Electronvolt

Unit of energy

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In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) measures the amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in a vacuum. When used as a unit of energy, the value of 1 eV in joules (symbol J) equals the value of the charge of an electron in coulombs (symbol C). Under the redefinition of the SI base units, this sets 1 eV to the exact value 1.×10&#;19 J.[1]

Historically, the electronvolt was devised as a standard unit of measure due to its usefulness in electrostatic particle accelerator sciences. A particle with electric charge q gains an energy E = qV after passing through a voltage of V. Since q must be an integer multiple of the elementary charge e for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.

Definition and Use

An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in a vacuum. Hence, one electronvolt is equal to 1.×10&#;19 J.[1]

The electronvolt (eV) is a unit of energy but is not an SI unit. It is commonly used in solid state physics, atomic physics, nuclear physics, particle physics, and high-energy astrophysics. It often uses SI prefixes like milli-, kilo-, mega-, giga-, tera-, peta-, or exa- (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 "B" stands for billion. Thus BeV is equivalent to GeV.

Relation to Other Physical Properties and Units

Mass

By mass-energy equivalence, the electronvolt corresponds to a unit of mass. In particle physics, mass and energy are often interchanged, expressing mass in units of eV/c², where c is the speed of light in a vacuum (E = mc²). Informally, mass is expressed in terms of eV as a unit of mass, using a system of natural units with c set to 1. The kilogram equivalent of 1 eV/c² is:

1 eV/c² = (1.602176634×10&#;19 C)×1 V / (299792458 m/s)² = 1.78266192×10&#;36 kg.

For instance, 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. Generally, the masses of all hadrons are around 1 GeV/c², making GeV/c² a convenient unit of mass for particle physics:

1 GeV/c² = 1.78266192×10&#;27 kg.

The atomic mass constant (mu), equal to one twelfth of the mass of a carbon-12 atom, is close to the mass of a proton. To convert to an electronvolt mass-equivalent, use the formula:

mu = 1 Da = 931. MeV/c² = 0.931 GeV/c².

Momentum

Dividing a particle's kinetic energy in electronvolts by c (the speed of light) describes the particle's momentum in units of eV/c. In natural units, where c equals 1, momentum is often expressed as electronvolts.

For example, the momentum p of an electron could be said to be 1 GeV when converted to MKS system units as:

p = 1 GeV/c = (1×10⁹)×(1.602176634×10&#;19 C)×1 V / (2.99792458×10⁸ m/s) = 5.344286×10&#;19 kg·m/s.

Distance

In particle physics, the system of natural units sets the speed of light in vacuum c and the reduced Planck constant ħ as dimensionless and equal to unity: c = ħ = 1. In such units, both distances and times are expressed in inverse energy units. Particle scattering lengths, for instance, are often presented in units of inverse particle masses.

Outside this unit system, the conversion factors between electronvolt, second, and nanometer are as follows:

ħ = 1.054571817646×10&#;34 J·s = 6.582119569509×10&#;16 eV·s.

The above relations 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 of cτ = 459.7 μm, or a decay width of (4.302±25)×10&#;4 eV.

Conversely, tiny meson mass differences responsible for meson oscillations are often expressed in inverse picoseconds.

Energy in electronvolts can sometimes be related to the wavelength of light with photons of the same energy.

E = hν = hc/λ = 4.135667516×10&#;15 eV·s × 299792458 m/s / λ = 1 239.841 93 eV·nm / λ.

532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV corresponds to an infrared photon of wavelength 1240 nm or frequency 241.8 THz.

Temperature

In certain fields, such as plasma physics, it is convenient to express temperature in terms of electronvolts. To convert to the Kelvin scale, divide the electronvolt by the Boltzmann constant:

1 eV/kB = 1.602176634×10&#;19 J / 1.380649×10&#;23 J/K = 11 604.518 12 K,

where kB is the Boltzmann constant.

When using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV, equivalent to 174 MK.

An approximation is kBT is about 0.025 eV (&#; 290 K/ K/eV) at a temperature of 20 °C.

Wavelength

The energy E, frequency ν, and wavelength λ of a photon are related by:

E = hν = hc/λ = 4.135667516×10&#;15 eV·s × 299792458 m/s / λ = 1 239.841 93 eV·nm / λ.

Scattering Experiments

In low-energy nuclear scattering experiments, nuclear recoil energy is often referred to in units of eVr, keVr, etc., distinguishing it from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. The relationship between eV, eVr, and eVee depends on the medium, 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, corresponding 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

References

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