Editing Electronvolt (section)

== Relation to other physical properties and units ==

{| class="wikitable" style="float:right; margin:0 0 1em 1em;"
|-
! Quantity !! Unit || SI value of unit
|-
| [[energy]] || eV || {{physconst|eV}}
|-
| [[mass]] || eV/''c''<sup>2</sup> || {{val|1.78266192|e=-36|u=kg}}
|-
| [[momentum]] || eV/''c'' || {{val|5.34428599|e=-28|u=kg·m/s}}
|-
| [[temperature]] || eV/''k''<sub>B</sub> || {{val|11604.51812|u=K}}
|-
| [[time]] || ''ħ''/eV || {{val|6.582119|e=-16|u=s}}
|-
| [[distance]] || ''ħc''/eV || {{val|1.97327|e=-7|u=m}}
|}
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/''c''<sup>2</sup>, where ''c'' is the [[speed of light]] in vacuum (from [[Mass–energy equivalence|{{nowrap|1=''E'' = ''mc''<sup>2</sup>}}]]). 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>{{cite journal | bibcode=1983QJRAS..24...24B | title=Natural Units Before Planck | last1=Barrow | first1=J. D. | journal=Quarterly Journal of the Royal Astronomical Society | year=1983 | volume=24 | page=24 }}</ref> The [[kilogram]] equivalent of {{val|1|u=eV/c2}} 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 {{val|0.511|u=MeV/c2}}, can [[Annihilation|annihilate]] to yield {{val|1.022|u=MeV}} of energy. A [[proton]] has a mass of {{val|0.938|u=GeV/c2}}. In general, the masses of all [[hadron]]s are of the order of {{val|1|u=GeV/c2}}, which makes the GeV/''c''<sup>2</sup> a convenient unit of mass for particle physics:<ref>{{cite web|url=https://indico.cern.ch/event/318730/contributions/737345/attachments/613347/843809/gevtypeunitshst14.pdf |title=Energy and momentum units in particle physics| author=Gron Tudor Jones| website=Indico.cern.ch| access-date=5 June 2022}}</ref>
{{block indent|em=1.2|text={{nowrap|1={{val|1|u=GeV/c2}} = {{val|1.78266192|e=-27|u=kg}}.}}}}

The [[atomic mass constant]] (''m''<sub>u</sub>), 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:
{{block indent|em=1.2|text={{nowrap|1=''m''<sub>u</sub> = 1 Da = {{val|931.4941|u=MeV/c2}} = {{val|0.9314941|u=GeV/c2}}.}}}}

=== 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">{{cite web |url=http://quarknet.fnal.gov/toolkits/ati/whatgevs.html |title=Units in particle physics |publisher=Fermilab |date=22 March 2002 |work=Associate Teacher Institute Toolkit |access-date=13 February 2011 |url-status=live |archive-url=https://web.archive.org/web/20110514152552/http://quarknet.fnal.gov/toolkits/ati/whatgevs.html |archive-date=14 May 2011 }}</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|thumb|The [[energy–momentum relation]] in [[natural units]], <math>E^2 = p^2 + m_0^2</math>, is a [[Pythagorean theorem|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 [[Invariant mass|rest mass]] <math>m_0</math> are the two [[Cathetus|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 [[Particle physics|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&nbsp;eV/''c''.

The dimension of momentum is {{dimanalysis|length=1|mass=1|time=−1}}. The dimension of energy is {{dimanalysis|length=2|mass=1|time=−2}}. Dividing a unit of energy (such as eV) by a fundamental constant (such as the speed of light) that has the dimension of velocity ({{dimanalysis|length=1|time=−1}}) facilitates the required conversion for using a unit of energy to quantify momentum.

For example, if the momentum ''p'' of an electron is {{val|1|u=GeV/''c''}}, 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 [[Planck constant|reduced Planck constant]] ''ħ'' are dimensionless and equal to unity is widely used: {{nowrap|1=''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 length]]s 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 {{nowrap|1=Γ = ''ħ''/''τ''}}. For example, the [[B meson|{{Subatomic particle|B0}} meson]] has a lifetime of 1.530(9)&nbsp;[[picosecond]]s, mean decay length is {{nowrap|1=''cτ'' = {{val|459.7|u=μm}}}}, or a decay width of {{val|4.302|(25)|e=-4|u=eV}}.

Conversely, the tiny meson mass differences responsible for [[Neutral particle oscillation|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''<sub>B</sub> is the [[Boltzmann constant]].

The ''k''<sub>B</sub> is assumed when using the electronvolt to express temperature, for example, a typical [[magnetic confinement fusion]] plasma is {{val|15|u=keV}} (kiloelectronvolt), which corresponds to 174&nbsp;MK (megakelvin).

As an approximation: at a temperature of {{nowrap|1=''T'' = {{val|20|u=degC}}}}, ''k''<sub>B</sub>''T'' is about {{val|0.025|u=eV}} (≈ {{sfrac|290 K|11604 K/eV}}).

=== Wavelength ===
[[File:Colors in eV.svg|thumb|Energy of photons in the visible spectrum in eV|239x239px]]
[[File:EV_to_nm_vis-en.svg|thumb|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 to{{physconst|h_eV/Hz|ref=only}}
<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 {{val|532|u=nm}} (green light) would have an energy of approximately {{val|2.33|u=eV}}. Similarly, {{val|1|u=eV}} would correspond to an infrared photon of wavelength {{val|1240|u=nm}} or frequency {{val|241.8|u=THz}}.