An electronvolt is the amount of energy gained or lost by a singleelectron when it moves through anelectric potential difference of onevolt. Hence, it has a value of onevolt, which is1 J/C, multiplied by theelementary chargee = 1.602176634×10−19 C.[2] Therefore, one electronvolt is equal to1.602176634×10−19 J.[1]
The electronvolt (eV) is a unit of energy, but is not anSI unit. It is a commonly usedunit of energy within physics, widely used insolid state,atomic,nuclear andparticle physics, andhigh-energy astrophysics. It is commonly used withSI prefixesmilli- (10−3),kilo- (103),mega- (106),giga- (109),tera- (1012),peta- (1015),exa- (1018),zetta- (1021),yotta- (1024),ronna- (1027), orquetta- (1030), the respective symbols being meV, keV, MeV, GeV, TeV, PeV, EeV, ZeV, YeV, ReV, and QeV. The SI unit of energy is the joule (J).
In some older documents, and in the nameBevatron, the symbolBeV is used, where theB stands forbillion. The symbolBeV is therefore equivalent toGeV, though neither is an SI unit.
In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from it; products with fundamental constants of importance in the theory are often used.
Bymass–energy equivalence, the electronvolt corresponds to a unit ofmass. It is common inparticle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, wherec is thespeed of light in vacuum (fromE =mc2). It is common to informally express mass in terms of eV as aunit of mass, effectively using a system ofnatural units withc set to 1.[3] Thekilogram equivalent of1 eV/c2 is:
For example, an electron and apositron, each with a mass of0.511 MeV/c2, canannihilate to yield1.022 MeV of energy. Aproton has a mass of0.938 GeV/c2. In general, the masses of allhadrons are of the order of1 GeV/c2, which makes the GeV/c2 a convenient unit of mass for particle physics:[4]
1 GeV/c2 =1.78266192×10−27 kg.
Theatomic mass constant (mu), one twelfth of the mass a carbon-12 atom, is close to the mass of a proton. To convert to electronvolt mass-equivalent, use the formula:
By dividing a particle's kinetic energy in electronvolts by the fundamental constantc (the speed of light), one can describe the particle'smomentum in units of eV/c.[5] In natural units in which the fundamental velocity constantc is numerically 1, thec may informally be omitted to express momentum using the unit electronvolt.
Theenergy–momentum relationin natural units (with)is aPythagorean equation. When a relatively high energy is applied to a particle with relatively lowrest mass, it can be approximated as inhigh-energy physics such that an applied energy with expressed in the unit eV conveniently results in a numerically approximately equivalent change of momentum when expressed with the unit eV/c.
The dimension of momentum isT−1LM. The dimension of energy isT−2L2M. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity (T−1L) facilitates the required conversion for using a unit of energy to quantify momentum.
For example, if the momentump of an electron is1 GeV/c, then the conversion toMKS system of units can be achieved by:
Inparticle physics, a system of natural units in which the speed of light in vacuumc and thereduced Planck constantħ 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, seemass–energy equivalence). In particular, particlescattering lengths are often presented using a unit of inverse particle mass.
Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:
The above relations also allow expressing themean lifetimeτ of an unstable particle (in seconds) in terms of itsdecay width Γ (in eV) viaΓ =ħ/τ. For example, theB0 meson has a lifetime of 1.530(9) picoseconds, mean decay length iscτ =459.7 μm, or a decay width of4.302(25)×10−4 eV.
Conversely, the tiny meson mass differences responsible formeson 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:
ThekB is assumed when using the electronvolt to express temperature, for example, a typicalmagnetic confinement fusion plasma is15 keV (kiloelectronvolt), which corresponds to 174 MK (megakelvin).
As an approximation: at a temperature ofT =20 °C,kBT is about0.025 eV (≈290 K/11604 K/eV).
Energy of photons in the visible spectrum in eVGraph of wavelength (nm) to energy (eV)
The energyE, frequencyν, and wavelengthλ of a photon are related bywhereh is thePlanck constant,c is thespeed of light. This reduces to[6]A photon with a wavelength of532 nm (green light) would have an energy of approximately2.33 eV. Similarly,1 eV would correspond to an infrared photon of wavelength1240 nm or frequency241.8 THz.
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 byscintillation light. For example, the yield of aphototube 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.
Photon frequency vs. energy particle in electronvolts. Theenergy of a photon varies only with the frequency of the photon, related by the speed of light. This contrasts with a massive particle of which the energy depends on its velocity andrest mass.[7][8][9]
the highest-energy neutrino detected by theIceCube neutrino telescope in Antarctica[10]
14 TeV
designed proton center-of-mass collision energy at theLarge Hadron Collider (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
Onemole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to theFaraday constant (F ≈96485 C⋅mol−1), where the energy in joules ofn moles of particles each with energyE eV is equal toE·F·n.
^"Units in particle physics".Associate Teacher Institute Toolkit. Fermilab. 22 March 2002.Archived from the original on 14 May 2011. Retrieved13 February 2011.
