Electronvolt

In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equal to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 revision of the SI, this sets 1 eV equal to the exact value Template:Physconst

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 gains an energy Template:Nowrap after passing through a voltage of V.

Definition and use

An electronvolt is the amount of energy gained or lost by a single electron when it moves through an electric potential difference of one volt. Hence, it has a value of one volt, which is Template:Val, multiplied by the elementary charge Template:Physconst Therefore, one electronvolt is equal to Template:Physconst

The electronvolt (eV) is a unit of energy, but is not an SI unit. It is a commonly used unit of energy within physics, widely used in solid state, atomic, nuclear and particle physics, and high-energy astrophysics. It is commonly used with SI prefixes milli- (10⁻³), kilo- (10³), mega- (10⁶), giga- (10⁹), tera- (10¹²), peta- (10¹⁵), exa- (10¹⁸), zetta- (10²¹), yotta- (10²⁴), ronna- (10²⁷), or quetta- (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 name Bevatron, the symbol BeV is used, where the B stands for billion. The symbol BeV is therefore equivalent to GeV, though neither is an SI unit.

Relation to other physical properties and units

Quantity	Unit	SI value of unit
energy	eV	Template:Physconst
mass	eV/c2	Template:Val
momentum	eV/c	Template:Val
temperature	eV/kB	Template:Val
time	ħ/eV	Template:Val
distance	ħc/eV	Template:Val

In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from the electronvolt as a product with fundamental constants of importance in the theory are often used.

Mass

By mass–energy equivalence, the electronvolt corresponds to 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/c², where c is the speed of light in vacuum (from [[Mass–energy equivalence|Template:Nowrap]]). It is common to informally express mass in terms of eV as a unit of mass, effectively using a system of natural units with c set to 1.<ref>Template:Cite journal</ref> The kilogram equivalent of Template:Val is:

<math display="block">1\; \text{eV}/c^2 = \frac{(1.602\ 176\ 634 \times 10^{-19} \, \text{C}) \times 1 \, \text{V}}{(299\ 792\ 458\; \mathrm{m/s})^2} = 1.782\ 661\ 92 \times 10^{-36}\; \text{kg}.</math>

For example, an electron and a positron, each with a mass of Template:Val, can annihilate to yield Template:Val of energy. A proton has a mass of Template:Val. In general, the masses of all hadrons are of the order of Template:Val, which makes the GeV/c² a convenient unit of mass for particle physics:<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Template:Block indent

The atomic mass constant (m_u), 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: Template:Block indent

Momentum

By dividing a particle's kinetic energy in electronvolts by the fundamental constant c (the speed of light), one can describe the particle's momentum in units of eV/c.<ref name="FNALunits">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In natural units in which the fundamental velocity constant c is numerically 1, the c may informally be omitted to express momentum using the unit electronvolt.

File:Einstein-triangle-in-natural-units.svg

The energy–momentum relation in natural units, <math>E^2 = p^2 + m_0^2</math>, is a Pythagorean equation that can be visualized as a right triangle where the total energy <math>E</math> is the hypotenuse and the momentum <math>p</math> and rest mass <math>m_0</math> are the two legs.

The energy–momentum relation <math display="block">E^2 = p^2 c^2 + m_0^2 c^4</math> in natural units (with <math>c=1</math>) <math display="block">E^2 = p^2 + m_0^2</math> is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as <math>E \simeq p</math> in high-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 is Template:Dimanalysis. The dimension of energy is Template:Dimanalysis. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity (Template:Dimanalysis) facilitates the required conversion for using a unit of energy to quantify momentum.

For example, if the momentum p of an electron is Template:Val, then the conversion to MKS system of units can be achieved by: <math display="block">p = 1\; \text{GeV}/c = \frac{(1 \times 10^9) \times (1.602\ 176\ 634 \times 10^{-19} \; \text{C}) \times (1 \; \text{V})}{2.99\ 792\ 458 \times 10^8\; \text{m}/\text{s}} = 5.344\ 286 \times 10^{-19}\; \text{kg} {\cdot} \text{m}/\text{s}.</math>

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: Template:Nowrap. 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 using a unit of inverse particle mass.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following: <math display="block">\hbar = 1.054\ 571\ 817\ 646\times 10^{-34}\ \mathrm{J{\cdot}s} = 6.582\ 119\ 569\ 509\times 10^{-16}\ \mathrm{eV{\cdot}s}.</math>

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 Template:Nowrap. For example, the [[B meson|Template:Subatomic particle meson]] has a lifetime of 1.530(9) picoseconds, mean decay length is Template:Nowrap, or a decay width of Template:Val.

