Unit of energy
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 redefinition of the SI base units
, this sets 1 eV equal to the exact value
1.602
176
634
×
10
?19
J
.
[1]
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
E
=
qV
after passing through a voltage of
V
.
Definition and use
[
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]
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
1 J/C
, multiplied by the
elementary charge
e
=
1.602
176
634
×
10
?19
C
.
[2]
Therefore, one electronvolt is equal to
1.602
176
634
×
10
?19
J
.
[1]
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-, kilo-, mega-, giga-, tera-, peta- or exa- (giving meV, keV, MeV, GeV, TeV, PeV and EeV respectively). 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
[
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]
Quantity
|
Unit
|
SI value of unit
|
energy
|
eV
|
1.602
176
634
×
10
?19
J
[1]
|
mass
|
eV/
c
2
|
1.782
661
92
×
10
?36
kg
|
momentum
|
eV/
c
|
5.344
285
99
×
10
?28
kg·m/s
|
temperature
|
eV/
k
B
|
11
604
.518
12
K
|
time
|
ħ
/eV
|
6.582
119
×
10
?16
s
|
distance
|
ħc
/eV
|
1.973
27
×
10
?7
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
[
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]
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
2
, where
c
is the
speed of light
in vacuum (from
E
=
mc
2
). 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.
[3]
The
kilogram
equivalent of
1 eV/
c
2
is:
![{\displaystyle 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}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d521426c1c50df8608d6e7e168c878e55f4b750)
For example, an electron and a
positron
, each with a mass of
0.511 MeV/
c
2
, can
annihilate
to yield
1.022 MeV
of energy. A
proton
has a mass of
0.938 GeV/
c
2
. In general, the masses of all
hadrons
are of the order of
1 GeV/
c
2
, which makes the GeV/
c
2
a convenient unit of mass for particle physics:
[4]
1 GeV/
c
2
=
1.782
661
92
×
10
?27
kg
.
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:
m
u
= 1 Da =
931.4941 MeV/
c
2
=
0.931
4941
GeV/
c
2
.
Momentum
[
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]
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
.
[5]
In natural units in which the fundamental velocity constant
c
is numerically 1, the
c
may be informally be omitted to express momentum using the unit electronvolt.
The
energy?momentum relation
in
natural units
,
, is a
Pythagorean equation
that can be visualized as a
right triangle
where the total
energy
is the
hypotenuse
and the
momentum
and
rest mass
are the two
legs
.
The
energy?momentum relation
![{\displaystyle E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ff33cff7f554bf4de95c58e7a4e9b8e1f1b522c)
in natural units (with
![{\displaystyle c=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e3467f9e219a5ea38a30da5c3a02c2c23f61a79)
)
![{\displaystyle E^{2}=p^{2}+m_{0}^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/527f323b9d0f683f723b66915c78cc05f670b110)
is a
Pythagorean equation
. When a relatively high energy is applied to a particle with relatively low
rest mass
, it can be approximated as
![{\displaystyle E\simeq p}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a2e9add2ddf41f349abe7bfe5ec4579e68e602a)
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
T
?1
L
M
. The dimension of energy is
T
?2
L
2
M
. 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
?1
L
) facilitates the required conversion for using a unit of energy to quantify momentum.
For example, if the momentum
p
of an electron is
1 GeV/
c
, then the conversion to
MKS system of units
can be achieved by:
![{\displaystyle 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}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28c52ab078b1ee53834417c06c25e39591305168)
Distance
[
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]
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 using a unit of inverse particle mass.
Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:
![{\displaystyle \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} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/63f5f1b4b732f6dd8bab435640b1c54762075421)
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
4.302(25)
×
10
?4
eV
.
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:
![{\displaystyle {\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}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0f0742511d4ae995aa2300c68b2ad0f41604879)
Temperature
[
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]
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
:
![{\displaystyle {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}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c374ea306dafd70c6a284daf8f4e8c37b1e24a5b)
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
15 keV
(kiloelectronvolt), which is equal to 174 MK (megakelvin).
As an approximation:
k
B
T
is about
0.025 eV
(?
290 K
/
11604 K/eV
) at a temperature of
20 °C
.
Wavelength
[
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]
Energy of photons in the visible spectrum in eV
Graph of wavelength (nm) to energy (eV)
The energy
E
, frequency
ν
, and wavelength
λ
of a photon are related by
![{\displaystyle 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 }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/40cd13fc0f79bdeeb58feb79cf4f37dfc2ae95fe)
where
h
is the
Planck constant
,
c
is the
speed of light
. This reduces to
[6]
![{\displaystyle {\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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/00656cf6edf1e4f4d8a4169e26b71a5ffc3d8e74)
A photon with a wavelength of
532 nm
(green light) would have an energy of approximately
2.33 eV
. Similarly,
1 eV
would correspond to an infrared photon of wavelength
1240 nm
or frequency
241.8 THz
.
Scattering experiments
[
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]
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
[
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]
Photon frequency vs. energy particle in electronvolts
. The
energy 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 and
rest mass
.
[7]
[8]
[9]
Energy
|
Source
|
52.5
Q
eV
|
energy released from a 20
kiloton of TNT equivalent
explosion (e.g. the
nuclear weapon yield
of the
Fat Man
fission bomb
)
|
12.2
R
eV
|
the
Planck energy
|
10
Y
eV
|
approximate
grand unification energy
|
300
E
eV
|
first
ultra-high-energy cosmic ray
particle observed, the so-called
Oh-My-God particle
[10]
|
62.4
E
eV
|
energy consumed by a 10-watt device (e.g. a typical
[11]
LED light bulb
) in one second (
10 W
=
10 J/s
?
