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.
Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric 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 potential 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 |
Definition
An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, , multiplied by the electron's 1 J/Celementary charge e, 1766208(98)×10^{−19} C.^{[3]} Therefore, one electronvolt is equal to 1.6021766208(98)×10^{−19} J.^{[4]} The electronvolt, as opposed to volt, is not an 1.602SI unit. Its derivation is empirical, which means its value in SI units must be obtained by experiment and is therefore not known exactly, unlike the litre, the light-year and such other non-SI units.^{[5]} Electonvolt (eV) is a unit of energy whereas volt (V) is the derived SI unit of electric potential. The SI unit for energy is joule (J). 1 eV is equal to 1766208(98)×10^{−19} J 1.602
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 is 1 eV/c^{2}
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 GeV (gigaelectronvolt) a convenient unit of mass for particle physics: 1 GeV/c^{2}
- = 1 GeV/c^{2}×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 = = 931.4941 MeV/c^{2}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., ). 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 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 , then the conversion to MKS can be achieved by: 1 GeV
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 = 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.
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 , or 170 MK. 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
where h is the Planck constant, c is the speed of light. This reduces to
- ^{[9]}
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 or frequency 1240 nm. 241.8 THz
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
- ×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 = 100 W ≈ 100 J/s×10^{20} eV/s) 6.24
- 300 EeV (×10^{20} eV = ~ 3J):^{[13]} the so-called 50 Oh-My-God particle (the most energetic cosmic ray particle ever observed)
- : two petaelectronvolts, the most high-energetic neutrino detected by the 2 PeVIceCube neutrino telescope in Antarctica^{[14]}
- : the designed proton collision energy at the 14 TeVLarge Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
- : a trillion electronvolts, or 1 TeV×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]}
- : 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 energy E_{G} required to break a 1.1 eVcovalent bond in silicon
- : the energy E_{G} required to break a 720 meVcovalent bond in germanium
- : the 25 meVthermal energy k_{B}T at room temperature; one air molecule has an average kinetic energy 38 meV
- : the thermal energy k_{B}T of the 230 µeVcosmic 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
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