# Electronvolt

## Overview

The electronvolt (symbol eV) is a unit of energy. It is the amount of energy equivalent to that gained by a single unbound electron when it is accelerated through an electrostatic potential difference of one volt, in vacuo. In other words, it is equal to one volt (1 volt = 1 joule per coulomb) times the (unsigned) charge of a single electron. The one-word spelling is the modern recommendation, 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.  (or approximately 0.160 aJ)

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. In a recorded lecture from 1961 Richard Feynman apologized to his students for this failure by atomic physicists to use the appropriate SI unit (which would be the attojoule):

"A single atom is such a small thing that to talk about its energy in joules would be inconvenient. But instead of taking a definite unit in the same system, like 10−20 J, [physicists] have unfortunately chosen, arbitrarily, a funny unit called an electronvolt (eV) ... I am sorry that we do that, but that's the way it is for the physicists." 

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 quantity is equal to 96.48538(2) kJ/mol. Ionization energies and other atomic properties are often quoted in electronvolts, especially in older texts.

## As a measurement of mass

Albert Einstein reasoned that energy is equivalent to mass, as famously expressed in the mass-energy equivalence formula E = mc² (1.0000 kg = 89.876 PJ). 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/c², making GeV (gigaelectronvolt) 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.

Since MeV as a unit often are used in nuclear energy equations, for example as in the stellar nuclear fusion process of carbon burning, among others the equation

 12C + 12C → 20Ne + 4He + 4.617 MeV

conversion of atomic mass unit u to MeV is often performed by the formula:

1 u = 931.4 MeV

and inversely

1 MeV = 1.074·10-3 u

## Energy

For comparison:

• 3.2×10−11 joule or 200 MeV - total energy released in nuclear fission of one U-235 atom (on average; depends on the precise break up); this is 82 TJ/kg = 20 kt TNT / kg
• 3.5×10−11 joule or 210 MeV - total energy released in fission of one Pu-239 atom (also on average)
• Molecular bond energies are on the order of an electronvolt per molecule.
• The typical atmospheric molecule has a kinetic energy of about 1/40 eV. This corresponds to room temperature.

Conversion factor:

• 1 eV per amu is 96.5 MJ/kg

## Photon properties

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

$E=hf={\frac {hc}{\lambda }}={\frac {1240~{\rm {nm~eV}}}{\lambda }}$ where h is Planck's constant and c is the speed of light. For example, the spectrum of visible light consists of wavelengths ranging from 400 nm to 700 nm. Photons of visible light therefore have energies ranging from

$E_{min}={\frac {1240~{\rm {nm~eV}}}{700~{\rm {nm}}}}=1.77~{\rm {eV}}$ to

$E_{max}={\frac {1240~{\rm {nm~eV}}}{400~{\rm {nm}}}}=3.10~{\rm {eV}}$ .

An electronvolt is also the energy of an infrared photon with a wavelength of approximately 1240 nm. Similarly, 10eV would correspond to ultraviolet of wavelength 124 nm, and so on.

## As a measurement for time and distance

In particle physics, distances and times are sometimes expressed in inverse electronvolts via the conversion factors

• $\hbar$ = 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.

## 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 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. 