Electronvolt

Several terms redirect here. For other uses, seeMEV (disambiguation),KEV (disambiguation),GEV (disambiguation),TEV (disambiguation),andPEV (disambiguation).

Inphysics,anelectronvolt(symboleV), also writtenelectron-voltandelectron volt,is the measure of an amount ofkinetic energygained by a singleelectronaccelerating through anelectric potential differenceof onevoltinvacuum.When used as aunit of energy,the numerical value of 1 eV injoules(symbol J) is equal to the numerical value of thechargeof an electron incoulombs(symbol C). Under the2019 revision of the SI,this sets 1 eV equal to the exact value1.602176634×10⁻¹⁹J.

Historically, the electronvolt was devised as a standardunit of measurethrough its usefulness inelectrostatic particle acceleratorsciences, because a particle withelectric chargeqgains an energyE=qVafter passing through a voltage ofV.

Definition and use

An electronvolt is the amount of energy gained or lost by a singleelectronwhen it moves through anelectric potential differenceof onevolt.Hence, it has a value of onevolt,which is1 J/C,multiplied by theelementary chargee=1.602176634×10⁻¹⁹C.Therefore, one electronvolt is equal to1.602176634×10⁻¹⁹J.

The electronvolt (eV) is a unit of energy, but is not anSI unit.It is a commonly usedunit of energywithin physics, widely used insolid state,atomic,nuclearandparticlephysics, andhigh-energy astrophysics.It is commonly used withSI prefixesmilli-(10^-3),kilo-(10³),mega-(10⁶),giga-(10⁹),tera-(10¹²),peta-(10¹⁵) orexa-(10¹⁸), the respective symbols being meV, keV, MeV, GeV, TeV, PeV and EeV. The SI unit of energy is the joule (J).

In some older documents, and in the nameBevatron,the symbolBeVis used, where theBstands forbillion.The symbolBeVis therefore equivalent toGeV,though neither is an SI unit.

Relation to other physical properties and units

Quantity	Unit	SI value of unit
energy	eV	1.602176634×10−19J‍
mass	eV/c2	1.78266192×10−36kg
momentum	eV/c	5.34428599×10−28kg·m/s
temperature	eV/kB	11604.51812K
time	ħ/eV	6.582119×10−16s
distance	ħc/eV	1.97327×10−7m

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

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,wherecis thespeed of lightin vacuum (fromE=mc²). It is common to informally express mass in terms of eV as aunit of mass,effectively using a system ofnatural unitswithcset to 1.Thekilogramequivalent of1 eV/c²is:

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

For example, an electron and apositron,each with a mass of0.511 MeV/c²,canannihilateto yield1.022 MeVof energy. Aprotonhas a mass of0.938 GeV/c².In general, the masses of allhadronsare of the order of1 GeV/c²,which makes the GeV/c²a convenient unit of mass for particle physics:

1 GeV/c²=1.78266192×10⁻²⁷kg.

Theatomic 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:

m_u= 1 Da =931.4941 MeV/c²=0.9314941GeV/c².

Momentum

By dividing a particle's kinetic energy in electronvolts by the fundamental constantc(the speed of light), one can describe the particle'smomentumin units of eV/c.In natural units in which the fundamental velocity constantcis numerically 1, thecmay be informally be omitted to express momentum using the unit electronvolt.

Theenergy–momentum relationinnatural units,$E^{2}=p^{2}+m_{0}^{2}$,is aPythagorean equationthat can be visualized as aright trianglewhere the totalenergy$E$is thehypotenuseand themomentum$p$andrest mass$m_{0}$are the twolegs.

Theenergy–momentum relation $$E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}$$ in natural units (with$c=1$) $$E^{2}=p^{2}+m_{0}^{2}$$ is aPythagorean equation.When a relatively high energy is applied to a particle with relatively lowrest mass,it can be approximated as$E\simeq p$inhigh-energy physicssuch 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 momentumpof an electron is1 GeV/c,then the conversion toMKS system of unitscan be achieved by: $$p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\times (1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\times (1\;{\text{V}})}{2.99\ 792\ 458\times 10^{8}\;{\text{m}}/{\text{s}}}}=5.344\ 286\times 10^{-19}\;{\text{kg}}{\cdot }{\text{m}}/{\text{s}}.$$

Distance

Inparticle physics,a system of natural units in which the speed of light in vacuumcand thereduced Planck constantħare 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 lengthsare 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: $$\hbar =1.054\ 571\ 817\ 646\times 10^{-34}\ \mathrm {J{\cdot }s} =6.582\ 119\ 569\ 509\times 10^{-16}\ \mathrm {eV{\cdot }s}.$$

The above relations also allow expressing themean lifetimeτof an unstable particle (in seconds) in terms of itsdecay widthΓ (in eV) viaΓ =ħ/τ.For example, the
B⁰
mesonhas a lifetime of 1.530(9)picoseconds,mean decay length iscτ=459.7 μm,or a decay width of4.302(25)×10⁻⁴eV.

