Electronvolt

In physics, the electron volt (symbol eV; also written electronvolt^[1][2]) is a unit of energy equal to approximately 1.602í—10^−19 J. By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb) multiplied by the electron charge (1 e, or 1.60217653(14)í—10^−19 C). Therefore, one electron volt is equal to 1.60217653(14)í—10^−19 J.^[3]

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

In chemistry, it is often useful to have the molar equivalent, that is the kinetic energy that would be gained by one 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 energy

Conversion factors:

• 1 eV = 1.602176487(40)í—10^−19 J (the conversion factor is numerically equal to the elementary charge expressed in coulombs).
• 1 eV is 96.485 MJ/kmol.^[5]

For comparison:

• >10⁸ TeV: The most-energetic known ultra-high-energy cosmic rays.
• 14 TeV: The collision energy of protons at the Large Hadron Collider.
• 1 TeV: A million million electronvolts, or 1.602í—10^−7 J, about the kinetic energy of a flying mosquito^[6]
• 210 MeV: The average energy released in fission of one Pu-239 atom.
• 200 MeV: The total energy released in nuclear fission of one U-235 atom (on average; depends on the precise break up).
• 17.6 MeV: The total energy released in the fusion of deuterium and tritium to form He-4 (also on average); this is 0.41 PJ per kilogram of product produced.
• 1 MeV: Or, 1.602í—10^−13 J, about twice the rest mass-energy of an electron.
• 13.6 eV: The energy required to ionize atomic hydrogen. Molecular bond energies are on the order of one 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.

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 momentum

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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 í— 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/c² = 0.93146 GeV/c²

1 MeV/c² = 1.074 í— 10^-3 amu

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:^[7]

ħ = 6.58211899±10í—10^−22 MeV s.

The above relations also allow expressing the mean lifetime Ï„ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/Ï„. For example, the B⁰ meson has a mean lifetime of 1.542(16) picoseconds, or a decay width of 4.269±44í—10^−4 eV, and its mean decay length is cÏ„ = 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

Energy of photons in the visible spectrum

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