

The inverse conversion is

For calculations, an energy’s numerical value in electronvolts is multiplied by $1.602176634\times10^{-19}$ to obtain its value in joules. An exact conversion factor does not imply that an experimentally measured energy is exact: the measurement retains its own uncertainty. (pml.nist.gov)

Prefixes and notation

SI prefixes are commonly attached to eV to accommodate widely differing energy scales. The prefixes change the unit’s magnitude, not its physical meaning. (nist.gov)

Capitalization matters: meV and MeV differ by a factor of one billion. For example, the exact conversion gives $1\ \mathrm{MeV}=1.602176634\times10^{-13}\ \mathrm{J}$ and $1\ \mathrm{TeV}=1.602176634\times10^{-7}\ \mathrm{J}$. Large electronvolt values can therefore still represent small energies on a macroscopic scale. (bipm.org)

Atomic energies and radiation

Electronvolts provide a practical scale for discussing atomic excitation and ionization energies. Removing the electron from an isolated, ground-state hydrogen atom requires approximately 13.5984 eV. This describes an energy difference between physical states, not a voltage applied to the atom. NIST’s atomic spectroscopy databases use electronvolts as an ionization-energy unit. (physics.nist.gov)

In spectroscopy, a photon associated with a transition carries the energy difference between the states. Its energy is related to frequency $\nu$ and vacuum wavelength $\lambda$ by

where $h$ is the Planck constant and $c$ the speed of light. Using the SI constants gives the convenient conversion

A photon of wavelength 500 nm therefore has an energy of approximately 2.48 eV. Energy, frequency, and wavelength remain distinct quantities, connected through this physical relation. (pml.nist.gov)

Mass, momentum, and natural units

In particle physics, mass–energy equivalence connects a particle’s rest energy and mass through $E_0=mc^2$. Electronvolt-based mass units therefore include eV/$c^2$ and MeV/$c^2$. The electron’s rest energy is approximately 0.510998951 MeV, corresponding to a mass of approximately 0.510998951 MeV/$c^2$. These expressions describe different quantities with matching numerical values in the stated units. (atlas.cern)

Likewise, momentum can be expressed in eV/$c$. In natural units, commonly chosen so that $c=\hbar=1$, physicists may write energy, mass, and momentum using electronvolts without displaying the factors of $c$. This convention simplifies equations; it does not mean that energy, mass, and momentum have identical dimensions in SI. Restoring the appropriate constants is necessary when converting back to SI quantities. (atlas.cern)

Temperature and energy equivalents

A temperature can be associated with an energy scale through $k_{\mathrm B}T$, where $k_{\mathrm B}$ is the Boltzmann constant. From the exact SI values,

Thus, $k_{\mathrm B}T=1\ \mathrm{eV}$ corresponds to approximately 11,604.518 K, while 300 kelvin corresponds to $k_{\mathrm B}T\approx0.025852\ \mathrm{eV}$. This converts a temperature into its associated thermal-energy scale, not into the total energy of a system. The kelvin remains the SI unit of temperature, and the electronvolt remains a unit of energy. (bipm.org)