Electronvolt
In physics, the electronvolt^{[1]}^{[2]} (symbol eV, also written electron-volt and electron volt) is a unit of energy equal to approximately ×10^{−19} 1.6joules (symbol J) in SI units. By definition, it is the amount of energy gained (or lost) by the charge of a single electron moving across an electric potential difference of one volt. Hence, it has a value of one volt, J/C, multiplied by the electron's 1elementary charge e, 1766208(98)×10^{−19} C^{[3]}. Therefore, one electronvolt is equal to 1.6021766208(98)×10^{−19} J 1.602.^{[4]} The electronvolt is not a SI unit, and its definition is empirical (unlike the litre, the light-year and other such non-SI units), where its value in SI units must be obtained experimentally.^{[5]}
Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic 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.
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 metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (10^{9}) electronvolts; it is equivalent to the GeV.
Measurement | Unit | SI value of unit |
---|---|---|
Energy | eV | 1766208(98)×10^{−19} J 1.602 |
Mass | eV/c^{2} | 662×10^{−36} kg 1.782 |
Momentum | eV/c | 286×10^{−28} kg⋅m/s 5.344 |
Temperature | eV/k_{B} | 4505(20)×10^{4} K 1.160 |
Time | ħ/eV | 119×10^{−16} s 6.582 |
Distance | ħc/eV | 27×10^{−7} m 1.973 |
Mass
By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where units of 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.^{[6]} The mass equivalent of eV/c^{2} is 1
For example, an electron and a positron, each with a mass of MeV/c^{2}, can 0.511annihilate to yield MeV of energy. The 1.022proton has a mass of GeV/c^{2}. In general, the masses of all 0.938hadrons are of the order of GeV/c^{2}, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics: 1
- GeV/c^{2} 1 = ×10^{−27} kg. 1.783
The unified atomic mass unit (u), 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 u = MeV/c^{2} 931.4941 = 4941 GeV/c^{2}. 0.931
Momentum
In high-energy physics, the electronvolt 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., eV). 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
The dimensions of momentum units are LMT^{−1}. The dimensions of energy units are L^{2}MT^{−2}. 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.
By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.^{[7]}
^{[8]}
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 GeV, then the conversion to MKS can be achieved by: 1
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:
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 = μm 459.7, 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.
Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy: 1 eV = 8065.544005(49) cm^{−1}.
Temperature
In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to the Kelvin scale is defined by using k_{B}, the Boltzmann constant:
For example, a typical magnetic confinement fusion plasma is keV, or 170 15 MK.
As an approximation: k_{B}T is about eV (≈ 0.025290 K/11604 K/eV) at a temperature of °C. 20
Properties
The energy E, frequency v, and wavelength λ of a photon are related by
where h is the Planck constant, c is the speed of light. This reduces to
- ^{[9]}
A photon with a wavelength of nm (green light) would have an energy of approximately 532 eV. Similarly, 2.33 eV would correspond to an infrared photon of wavelength 1 nm or frequency 1240 THz. 241.8
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 5.25 kt nuclear fission device
- ×10^{28} eV: the 1.22Planck energy
- 10 YeV (×10^{25} eV): the approximate 1grand unification energy
- ~624 EeV (×10^{20} eV): energy consumed by a single 100-watt light bulb in one second ( 6.24 W = 100 J/s ≈ 100×10^{20} eV/s) 6.24
- 300 EeV (×10^{20} eV = ~ 3 J):^{[13]} the so-called 50Oh-My-God particle (the most energetic cosmic ray particle ever observed)
- PeV: two petaelectronvolts, the most high-energetic neutrino detected by the 2IceCube neutrino telescope in Antarctica^{[14]}
- TeV: the designed proton collision energy at the 14Large Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
- TeV: a trillion electronvolts, or 1×10^{−7} J, about the kinetic energy of a flying 1.602mosquito^{[15]}
- 125.1±0.2 GeV: the energy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma^{[16]}
- MeV: the average energy released in fission of one 210Pu-239 atom
- MeV: the average energy released in 200nuclear fission of one U-235 atom
- MeV: the average energy released in the 17.6fusion of deuterium and tritium to form He-4; this is PJ per kilogram of product produced 0.41
- MeV ( 1×10^{−13} J): about twice the 1.602rest energy of an electron
- eV: the energy required to 13.6ionize atomic hydrogen; molecular bond energies are on the order of eV to 1 eV per bond 10
- eV to 1.6 eV: the 3.4photon energy of visible light
- eV: the energy E_{G} required to break a 1.1covalent bond in silicon
- meV: the energy E_{G} required to break a 720covalent bond in germanium
- meV: the 25thermal energy k_{B}T at room temperature; one air molecule has an average kinetic energy meV 38
- µeV: the thermal energy k_{B}T of the 230cosmic microwave background
Per mole
One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F ≈ 485 C mol^{−1}) where the energy in joules of N moles of particles each with energy X eV is X·F·N. 96
See also
Notes and references
- ↑ IUPAC Gold Book Archived 2009-01-03 at the Wayback Machine., p. 75
- ↑ SI brochure, Sec. 4.1 Table 7 Archived July 16, 2012, at the Wayback Machine.
- ↑ "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22.
2014 CODATA recommended values
- ↑ "CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22.
2014 CODATA recommended values
- ↑ "Definitions of the SI units: Non-SI units". The NIST Reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology. Retrieved 2018-07-01.
- ↑ Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24.
- ↑ "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Archived from the original on 14 May 2011. Retrieved 13 February 2011.
- ↑ "Special Relativity". Virtual Visitor Center. SLAC. 15 June 2009. Retrieved 13 February 2011.
- ↑ "CODATA Value: Planck constant in eV s". Archived from the original on 22 January 2015. Retrieved 30 March 2015.
- ↑ What is Light? Archived December 5, 2013, at the Wayback Machine. – UC Davis lecture slides
- ↑ Elert, Glenn. "Electromagnetic Spectrum, The Physics Hypertextbook". hypertextbook.com. Archived from the original on 2016-07-29. Retrieved 2016-07-30.
- ↑ "Definition of frequency bands on". Vlf.it. Archived from the original on 2010-04-30. Retrieved 2010-10-16.
- ↑ Open Questions in Physics. Archived 2014-08-08 at the Wayback Machine. German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
- ↑ "A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino". Archived from the original on 2015-03-19.
- ↑ Glossary Archived 2014-09-15 at the Wayback Machine. - CMS Collaboration, CERN
- ↑ ATLAS; CMS (26 March 2015). "Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments". Physical Review Letters. 114 (19): 191803. arXiv:1503.07589
. Bibcode:2015PhRvL.114s1803A. doi:10.1103/PhysRevLett.114.191803 . PMID 26024162.