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Electronvolt
Electronvolt
Electronvolt
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electronvolt
Unit systemNon-SI accepted unit
Unit ofenergy
SymboleV
Conversions
1 eV in ...... is equal to ...
   joules (SI)   1.602176634×10−19 J‍[1]

In physics, an electronvolt (symbol eV), also written as electron-volt and electron volt, is a unit of measurement equivalent to the 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 expressed in unit of joules (symbol J) is equal to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 revision of the SI, this sets 1 eV equal to the exact value 1.602176634×10−19 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 = 1.602176634×10−19 C.[2] Therefore, one electronvolt is equal to 1.602176634×10−19 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- (10−3), kilo- (103), mega- (106), giga- (109), tera- (1012), peta- (1015), exa- (1018), zetta- (1021), yotta- (1024), ronna- (1027), or quetta- (1030), the respective symbols being meV, keV, MeV, GeV, TeV, PeV, EeV, ZeV, YeV, ReV, and QeV. 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 1.602176634×10−19 J‍[1]
mass eV/c2 1.78266192×10−36 kg
momentum eV/c 5.34428599×10−28 kg·m/s
temperature eV/kB 11604.51812 K
time ħ/eV 6.582119×10−16 s
distance ħc/eV 1.97327×10−7 m

In the fields of physics in which the electronvolt is used, other quantities are typically measured using units derived from it; products 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/c2, where c is the speed of light in vacuum (from E = mc2). 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/c2 is:

For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. A proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV/c2 a convenient unit of mass for particle physics:[4]

1 GeV/c2 = 1.78266192×10−27 kg.

The atomic mass constant (mu), 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:

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

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 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 in natural units (with ) is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as 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−1LM. The dimension of energy is T−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 momentum p of an electron is 1 GeV/c, then the conversion to MKS system of units can be achieved by:

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:

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 B0
 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:

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: where kB is the Boltzmann constant.

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kiloelectronvolt), which corresponds to 174 MK (megakelvin).

As an approximation: at a temperature of T = 20 °C, kBT is about 0.025 eV (≈ ⁠290 K/11604 K/eV⁠).

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 where h is the Planck constant, c is the speed of light. This reduces to[6] 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]
Legend
γ: gamma rays MIR: mid-infrared HF: high freq.
HX: hard X-rays FIR: far infrared MF: medium freq.
SX: soft X-rays radio waves LF: low freq.
EUV: extreme ultraviolet 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: near infrared VHF: very high freq. ELF: extremely low freq.
Energy Source
10 YeV approximate grand unification energy
120 PeV the highest-energy neutrino detected by the IceCube neutrino telescope in Antarctica[10]
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)
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[11]
105.7 MeV rest mass energy of a muon
0.511 MeV rest mass energy of an electron
13.6 eV 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
38 meV average kinetic energy, ⁠3/2⁠kBT, of one gas molecule at room temperature
230 μeV thermal energy, kBT, 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 ≈ 96485 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

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Electronvolt

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from Grokipedia
The electronvolt (symbol: eV) is a unit of commonly used in physics, defined as the amount of gained or lost by a single unbound when accelerated through an electrostatic potential difference of one volt in . This unit equals exactly 1.602176634 × 10-19 joules. Due to its scale aligning with atomic, nuclear, and subatomic processes, the electronvolt is particularly convenient for expressing energies in , , and , where values in joules would be impractically small. For larger energies, multiples such as kiloelectronvolt (keV; 103 eV), megaelectronvolt (MeV; 106 eV), gigaelectronvolt (GeV; 109 eV), and teraelectronvolt (TeV; 1012 eV) are employed, with the latter relevant to high-energy particle accelerators like those at . The electronvolt also facilitates descriptions of energies in and binding energies in atomic and molecular systems.

Core Concepts

Definition

The electronvolt (eV) is a unit of energy defined as the amount of kinetic energy gained or lost by a single unbound electron when accelerated through an electric potential difference of one volt, in vacuum. Under the 2019 redefinition of the SI base units, this definition establishes the electronvolt as an exactly defined quantity tied to the fixed value of the elementary charge. The symbol for the unit is eV, with common multiples in scientific notation including keV (10310^3 eV), MeV (10610^6 eV), GeV (10910^9 eV), and TeV (101210^{12} eV); these are routinely employed in high-energy physics to denote energy scales spanning many orders of magnitude. This unit derives from the fundamental relation for electrostatic potential energy, E=qVE = qV, where qq is the charge of the electron (the elementary charge ee) and VV is the potential difference. With ee fixed at the exact value 1.602176634×10−191.602176634 \times 10^{-19} C and V=1V = 1 V (where 1 V = 1 J/C), it follows that $1eVeV= e \times 1J/CJ/C= 1.602176634 \times 10^{-19}$ J exactly. The electronvolt provides a convenient scale for energies in atomic, nuclear, and , where typical values range from a few eV (e.g., atomic transitions) to TeV (e.g., collider experiments), far below the joule thresholds relevant to everyday macroscopic phenomena.

