Electronvolt

Author: Leandro Alegsa Creation date: November 13, 2022

The electron-volt or electron volt, symbol eV, is used to measure energy. It is defined as the amount of energy an electron gains after being accelerated by 1 volt of electricity. Joules are used often for energy measurement, but it is sometimes useful to use electron-volts for very small amounts of energy, such as that carried by a single subatomic particle. To convert joules into electron-volts, divide joules by the charge of an electron, which is about 1.602×10⁻¹⁹ coulomb.

E.g. 5 J = 5/1.602×10⁻¹⁹
5 J = 3.121×10⁺¹⁹ eV.

The electronvolt is often used in atomic, nuclear and particle physics. For example, the energy of photons can be measured by the voltage necessary to overcome their photoelectric effect.

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 and the voltage passed through it as 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 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 $\Delta E_{\text{kin}}=e\,U$ ; for -times charged particles, the corresponding formula is Δ $\Delta E_{\text{kin}}=Ze\,U$ . 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

for the energy
for the mass and
stands for the speed of light.

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

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

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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