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: <math display="block">\frac{1\; \text{eV}}{hc} = \frac{1.602\ 176\ 634 \times 10^{-19} \; \text{J}}{(6.62\ 607\ 015 \times 10^{-34}\; \text{J} {\cdot} \text{s}) \times (2.99\ 792\ 458 \times 10^{11}\; \text{mm}/\text{s})} \thickapprox 806.55439 \; \text{mm}^{-1}.</math>

Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale: <math display="block">{1 \,\mathrm{eV} / k_{\text{B}}} = {1.602\ 176\ 634 \times 10^{-19} \text{ J} \over 1.380\ 649 \times 10^{-23} \text{ J/K}} = 11\ 604.518\ 12 \text{ K},</math> where k_B is the Boltzmann constant.

The k_B is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is Template:Val (kiloelectronvolt), which corresponds to 174 MK (megakelvin).

As an approximation: at a temperature of Template:Nowrap, k_BT is about Template:Val (≈ Template:Sfrac).

Wavelength

File:Colors in eV.svg

Energy of photons in the visible spectrum in eV

File:EV to nm vis-en.svg

Graph of wavelength (nm) to energy (eV)

The energy E, frequency ν, and wavelength λ of a photon are related by <math display="block">E = h\nu = \frac{hc}{\lambda} = \frac{\mathrm{4.135\ 667\ 696 \times 10^{-15}\;eV/Hz} \times \mathrm{299\, 792\, 458\;m/s}}{\lambda}</math> where h is the Planck constant, c is the speed of light. This reduces toTemplate:Physconst <math display="block">\begin{align} E &= 4.135\ 667\ 696 \times 10^{-15}\;\mathrm{eV/Hz}\times\nu \\[4pt] &=\frac{1\ 239.841\ 98\;\mathrm{eV{\cdot}nm}}{\lambda}. \end{align}</math> A photon with a wavelength of Template:Val (green light) would have an energy of approximately Template:Val. Similarly, Template:Val would correspond to an infrared photon of wavelength Template:Val or frequency Template:Val.

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

File:Light spectrum.svg

CitationClass=web }}</ref>

Legend
γ: gamma rays	MIR: mid-infrared	HF: high freq.
HX: hard X-rays	FIR: far infrared	MF: medium freq.
SX: soft X-rays	radio waves	LF: low freq.
EUV: extreme ultraviolet	EHF: extremely high freq.	VLF: very low freq.
NUV: near ultraviolet	SHF: super high freq.	ULF: ultra-low freq.
visible light	UHF: ultra high freq.	SLF: super low freq.
NIR: near infrared	VHF: very high freq.	ELF: extremely low freq.

Energy	Source
Template:Val	approximate grand unification energy
Template:Val	the highest-energy neutrino detected by the IceCube neutrino telescope in Antarctica<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
Template:Val	designed proton center-of-mass collision energy at the Large Hadron Collider (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
Template:Val	rest mass energy of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma<ref>Template:Cite journal</ref>
Template:Val	rest mass energy of a muon
Template:Val	rest mass energy of an electron
Template:Val	energy required to ionize atomic hydrogen; molecular bond energies are on the order of Template:Val to Template:Val per bond
Template:Val	range of photon energy <math>(\tfrac{hc}{\lambda})</math> of visible spectrum from red to violet
Template:Val	average kinetic energy, Template:Math[[kT (energy)|Template:Math]], of one gas molecule at room temperature
Template:Val	thermal energy, [[kT (energy)|Template:Math]], at the cosmic microwave background radiation temperature of ~2.7 kelvin

Molar energy

One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F ≈ Template:Val), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.

See also

• Orders of magnitude (energy)

External links

• Fundamental Physical Constants from NIST