# Electronvolt

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In physics, the **electron volt** (symbol **eV**; also written **electronvolt**^{[1]}^{[2]}) is a unit of energy equal to approximately Template:Val joules (symbol J). By definition, it is the amount of energy gained (or lost) by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, Template:Val) multiplied by the elementary charge (*e*, or Template:Val). Therefore, one electron volt is equal to **Template:Val**.^{[3]} Historically, the electron volt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences because a particle with charge *q* has an energy *E* = *qV* after passing through the potential *V*; if *q* is quoted in integer units of the elementary charge and the terminal bias in volts, one gets an energy in eV.

The electron volt is not an SI unit, and its definition is empirical (unlike the litre, the light year and other such non-SI units), thus its value in SI units must be obtained experimentally.^{[7]} Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 {{ safesubst:#invoke:Unsubst||$B=J/C}} Template:Sqrt. 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-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). Thus meV stands for milli-electron volt.

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.

Measurement | Unit | SI value of unit |
---|---|---|

Energy | eV | Template:Val |

Mass | eV/c^{2} |
Template:Val |

Momentum | eV/c |
Template:Val |

Temperature | eV/k_{B} |
Template:Val |

Time | ħ/eV |
Template:Val |

Distance | ħc/eV |
Template:Val |

## Contents

## Mass

By mass–energy equivalence, the electronvolt is also 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/*c*^{2}, where *c* is the speed of light in vacuum (from *E* = *mc*^{2}). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with *c* set to 1.^{[8]}

The mass equivalent of 1 eV is Template:Val.

For example, an electron and a positron, each with a mass of Template:Val, can annihilate to yield Template:Val of energy. The proton has a mass of Template:Val. In general, the masses of all hadrons are of the order of Template:Val, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:

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:^{[3]}

- 1 amu = Template:Val = Template:Val.

## Momentum

In high-energy physics, the electron volt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., Template:Val). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.

The dimensions of momentum units are Template:Dimanalysis. The dimensions of energy units are Template:Dimanalysis. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (Template:Dimanalysis), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum *c*. Thus, dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/*c*.^{[9]}
^{[10]}

The fundamental velocity constant *c* is often *dropped* from the units of momentum by way of defining units of length such that the value of *c* is unity. For example, if the momentum *p* of an electron is said to be Template:Val, then the conversion to MKS can be achieved by:

## 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: *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:^{[3]}

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 B^{0} meson has a lifetime of 1.530(9) picoseconds, mean decay length is *cτ* = Template:Val, or a decay width of Template:Val.

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

## Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to kelvin is defined by using *k*_{B}, the Boltzmann constant:

For example, a typical magnetic confinement fusion plasma is Template:Val, or 170 megakelvin.

As an approximation: *k*_{B}*T* is about Template:Val (≈ {{ safesubst:#invoke:Unsubst||$B=290 K/11604 K/eV}}) at a temperature of Template:Val.

## Properties

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

where *h* is the Planck constant, *c* is the speed of light. This reduces to

A photon with a wavelength of Template:Val (green light) would have an energy of approximately Template:Val. Similarly, Template:Val would correspond to an infrared photon of wavelength Template:Val, and so on.

## 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.

## Energy comparisons

- Template:Val: total energy released from a 20 kt nuclear fission device
- ~624 EeV (Template:Val): energy consumed by a single 100-watt light bulb in one second (Template:Val = Template:Val ≈ Template:Val)
- 300 EeV (Template:Val = ~Template:Val):
^{[11]}the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed) - Template:Val: one petaelectronvolt, the amount of energy measured in each of two different cosmic neutrino candidates detected by the IceCube neutrino telescope in Antarctica
^{[12]} - Template:Val: the designed proton collision energy at the Large Hadron Collider (which has operated at half of this energy Template:As of)
- Template:Val: a trillion electronvolts, or Template:Val, about the kinetic energy of a flying mosquito
^{[13]} - 125.3±0.6 GeV: the energy emitted by the decay of the Higgs boson, as measured by two separate detectors at the LHC to a certainty of 5 sigma
^{[14]} - Template:Val: the average energy released in fission of one Pu-239 atom
- Template:Val: the average energy released in nuclear fission of one U-235 atom
- Template:Val: the average energy released in the fusion of deuterium and tritium to form He-4; this is Template:Val per kilogram of product produced
- Template:Val (Template:Val): about twice the rest energy of an electron
- Template:Val: the energy required to ionize atomic hydrogen; molecular bond energies are on the order of Template:Val to Template:Val per bond
- Template:Val to Template:Val: the photon energy of visible light
- Template:Val: the thermal energy
*k*_{B}*T*at room temperature; one air molecule has an average kinetic energy Template:Val - Template:Val: the thermal energy
*k*_{B}*T*of the cosmic microwave background

## See also

## Notes and references

- ↑ IUPAC Gold Book, p. 75
- ↑
*SI brochure*, Sec. 4.1 Table 7 - ↑
^{3.0}^{3.1}^{3.2}Template:Cite web - ↑ What is Light? – UC Davis lecture slides
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24.
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Open Questions in Physics. German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
- ↑ Ice-bound hunter sees first hint of cosmic neutrinos New Scientist. 22:49 24 April 2013. by Anil Ananthaswamy.
- ↑ Glossary - CMS Collaboration, CERN
- ↑ Template:Cite web