Conversely, the tiny meson mass differences responsible formeson oscillationsare 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: $${\frac {1\;{\text{eV}}}{hc}}={\frac {1.602\ 176\ 634\times 10^{-19}\;{\text{J}}}{(2.99\ 792\ 458\times 10^{10}\;{\text{cm}}/{\text{s}})\times (6.62\ 607\ 015\times 10^{-34}\;{\text{J}}{\cdot }{\text{s}})}}\thickapprox 8065.5439\;{\text{cm}}^{-1}.$$

Temperature

In certain fields, such asplasma physics,it is convenient to use the electronvolt to express temperature. The electronvolt is divided by theBoltzmann constantto convert to theKelvin scale: $${1\,\mathrm {eV} /k_{\text{B}}}={1.602\ 176\ 634\times 10^{-19}{\text{ J}} \over 1.380\ 649\times 10^{-23}{\text{ J/K}}}=11\ 604.518\ 12{\text{ K}},$$ wherek_Bis theBoltzmann constant.

Thek_Bis assumed when using the electronvolt to express temperature, for example, a typicalmagnetic confinement fusionplasma is15 keV(kiloelectronvolt), which is equal to 174 MK (megakelvin).

As an approximation:k_BTis about0.025 eV(≈⁠290 K/11604 K/eV⁠) at a temperature of20 °C.

Wavelength

Energy of photons in the visible spectrum in eV

Graph of wavelength (nm) to energy (eV)

The energyE,frequencyν,and wavelengthλof a photon are related by $$E=h\nu ={\frac {hc}{\lambda }}={\frac {\mathrm {4.135\ 667\ 696\times 10^{-15}\;eV/Hz} \times \mathrm {299\,792\,458\;m/s} }{\lambda }}$$ wherehis thePlanck constant,cis thespeed of light.This reduces to $${\begin{aligned}E&=4.135\ 667\ 696\times 10^{-15}\;\mathrm {eV/Hz} \times \nu \\[4pt]&={\frac {1\ 239.841\ 98\;\mathrm {eV{\cdot }nm} }{\lambda }}.\end{aligned}}$$ A photon with a wavelength of532 nm(green light) would have an energy of approximately2.33 eV.Similarly,1 eVwould correspond to an infrared photon of wavelength1240 nmor frequency241.8 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 byscintillationlight. For example, the yield of aphototubeis measured in phe/keVee (photoelectronsper 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

Photon frequency vs. energy particle in electronvolts.Theenergy of a photonvaries 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.

Legend
γ:gamma rays	MIR: mid-infrared	HF:high freq.
HX: hardX-rays	FIR: far infrared	MF:medium freq.
SX: soft X-rays	radio waves	LF:low freq.
EUV: extremeultraviolet	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: nearinfrared	VHF:very high freq.	ELF:extremely low freq.

Energy	Source
3×1058QeV	mass-energyof allordinary matterin theobservable universe
52.5QeV	energy released from a 20kiloton of TNT equivalentexplosion (e.g. thenuclear weapon yieldof theFat Manfission bomb)
12.2ReV	thePlanck energy
10YeV	approximategrand unification energy
300EeV	firstultra-high-energy cosmic rayparticle observed, the so-calledOh-My-God particle
62.4EeV	energy consumed by a 10-watt device (e.g. a typicalLED light bulb) in one second (10 W=10 J/s≈6.24×1019eV/s)
2PeV	the highest-energy neutrino detected by theIceCubeneutrino telescope in Antarctica
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)
1 TeV	0.1602 μJ,about the kinetic energy of a flyingmosquito
172 GeV	rest mass energyof thetop quark,the heaviestelementary particlefor which this has been determined
125.1±0.2 GeV	rest mass energyof theHiggs boson,as measured by two separate detectors at theLHCto a certainty better than5 sigma
210 MeV	average energy released infissionof onePu-239atom
200 MeV	approximate average energy released innuclear fissionof oneU-235atom.
105.7 MeV	rest mass energyof amuon
17.6 MeV	average energy released in thenuclear fusionofdeuteriumandtritiumto formHe-4;this is0.41 PJper kilogram of product produced
2 MeV	approximate average energy released in anuclear fissionneutron released from oneU-235atom.
1.9 MeV	rest mass energyofup quark,the lowest-mass quark.
1 MeV	0.1602 pJ,about twice therest mass energyof an electron
1 to 10 keV	approximatethermal energy,kBT,innuclear fusionsystems, like the core of thesun,magnetically confined plasma,inertial confinementandnuclear weapons
13.6 eV	the energy required toionizeatomic hydrogen;molecularbond energiesare on theorderof1 eVto10 eVper bond
1.65 to 3.26 eV	range ofphoton energy$({\tfrac {hc}{\lambda }})$ofvisible spectrumfromredtoviolet
1.1 eV	energy$E_{g}$required to break acovalentbond insilicon
720 meV	energy$E_{g}$required to break acovalentbond ingermanium
<120 meV	upper bound on therest mass energyofneutrinos(sum of 3 flavors)
38 meV	average kinetic energy,⁠3/2⁠kBT,of one gas molecule atroom temperature
25 meV	thermal energy,kBT,at room temperature
230 μeV	thermal energy,kBT,at thecosmic microwave backgroundradiation temperature of ~2.7kelvin

Molar energy

One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to theFaraday constant(F≈96485C⋅mol⁻¹), where the energy in joules ofnmoles of particles each with energyEeV is equal toE·F·n.

See also

• Orders of magnitude (energy)

External links

• Fundamental Physical Constants from NIST