In ^{9}) electronvolts; it is equivalent to the GeV.

^{2}, where ''c'' is the

^{0} meson has a lifetime of 1.530(9)

_{B} is the _{B} is assumed when using the electronvolt to express temperature, for example, a typical _{B}''T'' is about (≈ ) at a temperature of .

BIPM's definition of the electronvolt

physical constants reference; CODATA data

{{DEFAULTSORT:Electron Volt Particle physics Units of chemical measurement Units of energy Voltage

physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

gained by a single electron
The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family,
and are general ...

accelerating from rest through an electric potential difference
Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electr ...

of one volt
The volt is the derived unit for electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

in vacuum. When used as a unit of energy
Unit may refer to:
Arts and entertainment
* UNIT
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in ...

, the numerical value of 1 eV in joule
The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an object when a force of one Newton (unit), newton acts on th ...

s (symbol J) is equivalent to the numerical value of the charge of an electron in (symbol C). Under the 2019 redefinition of the SI base units
upright=1.35, The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second
The ...

, this sets 1 eV equal to the exact value J.
Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator upright=1.5, The Westinghouse Atom Smasher, an early Van de Graaff accelerator built 1937 at the Westinghouse Research Center in Forest Hills, Pennsylvania. The cutaway shows the fabric belts that carry charge up to the mushroom-shaped high voltage ...

sciences, because a particle with electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectively). Like c ...

''q'' has an energy after passing through the potential ''V''; if ''q'' is quoted in integer units of the elementary charge and the potential in volts
The volt is the derived unit for electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the amount of work energy needed to move a unit of electric charge
...

, one gets an energy in eV.
It is a common unit of energy
Unit may refer to:
Arts and entertainment
* UNIT
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in ...

within physics, widely used in solid state, atomic, nuclear, and particle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...

. It is commonly used with the metric prefix
A metric prefix is a unit prefixA unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of such ...

es milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron
The Bevatron was a particle accelerator
, a synchrotron collider type particle accelerator at Fermi National Accelerator Laboratory (Fermilab), Batavia, Illinois, USA. Shut down in 2011, until 2007 it was the most powerful particle accelerator i ...

, the symbol BeV is used, which stands for billion
A billion is a number with two distinct definitions:
*1,000,000,000
1,000,000,000 (one billion, short scale; one thousand million or milliard, yard, long scale) is the natural number
In mathematics, the natural numbers are those used for ...

(10Definition

An electronvolt is the amount of kinetic energy gained or lost by a singleelectron
The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family,
and are general ...

accelerating from rest through an electric potential difference
Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electr ...

of one volt
The volt is the derived unit for electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

in vacuum. Hence, it has a value of one volt
The volt is the derived unit for electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

, , multiplied by the electron's elementary charge
The elementary charge, usually denoted by or sometimes e is the electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive' ...

''e'', Therefore, one electronvolt is equal to
The electronvolt, as opposed to the volt, is not an SI unit
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system
The metric system is a that succeeded the decimal ...

. The electronvolt (eV) is a unit of energy whereas the volt (V) is the derived SI unit of electric potential. The SI unit for energy is the joule (J).
Mass

Bymass–energy equivalence
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

, the electronvolt is also a unit of mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...

. It is common in particle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...

, where units of mass and energy are often interchanged, to express mass in units of eV/''c''speed of light
The speed of light in vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...

in vacuum (from ). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Phy ...

with ''c'' set to 1.Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24. The mass equivalent of is
$$1\backslash ;\; \backslash text/c^2\; =\; \backslash frac\; =\; 1.782\backslash \; 661\backslash \; 92\; \backslash times\; 10^\backslash ;\; \backslash text.$$
For example, an electron and a positron
The positron or antielectron is the antiparticle
s (left) and antiparticles (right). From top to bottom; electron
The electron is a subatomic particle
In physical sciences, subatomic particles are smaller than atom
An atom is ...

, each with a mass of , can to yield of energy. The proton
A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

has a mass of . In general, the masses of all hadron
In particle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the ...

s are of the order of , which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:
The unified atomic mass unit
The dalton or unified atomic mass unit (symbols: Da or u) is a unit
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of ...

(u), almost exactly 1 gram divided by the Avogadro number
The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule
File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...

, is almost the mass of a hydrogen atom #REDIRECT Hydrogen atom
A hydrogen atom is an atom
An atom is the smallest unit of ordinary matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday o ...

, which is mostly the mass of the proton. To convert to electron volts, use the formula:
Momentum

Inhigh-energy physics
Particle physics (also known as high energy physics) is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word ''particle'' can refer to various types of very small objects (e.g. pro ...

, the electronvolt is often used as a unit of momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...

. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., ). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.
The dimensions of momentum units are . The dimensions of energy units are . Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum ''c''.
By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/''c''.
The fundamental velocity constant ''c'' is often ''dropped'' from the units of momentum by way of defining units of length such that the value of ''c'' is unity. For example, if the momentum ''p'' of an electron is said to be , then the conversion to MKS can be achieved by:
$$p\; =\; 1\backslash ;\; \backslash text/c\; =\; \backslash frac\; =\; 5.344\backslash \; 286\; \backslash times\; 10^\backslash ;\; \backslash text\; \backslash cdot\; \backslash text/\backslash text.$$
Distance

Inparticle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...

, a system of "natural units" in which the speed of light in vacuum ''c'' and the reduced Planck constant
The Planck constant, or Planck's constant, is the quantum of electromagnetic action that relates a photon's energy to its frequency. The Planck constant multiplied by a photon's frequency is equal to a photon's energy. The Planck constant i ...

''ħ'' are dimensionless and equal to unity is widely used: . 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 physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

). In particular, particle scattering lengthThe scattering length in quantum mechanics
Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundat ...

s are often presented in units of inverse particle masses.
Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:
:$\backslash hbar\; =\; \backslash frac\; h\; =\; 1.054\backslash \; 571\backslash \; 817\backslash \; 646\backslash times\; 10^\backslash \; \backslash mbox\; =\; 6.582\backslash \; 119\backslash \; 569\backslash \; 509\backslash times\; 10^\backslash \; \backslash mbox.$
The above relations also allow expressing the mean lifetime
Image:Plot-exponential-decay.svg, upright=1.5, A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5.
A ...

''τ'' of an unstable particle (in seconds) in terms of its decay width
Decay may refer to:
Science and technology
* Bit decay, in computing
* Software decay, in computing
* Distance decay, in geography
* Decay time (fall time), in electronics
Biology
* Decomposition
Decomposition is the process by which dead ...

Γ (in eV) via . For example, the Bpicosecond
A picosecond is an SI unit of time equal to 10−12 or (one trillionth) of a second
The second (symbol: s, abbreviation: sec) is the SI base unit, base unit of time in the International System of Units (SI) (French: Système International d ...

s, mean decay length is , or a decay width of .
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:
:$\backslash frac\; =\; \backslash frac\; \backslash thickapprox\; 8065.5439\; \backslash ;\; \backslash text^.$
Temperature

In certain fields, such asplasma physics
Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are ''anisotropic'', meaning that their properties ...

, it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor
In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality,
Multiplication, multiplicatively connected to a Constant (mathematics), c ...

to convert to the Kelvin scale
The kelvin is the base unit of temperature in the International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonasticall ...

:
:$=\; =\; 11\backslash \; 604.518\backslash \; 12\; \backslash text.$
Where ''k''Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor
In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality,
Multiplication, multiplicatively connected to a Constant (mathematics), c ...

, K is Kelvin, J is Joules, eV is electronvolts.
The ''k''magnetic confinement fusion
Magnetic confinement fusion is an approach to generate thermonuclear fusion power
Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion, nuclear fusion reactions. In a fusion proces ...

plasma is (kilo-electronvolts), which is equal to 174 MK (million Kelvin).
As an approximation: ''k''Properties

The energy ''E'', frequency ''v'', and wavelength ''λ'' of a photon are related by $$E\; =\; h\backslash nu\; =\; \backslash frac\; =\; \backslash frac$$ where ''h'' is thePlanck constant
The Planck constant, or Planck's constant, is a fundamental physical constant
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...

, ''c'' is the speed of light
The speed of light in vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...

. This reduces to
$$\backslash begin\; E\backslash mathrm\; \&=4.135\backslash \; 667\backslash \; 516\backslash ,\backslash mbox\backslash cdot\backslash nu\backslash \; \backslash mbox\; \backslash \backslash $$&=\frac.
\end
A photon with a wavelength of (green light) would have an energy of approximately . Similarly, would correspond to an infrared photon of wavelength or frequency .
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 aphototube
A phototube or photoelectric cell is a type of gas-filled or vacuum tube
A vacuum tube, an electron tube, valve (British usage) or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to whi ...

is measured in phe/keVee (photoelectron
The photoelectric effect is the emission of electron
The electron is a subatomic particle, symbol or , whose electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electrom ...

s 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

Per mole

One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to theFaraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge of one mole (unit), mole of electrons. It can be thought of as the conversion factor between the mole (used in chemistry) and ...

(''F'' ≈ ), 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)References

External links

BIPM's definition of the electronvolt

physical constants reference; CODATA data

{{DEFAULTSORT:Electron Volt Particle physics Units of chemical measurement Units of energy Voltage