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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.

1 eV = 1.60217653(14)×10−19 J. [1]

So an electron volt (electronvolt according to the NIST, IUPAC,[2] BIPM[3], and pretty much any professional, national, or international standards organization which has addressed the issue) is 1 volt (1 joule divided by 1 coulomb) multiplied by the electron charge (1.60217653(14)×10−19 coulomb).

The electron volt is now accepted within SI[4]. 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 a recorded lecture from 1961, Richard Feynman apologized to his students for using electron volts to measure energy instead of some multiple of the joule:

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.[5]

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

[edit] 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 gigaelectronvolt a very convenient unit of mass for particle physics.

1 GeV/c2 = 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 megaelectronvolts，use the formula:

1 amu = 931.46 MeV = .93146 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 volts"; it is equivalent to the GeV.

Since the megaelectronvolt 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

[edit] As a unit of energy

For comparison:

  • 210 MeV: average energy released in fission of one Pu-239 atom.
  • 200 MeV: total energy released in nuclear fission of one U-235 atom (on average; depends on the precise break up); this is 82 terajoules per kilogram, or twenty thousand tonnes of TNT equivalent per kilogram.
  • 17.6 MeV: total energy released in fusion of deuterium and tritium to form helium-4 (also on average); this is 0.41 PJ/kg of product produced.
  • 13.6 eV: energy required to ionize atomic hydrogen. Molecular bond energies are on the order of an eV per molecule.
  • 1/40 eV: the thermal energy at room temperature. A single molecule in the air has an average kinetic energy 3/80 eV.

Conversion factor:

  • 1 eV/amu is 96.5 MJ/kg

[edit] Relation to units of time and distance

In particle physics, a system of units in which the speed of light c and the reduced Planck constant \hbar are dimensionless and equal to unity is widely used: c=\hbar=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:[6]

  • \hbar = 6.582 118 99(16) x 10-16 eV s;
  • \hbar c = 197.326 9631(49) eV nm (or MeV fm).

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 \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)×10−4 eV, and its mean decay length is cτ = 462 µm.

[edit] 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 170 megakelvins.

[edit] 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.

[edit] 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. http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/other%20rmp%20articles/CODATA2005.pdf. Retrieved on 1 July 2006.  An in-depth discussion of how the CODATA constants were selected and determined.
  2. ^ IUPAC Gold Book, p. 75
  3. ^ SI brochure, Sec. 4.1 Table 7
  4. ^ "Non-SI units whose values in SI units must be obtained experimentally". International Bureau of Weights and Measures. Retrieved on 2008-09-10.
  5. ^ Transcript of part of a 1961 lecture by Richard Feynman
  6. ^ C. Amsler et al., Review of Particle Physics, Phys. Lett. B667, 1 (2008)

[edit] See also

[edit] External links


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