History

The unit of the electronvolt emerged in the early 20th century, shortly after J. J. Thomson's discovery of the in 1897, as researchers sought convenient ways to express the energies of in atomic and photoelectric experiments. Robert A. Millikan played a key role in its introduction during his investigations of the , where he measured the energy required to eject from metals in terms of the electron's charge times a potential difference; his 1911 paper on the topic laid foundational measurements that implicitly relied on this energy scale, though the explicit term appeared in his subsequent work. The oil-drop experiment by Millikan, conducted between 1909 and 1913, further refined the value of the e, providing the numerical basis for quantifying electron energies in volts, which influenced the unit's development in . The term "electron-volt" was first explicitly used in scientific literature in 1925 by Ralph H. Fowler in a discussing electron emission from metals, where he equated one electron-volt to approximately 1.59 × 10^{-12} erg. Initially written as "electron-volt" with a , reflecting its composite nature as the energy gained by an accelerated through one volt, the naming evolved over the mid-20th century to the unhyphenated "electronvolt" in standard usage, particularly as experiments proliferated. This evolution was driven by practical needs in quantifying binding energies and ionization potentials, building on Millikan's precise determination of e from oil-drop experiments. The electronvolt gained widespread adoption in following the invention of the by Ernest O. Lawrence in 1929–1930, which accelerated particles to energies expressed in electronvolts, such as protons reaching 80,000 eV in early models. By , as accelerators like the enabled higher-energy collisions, the unit became indispensable for describing particle kinematics and interaction energies, supplanting less convenient SI units like joules in high-energy contexts. The International Bureau of Weights and Measures (BIPM) formalized the electronvolt as an accepted non-SI unit compatible with the (SI) following the SI's establishment at the 11th General Conference on Weights and Measures in 1960, with it first appearing in the inaugural edition of the SI Brochure in 1970. A significant milestone occurred with the 2019 revision of the SI, effective May 20, 2019, which fixed the e exactly at 1.602176634 × 10^{-19} C, rendering the electronvolt exactly 1.602176634 × 10^{-19} J without experimental uncertainty and linking it precisely to the SI base units. This redefinition, adopted by the 26th General Conference on Weights and Measures, eliminated variability in the unit's value arising from measurements of e, enhancing its stability for applications in and beyond.

Relation to SI Units

The electronvolt (eV) is precisely related to the joule (J), the SI unit of energy, by the exact conversion factor established following the 2019 redefinition of the SI base units: 1 eV=1.602176634×10−19 J1 \, \mathrm{eV} = 1.602176634 \times 10^{-19} \, \mathrm{J} This relation is exact because the ee is now defined as exactly 1.602176634×10−19 C1.602176634 \times 10^{-19} \, \mathrm{C}, and the volt (V) is defined through fixed values of other fundamental constants such as the hh and the cc, thereby eliminating any in the product e×1 Ve \times 1 \, \mathrm{V}. The inverse conversion is likewise exact: 1 J=11.602176634×10−19 eV=6.241509074×1018 eV1 \, \mathrm{J} = \frac{1}{1.602176634 \times 10^{-19}} \, \mathrm{eV} = 6.241509074 \times 10^{18} \, \mathrm{eV} In microscopic physical systems, such as those involving atomic or subatomic particles, the electronvolt provides a convenient scale because corresponding energies expressed in joules are impractically small. For instance, the of the is 13.6 eV, equivalent to approximately 2.18×10−18 J2.18 \times 10^{-18} \, \mathrm{J}, avoiding cumbersome numerical representations in calculations. The electronvolt is recognized as a non-SI unit accepted for use with the (SI) by the International Bureau of Weights and Measures (BIPM). It is routinely employed in international standards, such as the CODATA recommended values for fundamental physical constants, where many quantities like particle rest masses and transition energies are tabulated in electronvolts for precision and practicality.

Connections to Physical Properties

Mass Equivalence

In special relativity, the rest energy EE of a particle is related to its rest mass mm by Einstein's equation E=mc2E = mc^2, where cc is the speed of light in vacuum, exactly 299792458299792458 m/s. Thus, the equivalent rest mass corresponding to an energy in electronvolts can be expressed as m=E/c2m = E / c^2, with EE in eV yielding mm in eV/c2c^2. In particle physics, this convention is standard, where particle masses are routinely tabulated in units of eV/c2c^2 to directly reflect their rest energies in eV when multiplied by c2c^2. For the electron, the rest energy is precisely 0.51099895069(16)0.51099895069(16) MeV, so its rest mass is me=0.51099895069(16)m_e = 0.51099895069(16) MeV/c2c^2. To convert to SI units, note that 11 eV/c2=1.782661921×10−36c^2 = 1.782661921 \times 10^{-36} kg, derived from the and via 11 eV =1.602176634×10−19= 1.602176634 \times 10^{-19} J and c2c^2. Thus, the electron mass is approximately 9.1093837015×10−319.1093837015 \times 10^{-31} kg. The proton provides another key example, with a rest energy of 938.27208816(29)938.27208816(29) MeV, corresponding to a rest mass of 938.27208816(29)938.27208816(29) MeV/c2≈1.67262192369(51)×10−27c^2 \approx 1.67262192369(51) \times 10^{-27} kg. Particle data tables, such as those from the Particle Data Group, quote masses for a wide range of fundamental particles and composites in eV/c2c^2, facilitating comparisons of their intrinsic . While the electronvolt equivalence primarily addresses rest mass for particles where the rest energy dominates, in the non-relativistic limit—where ≪mc2\ll mc^2—total energy approximates rest energy plus small kinetic contributions, but the focus here remains on the intrinsic rest mass scale.

Momentum

In the non-relativistic regime, applicable when the kinetic energy EE is much smaller than the particle's rest energy mc2m c^2, the magnitude of the pp is given by the formula p=2mE,p = \sqrt{2 m E},
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