6.24
×
10
19
eV/s
)
|
2
P
eV
|
the highest-energy neutrino detected by the
IceCube
neutrino telescope in Antarctica
[12]
|
14 TeV
|
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)
|
1 TeV
|
0.1602 μJ
, about the kinetic energy of a flying
mosquito
[13]
|
172 GeV
|
rest mass energy
of the
top quark
, the heaviest
elementary particle
for which this has been determined
|
125.1
±
0.2 GeV
|
rest mass energy
of the
Higgs boson
, as measured by two separate detectors at the
LHC
to a certainty better than
5 sigma
[14]
|
210 MeV
|
average energy released in
fission
of one
Pu-239
atom
|
200 MeV
|
approximate average energy released in
nuclear fission
of one
U-235
atom.
|
105.7 MeV
|
rest mass energy
of a
muon
|
17.6 MeV
|
average energy released in the
nuclear fusion
of
deuterium
and
tritium
to form
He-4
; this is
0.41 PJ
per kilogram of product produced
|
2 MeV
|
approximate average energy released in a
nuclear fission
neutron released from one
U-235
atom.
|
1.9 MeV
|
rest mass energy
of
up quark
, the lowest-mass quark.
|
1 MeV
|
0.1602 pJ
, about twice the
rest mass energy
of an electron
|
1 to 10 keV
|
approximate
thermal energy
,
k
B
T
, in
nuclear fusion
systems, like the core of the
sun
,
magnetically confined plasma
,
inertial confinement
and
nuclear weapons
|
13.6 eV
|
the energy required to
ionize
atomic hydrogen
;
molecular
bond energies
are on the
order
of
1 eV
to
10 eV
per bond
|
1.65 to 3.26 eV
|
range of
photon energy
of
visible spectrum
from
red
to
violet
|
1.1 eV
|
energy
required to break a
covalent
bond in
silicon
|
720 meV
|
energy
required to break a
covalent
bond in
germanium
|
<
120 meV
|
upper bound on the
rest mass energy
of
neutrinos
(sum of 3 flavors)
[15]
|
38 meV
|
average kinetic energy
,
3
/
2
k
B
T
, of one gas molecule at
room temperature
|
25 meV
|
thermal energy
,
k
B
T
, at room temperature
|
230 μeV
|
thermal energy
,
k
B
T
, at the
cosmic microwave background
radiation temperature of ~2.7
kelvin
|
Molar energy
[
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]
One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy ? this corresponds to the
Faraday constant
(
F
≈
96
485
C?mol
?1
), where the energy in joules of
n
moles of particles each with energy
E
eV is equal to
E
·
F
·
n
.
See also
[
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]
References
[
edit
]
- ^
a
b
c
"2022 CODATA Value: electron volt"
.
The NIST Reference on Constants, Units, and Uncertainty
.
NIST
. May 2024
. Retrieved
2024-05-18
.
- ^
"2022 CODATA Value: elementary charge"
.
The NIST Reference on Constants, Units, and Uncertainty
.
NIST
. May 2024
. Retrieved
2024-05-18
.
- ^
Barrow, J. D. (1983). "Natural Units Before Planck".
Quarterly Journal of the Royal Astronomical Society
.
24
: 24.
Bibcode
:
1983QJRAS..24...24B
.
- ^
Gron Tudor Jones.
"Energy and momentum units in particle physics"
(PDF)
.
Indico.cern.ch
. Retrieved
5 June
2022
.
- ^
"Units in particle physics"
.
Associate Teacher Institute Toolkit
. Fermilab. 22 March 2002.
Archived
from the original on 14 May 2011
. Retrieved
13 February
2011
.
- ^
"2022 CODATA Value: Planck constant in eV/Hz"
.
The NIST Reference on Constants, Units, and Uncertainty
.
NIST
. May 2024
. Retrieved
2024-05-18
.
- ^
What is Light?
Archived
December 5, 2013, at the
Wayback Machine
?
UC Davis
lecture slides
- ^
Elert, Glenn.
"Electromagnetic Spectrum, The Physics Hypertextbook"
. hypertextbook.com.
Archived
from the original on 2016-07-29
. Retrieved
2016-07-30
.
- ^
"Definition of frequency bands on"
. Vlf.it.
Archived
from the original on 2010-04-30
. Retrieved
2010-10-16
.
- ^
Open Questions in Physics.
Archived
2014-08-08 at the
Wayback Machine
German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
- ^
"How Many Watts Does a Light Bulb Use?"
.
EnergySage
. Retrieved
2024-06-06
.
- ^
"A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino"
. 21 May 2014.
Archived
from the original on 2015-03-19.
- ^
Glossary
Archived
2014-09-15 at the
Wayback Machine
- CMS Collaboration, CERN
- ^
ATLAS
;
CMS
(26 March 2015).
"Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments"
.
Physical Review Letters
.
114
(19): 191803.
arXiv
:
1503.07589
.
Bibcode
:
2015PhRvL.114s1803A
.
doi
:
10.1103/PhysRevLett.114.191803
.
PMID
26024162
.
- ^
Mertens, Susanne (2016). "Direct neutrino mass experiments".
Journal of Physics: Conference Series
.
718
(2): 022013.
arXiv
:
1605.01579
.
Bibcode
:
2016JPhCS.718b2013M
.
doi
:
10.1088/1742-6596/718/2/022013
.
S2CID
56355240
.
External links
[
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]