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Electronvolt: definition, uses, and common scales

The electronvolt (eV) is a small unit of energy used in atomic, nuclear and particle physics. This article explains its definition, conversions, typical magnitudes, history, and related concepts.

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The electronvolt (abbreviated eV) is a unit of energy commonly used in physics to describe the energies of particles, photons and atomic processes. It is defined as the kinetic energy gained by a single electron when it is accelerated through an electric potential difference of one volt. Although the SI unit of energy is the joule, the electronvolt is a convenient, human-scaled unit for the very small energies typical in atomic and subatomic systems; see energy and electron for background.

Definition and conversion

By definition, 1 eV = 1 elementary charge × 1 volt. In SI units this is approximately 1.602×10−19 joule (J). Many references quote the elementary charge explicitly; consult material on the volt and the joule for context. To convert joules to electronvolts, divide the energy in joules by the elementary charge (≈1.602×10−19 C). For example, 5 J corresponds to about 3.12×1019 eV.

Common scales and examples

  • eV: individual electronic transitions and visible photons (visible light photons are typically on the order of 1–3 eV). See subatomic particle examples and charge references.
  • keV (kiloelectronvolt, 103 eV): X-ray photons and inner-shell binding energies in heavier atoms.
  • MeV (megaelectronvolt, 106 eV): nuclear reaction energies and many radioactive decay processes; common in atomic and nuclear physics.
  • GeV–TeV (giga- and teraelectronvolt): typical scales in high-energy and particle physics, such as accelerator collision energies.

Applications and practical importance

The electronvolt is used wherever the typical energies are far smaller than everyday macroscopic values. It simplifies numerical work and communication: a photon energy can be expressed directly in eV rather than in a very small fraction of a joule. The unit appears in spectroscopy, condensed-matter physics, astrophysics and accelerator physics. Photons measured by experiments exploiting the photoelectric effect are often characterized by the voltage necessary to liberate electrons; see photon and photoelectric effect discussions.

Although the electronvolt is derived from the volt, it represents energy, not electric potential. It is also convenient to express mass via mass–energy equivalence: particle masses are frequently quoted in units of eV/c2 (for example, MeV/c2 or GeV/c2), where c is the speed of light. Temperature-like comparisons use Boltzmann's constant: 1 eV corresponds to roughly 11,600 kelvins. When reading or converting values, be careful to note the multiple prefix (keV, MeV, GeV, TeV) and whether a quantity is energy, mass (via c2), or an electric potential.

Historically, the electronvolt arose as experiments with electric potentials and cathode rays made it natural to measure small energies in terms of volt-driven gains. Today it remains a standard and practical unit in many branches of physics and in applied fields such as materials science and radiation physics. For introductory definitions and deeper technical data consult the linked topics on energy, electron, the volt, the joule, and the specific areas of atomic, nuclear and particle physics.

Naming

In German-language literature, the unit is predominantly referred to as "electron volt", i.e. with the morpheme "en" between "electron" and "volt".

On the other hand, Annex 1 No. 10 (to Section 1) of the Units Ordinance specifies the special name "electron volt" for the legal unit. Since 3 October 2009, § 1 (2) of the Ordinance on Units refers to the definitions listed in Chapter I of the Annex to Directive 80/181/EEC of 20 December 1979, as amended.

DIN standard 1301-1 "Units - Unit names, unit symbols" of October 2010 recommends the form "electron volt". In data processing systems with a limited character set, the unit names and prefixes may be displayed in accordance with DIN 66030, May 2002 edition (§ 2 of the Unit Ordinance). This uses the designation "electron volt".

Usage

As a unit for the energy

The electron volt is used as a "handy" unit of energy in atomic physics and related fields such as experimental nuclear and elementary particle physics. For example, the kinetic energy to which a particle is brought in a particle accelerator is always given in electron volts. This is handy because the change in kinetic energy Δ \Delta E_{{{\text{kin}}}}any particle accelerated in the electric field can be calculated from its charge Q and the voltage passed through it Uas Δ \Delta E_{{{\text{kin}}}}=UQ and is independent of other influences: The mass of the particle, the length of the path, or the exact spatial variation of the field strength do not matter.

The amount of charge of a free, observable particle is always the elementary charge e or an integer multiple of it. Instead of using the elementary charge and specifying the energy in joules, one can therefore specify the change in kinetic energy resulting from an electric acceleration directly in the unit eV. Here, for singly charged particles - such as electrons, protons, and singly charged ions - the formula{\displaystyle \Delta E_{\text{kin}}=e\,U}; for Z -times charged particles, the corresponding formula is Δ {\displaystyle \Delta E_{\text{kin}}=Ze\,U}. For example, the kinetic energy of a proton changes by 100 eV when passing through a potential difference of 100 V, and the energy of a doubly charged helium nucleus changes by 200 eV.

The kinetic energy of a positively charged particle increases by the amount mentioned if the voltage passed through is polarized in such a way that the electric potential on the particle's path decreases (colloquially: "when the particle moves from plus to minus"); in the opposite case it decreases. For negatively charged particles, the same applies with the opposite sign (see, for example, the counter-field method in the photoelectric effect).

The use of the unit electron volt is not limited to acceleration work on charged particles in the electric field. Since it has a convenient order of magnitude for atomic and nuclear physics, it is often used for quite different energies on a microscopic scale, such as binding energies in the atomic shell or nucleus, or for the energy of single photons.

As a unit for mass in particle physics

The electron volt can also be used as a unit of the mass of particles. The conversion of mass into energy is done according to the equivalence of mass and energy. This energy is called rest energy.

E=mc^{2}\quad \Leftrightarrow \quad m={\dfrac {E}{c^{2}}},

where

So the corresponding unit of mass is {\mathrm {eV}}/c^{2}. The conversion to kilograms is:

{\displaystyle 1\,\mathrm {eV} /c^{2}\approx 1{,}783\cdot 10^{-36}\,\mathrm {kg} }.

For example, the mass of an electron is 9.11 - 10-31 kg = 511 keV/c².

In particle physics, a system of "natural" units is often used. Here, c=1 is set. Thus the mass of a particle has the same unit as its kinetic energy. Both are then usually given in electron volts.

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