Electronvolt

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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. 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. ^[2]

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 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.

1 Using electronvolts to measure mass
2 Electronvolts and energy
3 Electronvolts and photon properties
4 Using electronvolts to measure time and distance
5 Electronvolts and temperature
6 Reference
7 See also
8 External links

[edit] 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/c², 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

See: Orders of magnitude (mass)

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).

[edit] Electronvolts and 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 a kinetic energy of about 1/40 eV. This corresponds to room temperature.

[edit] Electronvolts and photon properties

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

<math>E=h\nu=\frac{hc}{\lambda}=\frac{1240~\rm{nm~eV}}{\lambda}</math>

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

<math>E_{max} = \frac{1240~\rm{nm~eV}}{400~\rm{nm}} = 3.10~\rm{eV}</math>.

An electronvolt is also the energy of a infrared photon with a wavelength of approximately 1240nm. 10eV would correspond to UV of 124nm, etc.

[edit] Using electronvolts to measure time and distance

In particle physics, distances and times are sometimes expressed in inverse electronvolts via the conversion factors^[3]

<math>\hbar</math> = 6.582 118 89(26) x 10^-16 eV s
<math>\hbar c</math> = 197.326 960 2(77) eV nm

In these units, the mean lifetime <math>\tau</math> of an unstable particle can be reexpressed in terms of its decay width <math>\Gamma</math> (in eV) via <math>\Gamma = \hbar/\tau</math>. 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 <math>c\tau</math> = 462 <math>\mu</math>m.

[edit] 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 by using k_B, the Boltzmann constant:

<math>{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}</math>

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

[edit] Reference

^ NIST: Units outside the SI
^ Peter J. Mohr and Barry N. Taylor (January 2005). "CODATA recommended values of the fundamental physical constants: 2002" (PDF). Reviews of Modern Physics 77: 1–107. Retrieved on 2006-07-01. An in-depth discussion of how the CODATA constants were selected and determined.
^ K. Hagiwara et al, Review of Particle Physics, Phys. Rev. D66, 010001 (2002)