Electronvolt
In physics, the electron volt (symbol eV; also written electronvolt^{[1]}^{[2]}) is a unit of energy equal to approximately ×10^{−19} 1.6joule (symbol J). By definition, it is the amount of energy gained (or lost) by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, ) multiplied by the 1 J/Celementary charge (e, or 176565(35)×10^{−19} C). Therefore, one electron volt is equal to 1.602176565(35)×10^{−19} J.^{[3]} Historically, the electron volt was devised as a standard unit of measure through its usefulness in 1.602electrostatic particle accelerator sciences because a particle with charge q has an energy E = qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the terminal bias in volts, one gets an energy in eV.
The electron volt is not an SI unit, and thus its value in SI units must be obtained experimentally.^{[4]} Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ_{0}c_{0}. It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the SI prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). Thus meV stands for milli-electron volt.
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.
Measurement | Unit | SI value of unit |
---|---|---|
Energy | eV | 176565(35)×10^{−19} J 1.602 |
Mass | eV/c^{2} | ×10^{−36} kg 1.783 |
Momentum | eV/c | 286×10^{−28} kg⋅m/s 5.344 |
Temperature | eV/k_{B} | 604.505(20) K 11 |
Time | ħ/eV | |
Distance | ħc/eV |
Contents
Mass
By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where mass and energy are often interchanged, to express mass in units of eV/c^{2}, where c is the speed of light in vacuum (from E = mc^{2}). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1.^{[citation needed]}
The Mass equivalent of 1 eV is ×10^{−36} kg. 1.783
For example, an electron and a positron, each with a mass of , can 0.511 MeV/c^{2}annihilate to yield of energy. The 1.022 MeVproton has a mass of . In general, the masses of all 0.938 GeV/c^{2}hadrons are of the order of , which makes the 1 GeV/c^{2}GeV (gigaelectronvolt) a convenient unit of mass for particle physics:
- = 1 GeV/c^{2}×10^{−27} kg 1.783
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 ^{[3]}:
- 1 amu = = 931.4941 MeV/c^{2}4941 GeV/c^{2} 0.931
Momentum
In high-energy physics, the electron volt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., ). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle. 1 eV
The dimensions of momentum units are LT^{−1}M. The dimensions of energy units are L^{2}T^{−2}M. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT^{−1}), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c. Thus, dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.^{[5]} ^{[6]}
The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be , then the conversion to MKS can be achieved by: 1 GeV
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle p = 1\; \text{GeV}/c = \frac{(1 \times 10^{9}) \cdot (1.60217646 \times 10^{-19} \; \text{C}) \cdot \text{V}}{(2.99792458 \times 10^{8}\; \text{m}/\text{s})} = 5.344286 \times 10^{-19}\; \text{kg}{\cdot}\text{m}/\text{s} }
Distance
In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 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:^{[3]}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \hbar = {{h}\over{2\pi}} = 1.054\ 571\ 726(47)\times 10^{-34}\ \mbox{J s} = 6.582\ 119\ 28(15)\times 10^{-16}\ \mbox{eV s}.}
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 Γ = ħ/τ. For example, the B^{0} meson has a lifetime of 1.530(9) picoseconds, mean decay length is cτ = 459.7 μm, or a decay width of ±25)×10^{−4} eV. (4.302
Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.
Temperature
In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to kelvin is defined by using k_{B}, the Boltzmann constant:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle {1 \over k_{\text{B}}} = {1.602\,176\,53(14) \times 10^{-19} \text{ J/eV} \over 1.380\,6505(24) \times 10^{-23} \text{ J/K}} = 11\,604.505(20) \text{ K/eV}.}
For example, a typical magnetic confinement fusion plasma is , or 170 megakelvin. 15 keV
As an approximation: k_{B}T is about (≈ 0.025 eV290 K/11604 K/eV) at a temperature of . 20 °C
Properties
The energy E, frequency v, and wavelength λ of a photon are related by
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle E=h\nu=\frac{hc}{\lambda}=\frac{(4.135 667 33\times 10^{-15}\,\mbox{eV}\,\mbox{s})(299\,792\,458\,\mbox{m/s})}{\lambda}}
where h is the Planck constant, c is the speed of light. This reduces to
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle E\mbox{(eV)}=\frac{1239.84187\,\mbox{eV}\,\mbox{nm}}{\lambda\ \mbox{(nm)}}}
A photon with a wavelength of (green light) would have an energy of approximately 532 nm. Similarly, 2.33 eV would correspond to an infrared photon of wavelength 1 eV, and so on. 1240 nm
Scattering experiments
In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.
Energy comparisons
- ×10^{32} eV: total energy released from a 20 5.25kt nuclear fission device
- ~624 EeV (×10^{20} eV): energy consumed by a single 100-watt light bulb in one second ( 6.24 = 100 W = ~ 100 J/s×10^{20} eV/s) 6.24
- 300 EeV (×10^{20} eV = ~ 3J):^{[7]} the so-called 50 Oh-My-God particle (the most energetic cosmic ray particle ever observed)
- : one petaelectronvolt, the amount of energy measured in each of two different cosmic neutrino candidates detected by the IceCube neutrino telescope in Antarctica^{[8]} 1 PeV
- : the designed proton collision energy at the 14 TeVLarge Hadron Collider (which has operated at half of this energy since 30 March 2010^{[update]})
- : a trillion electronvolts, or 1 TeV×10^{−7} J, about the kinetic energy of a flying 1.602mosquito^{[9]}
- 125.3±0.6 GeV: the energy emitted by the decay of the Higgs Boson, as measured by two separate detectors at the LHC to a certainty of 5 sigma^{[10]}
- : the average energy released in fission of one 210 MeVPu-239 atom
- : the average energy released in 200 MeVnuclear fission of one U-235 atom
- : the average energy released in the 17.6 MeVfusion of deuterium and tritium to form He-4; this is per kilogram of product produced 0.41 PJ
- ( 1 MeV×10^{−13} J): about twice the 1.602rest energy of an electron
- : the energy required to 13.6 eVionize atomic hydrogen; molecular bond energies are on the order of to 1 eV per bond 10 eV
- to 1.6 eV: the 3.4 eVphoton energy of visible light
- : the 25 meVthermal energy k_{B}T at room temperature; one air molecule has an average kinetic energy 38 meV
- : the 230 µeVthermal energy k_{B}T of the cosmic microwave background
See also
Notes and references
- ↑ IUPAC Gold Book, p. 75
- ↑ SI brochure, Sec. 4.1 Table 7
- ↑ ^{3.0} ^{3.1} ^{3.2} http://physics.nist.gov/constants
- ↑ http://physics.nist.gov/cuu/Units/outside.html
- ↑ "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Retrieved 13 February 2011.
- ↑ "Special Relativity". Virtual Visitor Center. SLAC. 15 June 2009. Retrieved 13 February 2011.
- ↑ Open Questions in Physics. German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
- ↑ Ice-bound hunter sees first hint of cosmic neutrinos New Scientist. 22:49 24 April 2013. by Anil Ananthaswamy.
- ↑ CERN - Glossary
- ↑ http://press.web.cern.ch/press/PressReleases/Releases2012/PR17.12E.html
External links
- BIPM's definition of the electronvolt
- http://physics.nist.gov/cuu/Constants physical constants reference; CODATA data