Electron volt

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In physics, the electron volt (eV) is a unit of energy. By definition, it is equal to the amount of energy gained by a single unbound electron when it accelerates through an electrostatic potential difference of one volt. In SI units, it is the number which measures the charge of the electron with the unit changed from C to J.

1 eV = 1.602 176 53(14)×10−19 J.

So an electron volt (electronvolt according to the NIST) is 1 volt ( 1 joule / 1 coulomb ) multiplied by the electron charge ( 1.602 176 53(14)×10−19 coulomb ).

The electron volt is now accepted within SI. It is the most common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics, often with SI prefixes milli, kilo, mega, giga, tera, or peta (meV, KeV, MeV, GeV, TeV and PeV respectively).

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 is equal to 96.48538(2) kJ/mol. Atomic properties like the ionization energy are often quoted in electron volts.

Contents

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, or more commonly simply 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, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV, making a GeV a very convenient unit of mass for particle physics.

1 GeV = 1.783×10−27 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 MeV,use the formula:

1 amu = 931.4 MeV = .9314 GeV
1 MeV = 1.074·10-3 amu

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 is often 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

As a unit of energy

For comparison:

Conversion factor:

Relation to units of time and distance

\hbar

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:

\Gamma = \hbar/\tau

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 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.

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}}{\lambda}\rm~eV

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_\mbox{min} = \frac{1240~\rm{nm}}{700~\rm{nm}}\rm~eV= 1.77~\rm{eV}

to

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

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

References

  1. ^ 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. doi:10.1103/RevModPhys.77.1. Retrieved on 2006-07-01.  An in-depth discussion of how the CODATA constants were selected and determined.
  2. ^ "Non-SI units whose values in SI units must be obtained experimentally". International Bureau of Weights and Measures. Retrieved on 2008-09-10.
  3. ^ CERN: The Large Hadron Collider in general
  4. ^ C. Amsler et al., Review of Particle Physics, Phys. Lett. B667, 1 (2008)