In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
gained by a single
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
accelerating from rest through an
electric potential difference
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to mo ...
of one
volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...
in
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
. When used as a
unit of energy
Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, is ...
, the numerical value of 1 eV in
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
s (symbol J) is equivalent to the numerical value of the
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqua ...
of an electron in
coulomb
The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI).
In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
s (symbol C). Under the
2019 redefinition of the SI base units
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram.
Effective 20 May 2019, the 144t ...
, this sets 1 eV equal to the exact value
Historically, the electronvolt was devised as a standard
unit of measure
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multip ...
through its usefulness in
electrostatic particle accelerator
An electrostatic particle accelerator is a particle accelerator in which charged particles are accelerated to a high energy by a static high voltage potential. This contrasts with the other major category of particle accelerator, oscillating fie ...
sciences, because a particle with
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
''q'' gains an energy after passing through a voltage of ''V.'' Since ''q'' must be an
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
multiple of the
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
''e'' for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.
It is a common
unit of energy
Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, is ...
within physics, widely used in
solid state,
atomic,
nuclear
Nuclear may refer to:
Physics
Relating to the nucleus of the atom:
* Nuclear engineering
*Nuclear physics
*Nuclear power
*Nuclear reactor
*Nuclear weapon
*Nuclear medicine
*Radiation therapy
*Nuclear warfare
Mathematics
*Nuclear space
*Nuclear ...
, and
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, and
high-energy astrophysics High energy astronomy is the study of astronomical objects that release electromagnetic radiation of highly energetic wavelengths. It includes X-ray astronomy, gamma-ray astronomy, extreme UV astronomy, neutrino astronomy, and studies of cosmic ...
. It is commonly used with
SI prefix
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 and the world's most widely used system of measurement. E ...
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 — specifically, a weak-focusing proton synchrotron — at Lawrence Berkeley National Laboratory, U.S., which began operating in 1954. The antiproton was discovered there in 1955, resulting in the ...
, the symbol BeV is used, which stands for
billion
Billion is a word for a large number, and it has two distinct definitions:
*1,000,000,000, i.e. one thousand million, or (ten to the ninth power), as defined on the short scale. This is its only current meaning in English.
* 1,000,000,000,000, i.e ...
(10
9) electronvolts; it is equivalent to the GeV.
Definition
An electronvolt is the amount of kinetic energy gained or lost by a single
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
accelerating from rest through an
electric potential difference
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to mo ...
of one
volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...
in vacuum. Hence, it has a value of one
volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...
, , multiplied by the
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
Therefore, one electronvolt is equal to
The electronvolt (eV) is a unit of energy, but 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 and the world's most widely used system of measurement. E ...
. The SI unit of energy is the joule (J).
Relation to other physical properties and units
Mass
By
mass–energy equivalence
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...
, the electronvolt corresponds to a unit of
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
. It is common in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, 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
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum (from
). It is common to informally express mass in terms of eV as a
unit of mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
, effectively using a system of
natural units
In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a Coherence (units of measurement), coherent unit of a quantity. For e ...
with ''c'' set to 1. The
kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
equivalent of is:
For example, an electron and a
positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
, each with a mass of , can
annihilate to yield of energy. A
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
has a mass of . In general, the masses of all
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
s are of the order of , which makes the GeV/''c''
2 a convenient unit of mass for particle physics:
The
atomic mass constant
The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at ...
(''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:
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 Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
in units of eV/''c''.
In natural units in which the fundamental velocity constant ''c'' is numerically 1, the ''c'' may informally be omitted to express momentum as electronvolts.
The
energy momentum relation
in natural units (with
)
is a
Pythagorean equation
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...
. When a relatively high energy is applied to a particle with relatively low
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
, it can be approximated as
in
high-energy physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and b ...
such that an applied energy in units of eV conveniently results in an approximately equivalent change of momentum in units of eV/''c''.
The dimensions of momentum units are . The dimensions of energy units are . Dividing the units of energy (such as eV) by a fundamental constant (such as the speed of light) that has units of velocity () facilitates the required conversion for using energy units to describe momentum.
For example, if the momentum ''p'' of an electron is said to be , then the conversion to
MKS system of units
The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units. It forms the base of the International System of Units (SI), though SI has since been redefined by different fundamental co ...
can be achieved by:
Distance
In
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, 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 a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
''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, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...
). In particular, particle
scattering length The scattering length in quantum mechanics describes low-energy scattering. For potentials that decay faster than 1/r^3 as r\to \infty, it is defined as the following low-energy limit:
:
\lim_ k\cot\delta(k) =- \frac\;,
where a is the scatterin ...
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:
:
The above relations also allow expressing the
mean lifetime
A quantity is subject to exponential decay if it decreases at a rate Proportionality (mathematics), proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ...
''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 of organic matter
* Tooth decay (dental caries) ...
Γ (in eV) via . For example, the
meson has a lifetime of 1.530(9)
picosecond
A picosecond (abbreviated as ps) is a unit of time in the International System of Units (SI) equal to 10−12 or (one trillionth) of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000  ...
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:
:
Temperature
In certain fields, such as
, 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 that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
to convert to the
Kelvin scale
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
:
:
where ''k''
B is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
.
The ''k''
B is assumed when using the electronvolt to express temperature, for example, a typical
magnetic confinement fusion
Magnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with i ...
plasma is (kiloelectronvolt), which is equal to 174 MK (megakelvin).
As an approximation: ''k''
B''T'' is about (≈ ) at a temperature of .
Wavelength
![EV to nm vis](https://upload.wikimedia.org/wikipedia/commons/7/71/EV_to_nm_vis.png)
The energy ''E'', frequency ''v'', and wavelength ''λ'' of a photon are related by
where ''h'' is the
Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, ''c'' is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. This reduces to
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
Scintillation can refer to:
*Scintillation (astronomy), atmospheric effects which influence astronomical observations
*Interplanetary scintillation, fluctuations of radio waves caused by the solar wind
*Scintillation (physics), a flash of light pro ...
light. For example, the yield of a
phototube
A phototube or photoelectric cell is a type of gas-filled or vacuum tube that is sensitive to light. Such a tube is more correctly called a 'photoemissive cell' to distinguish it from photovoltaic or photoconductive cells. Phototubes were previ ...
is measured in phe/keVee (
photoelectron
The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid sta ...
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 each has approximately 96.5 kJ of energy – this corresponds to the
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
(''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)
This list compares various energies in joules (J), organized by order of magnitude.
Below 1 J
1 to 105 J
106 to 1011 J
1012 to 1017 J
1018 to 1023 J
Over 1023 J
}
, -
, 1050
,
, ≳1050 J
, Upper limit of 'apparent'/isotropic energy ' ...
References
External links
BIPM's definition of the electronvoltphysical constants reference; CODATA data
{{DEFAULTSORT:Electron Volt
Particle physics
Units of chemical measurement
Units of energy
Voltage