# Electronvolt

(Redirected from Electron volt)

The electronvolt (symbol eV, or, rarely and incorrectly, ev) is a unit of energy. It is the amount of kinetic energy gained by a single unbound electron when it passes through an electrostatic potential difference of one volt, in vacuum. In other words, it is equal to one volt (1 volt = 1 joule per coulomb) times the charge of a single electron (in coulombs). The one-word spelling is the modern recommendation[1] although the use of the earlier electron volt still exists.

One electronvolt is a very small amount of energy:

1 eV = 1.602 176 53(14)×10−19 J. (Source: CODATA 2002 recommended values)

The unit electronvolt is accepted (but not encouraged) for use with SI. It is widely used in solid state, atomic, nuclear, and particle physics, often with prefixes m, k, M, G or T.

## Using electronvolts to measure mass

Albert Einstein reasoned that energy is equivalent to mass, as famously expressed in the formula E=mc² (1 kg = 90 petajoules). It is thus common in particle physics, where mass and energy are often interchanged, to use eV/c² or even simply eV 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, making GeV a very convenient unit of mass for particle physics.

1 eV/c² = 1.783×10−36 kg
1 keV/c² = 1.783×10−33 kg
1 MeV/c² = 1.783×10−30 kg
1 GeV/c² = 1.783×10−27 kg
1 TeV/c² = 1.783×10−24 kg
1 PeV/c² = 1.783×10−21 kg
1 EeV/c² = 1.783×10−18 kg

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

## Electronvolts and kinetic energy

For comparison:

• 3.2×10−11 joule or 200 MeV - total energy released in nuclear fission of one U-235 atom (on average, it depends on the precise break up)
• 3.5×10−11 joule or 210 MeV - total energy released in fission of one Pu-239 atom (on average, it depends on the precise break up)
• Molecular bond energies are on the order of an electronvolt per molecule.
• The typical atmospheric molecule has an energy of about 1/40 eV. This corresponds to room temperature.
• $1eV = 1V \times q_e$ which indicates why the eV is fundamentally a unit of energy since $V \ \stackrel{\mathrm{def}}{=}\ {W\over q_0}$ or equivalently $V \ \stackrel{\mathrm{def}}{=}\ {\triangle E\over q_0}$ this is to dispel the common misconceptions of the eV as being a unit of potential or charge, which it is not.

## Electronvolts and 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, in part, by using kB, the Boltzmann constant.

${1 \mbox{ eV} \over k_B} = {1.60217653(14) \times 10^{-19} \mbox{J} \over 1.3806505(24) \times 10^{-23} \mbox{J/K}} = 11604.505(20) \mbox{ kelvins}$

For example, a typical magnetic confinement fusion plasma is 15 keV, or 174 megakelvins.

## Using electronvolts to measure time and distance

In particle physics, distances and times are sometimes expressed in inverse electronvolts via the conversion factors<ref>K. Hagiwara et al, Review of Particle Physics, Phys. Rev. D66, 010001 (2002)</ref>

• $\hbar$ = 6.582 118 89(26) x 10-16 eV s
• $\hbar c$ = 197.326 960 2(77) eV nm

In these units, the mean lifetime $\tau$ of an unstable particle can be reexpressed in terms of its decay width $\Gamma$ (in eV) via $\Gamma = \hbar/\tau$. For example, the B0 meson has a mean lifetime of 1.542(16) picoseconds, or a decay width of 4.269(44) x 10-4 eV, and its mean decay length is $c\tau$ = 462 $\mu$m.

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