electron volt

In physics, the electron volt (symbol eV; also written electronvolt according to the NIST, IUPAC,^[1] and BIPM^[2]) is a unit of energy. By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electrostatic potential difference of one volt. Thus it is 1 volt (1 joule divided by 1 coulomb) multiplied by the electron charge, 1.60217653(14)×10⁻¹⁹ coulomb. One electron volt is equal to 1.60217653(14)×10⁻¹⁹ joules.^[3]

The electron volt is not an SI unit and its value must be obtained experimentally.^[4] It is the most common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with SI prefixes milli, kilo, mega, giga, tera, or peta (meV, keV, MeV, GeV, TeV and PeV respectively).

In chemistry, it is often useful to have the molar equivalent, that is the kinetic energy that would be gained by a mole of electrons passing through a potential difference of one volt. This is equal to 96.48538(2) kJ/mol. Atomic properties like the ionization energy are often quoted in electron volts.

As a unit of mass

By mass-energy equivalence, the electron volt is also a unit of mass. It is common in particle physics, where mass and energy are often interchanged, to use eV/c², where c is the speed of light in a vacuum (from E = mc²). Even more common is to use a system of natural units and simply use eV, with c set to 1 as a unit of mass.

For example, an electron and a positron, each with a mass of 0.511 MeV/c², can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c², making a gigaelectronvolt a very convenient unit of mass for particle physics.

1 GeV/c² = 1.783 × 10⁻²⁷ kg

The atomic mass unit, 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:

1 amu = 931.46 MeV = 0.93146 GeV

1 MeV = 1.074 × 10^–3 amu

In some older documents, and in the name Bevatron, the symbol "BeV" is used, which stands for "billion electron volts"; it is equivalent to the GeV.

As a unit of energy

Conversion factors:

• 1 eV = 1.602176487(40)×10⁻¹⁹ joules (the conversion factor is numerically equal to the elementary charge expressed in Coulombs).
• 1 eV/amu is 96.5 MJ/kg.

For comparison:

• >10²⁰ eV: highest energy cosmic ray Ultra-high-energy cosmic ray.
• 14 TeV: the combined energy of future protons before collision in the Large Hadron Collider.
• 210 MeV: average energy released in fission of one Pu-239 atom.
• 200 MeV: total energy released in nuclear fission of one U-235 atom (on average; depends on the precise break up); this is 82 terajoules per kilogram, or twenty thousand tonnes of TNT equivalent per kilogram.
• 17.6 MeV: total energy released in fusion of deuterium and tritium to form helium-4 (also on average); this is 0.41 petajoule per kilogram of product produced, which is equivalent to the energy released in a 100-kiloton explosion of TNT.
• 13.6 eV: energy required to ionize atomic hydrogen. Molecular bond energies are on the order of an eV per molecule.
• 1/40 eV: the thermal energy at room temperature. A single molecule in the air has an average kinetic energy 3/80 eV.

Relation to units of time and distance

In particle physics, a system of units in which the speed of light in a 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 in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:^[5]

ħ = 6.58211899±10×10⁻²² MeV 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 mean lifetime of 1.542(16) picoseconds, or a decay width of 4.269±44×10⁻⁴ eV, and its mean decay length is cτ = 462 µm.

As a unit of temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to kelvins (symbol: uppercase K) is defined by using k_B, the Boltzmann constant:

For example, a typical magnetic confinement fusion plasma is 15 keV, or 170 megakelvins.

Photon properties

The energy E, frequency ν, and wavelength λ of a photon are related by

where h is Planck's constant, c is the speed of light. For quick calculations, this reduces to

A stream of photons with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to a stream of infrared photons of wavelength 1240 nm, and so on.

1 eV = 8065.5447 cm^-1

In 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.

See also

• Orders of magnitude (energy)

References

External links

• BIPM's definition of the electronvolt
• http://physics.nist.gov/cuu/Constants physical constants reference; CODATA data