# Electron volts

Physical unit
Unit name Electron volts
Unit symbol ${\ displaystyle \ mathrm {eV}}$
Physical quantity (s) energy
Formula symbol ${\ displaystyle E}$
dimension ${\ displaystyle {\ mathsf {M \; L ^ {2} \; T ^ {- 2}}}}$
system Approved for use with the SI
In SI units ${\ displaystyle \ mathrm {1 \; eV = 1 {,} 602 \, 176 \, 634 \ cdot 10 ^ {- 19} \; J}}$ (exactly)
Named after Elektron , Alessandro Volta
Derived from Volts , elemental charge

The electron volt , officially electron volt , is a unit of energy that is often used in atomic , nuclear and particle physics . It is made up of the elementary charge  e and the voltage in volts  (V). Your unit symbol is therefore eV.

If a singly charged particle such as an electron or a proton is accelerated in a vacuum in an electric field , its kinetic energy changes by exactly one electron volt if the acceleration voltage is 1 volt. Expressed in the SI unit Joule , its value is exactly:

${\ displaystyle \ mathrm {1 \; eV = 1 {,} 602 \, 176 \, 634 \ cdot 10 ^ {- 19} \; J}}$

The value is exact because for the definition of the SI units (including the volt) the elementary charge has a fixed value of 1.602 176 634e-19 Cwas assigned. The electron volt, like the joule, does not belong to theInternational System of Units, but it is approved for use with it and is alegal unit of measurementin the EU and Switzerland.

## designation

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

On the other hand, Annex 1 No. 10 (to Section 1) of the Unit Ordinance specifies the special name “electron volt” for the statutory unit. Since October 3, 2009, Section 1 (2) of the Unit Ordinance has referred to the definitions that are listed in Chapter I of the Annex to Directive 80/181 / EEC of December 20, 1979 in its current version.

The DIN standard  1301-1 "Units - unit names, unit symbols" from October 2010 recommends the form "electron volt". In data processing systems with a limited number of characters, the unit names and prefixes according to DIN 66030, May 2002 edition, may be displayed ( Section 2 of the Unit Ordinance ). This uses the term "electron volt".

## use

### As a unit for 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. Handy, which is, therefore, because the change of the kinetic energy of each in the electric field accelerated particle from its load and the traversed voltage as can be calculated and is independent of other factors: the mass of the particle, the length of the path or the exact spatial profile of the Field strength does not matter. ${\ displaystyle \ Delta E _ {\ text {kin}}}$${\ displaystyle Q}$${\ displaystyle U}$${\ displaystyle \ Delta E _ {\ text {kin}} = UQ}$

The amount of charge of a free, observable particle is always the elementary charge or an integral multiple thereof. Instead of using the elementary charge and specifying the energy in joules , the change in kinetic energy resulting from an electrical acceleration can be specified directly in the unit eV. The formula applies to singly charged particles - such as electrons, protons and singly charged ions ; for -fold charged particles applies accordingly . For example, the kinetic energy of a proton changes by 100 eV when it flies through a potential difference of 100 V, the energy of a doubly charged helium nucleus changes by 200 eV. ${\ displaystyle e}$${\ displaystyle \ Delta E _ {\ text {kin}} = e \, U}$${\ displaystyle Z}$${\ displaystyle \ Delta E _ {\ text {kin}} = Ze \, U}$

The kinetic energy of a positively charged particle decreases by the amount indicated to when the traversed voltage is polarized such that the electric potential on the path of the particle from taking (colloquially called "while the particles from plus to minus move"); in the opposite case it decreases. For negatively charged particles the same applies with the opposite sign (see e.g. opposing field method for photoelectric effects ).

The use of the unit electron volt is not restricted to acceleration work on charged particles in an electric field. Since it is of an order of magnitude that is favorable for atomic and nuclear physics, it is often used for completely different energies on a microscopic scale, for example for binding energies in the atomic shell or in the atomic nucleus or for the energy of individual photons .

### As a unit for mass in particle physics

The electron volt can also be used as the unit of 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 .

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

in which

• ${\ displaystyle E}$ for the energy
• ${\ displaystyle m}$ for the crowd and
• ${\ displaystyle c}$stands for the speed of light .

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

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

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

A system of “natural” units is often used in particle physics . It is set. Thus the mass of a particle has the same unit as its kinetic energy. Both are then usually given in electron volts. ${\ displaystyle c = 1}$

## Decimal multiples

Common decimal multiples of the electron volt are:

• meV (milli-electron volts; 10 −3  eV). Example: a free particle has a thermal energy of about 25 meV at room temperature
• keV (kiloelectron volt; 10 3  eV). For example, a photon of X-rays has about 1-250 keV
• MeV (megaelectron volt; 10 6  eV). Example: the rest energy of an electron is about 0.511 MeV
• GeV (gigaelectron volt; 10 9  eV). Example: the rest energy of a proton is about 0.94 GeV
• TeV (teraelectron volt; 10 12  eV). Example: Protons in the Large Hadron Collider  (LHC) at CERN have a maximum kinetic energy of 6.5 TeV
• PeV (petaelectron volt; 10 15 eV). For example, in high-energy neutrino observatory IceCube detected neutrinos , z. B. 2.5 PeV.

The kinetic energy of rapidly moving heavier atomic nuclei ( heavy ions ) is often given per nucleon . The unit is then written AGeV, where A stands for the mass number . Every core with 1 AGeV has the same speed. Similarly, there are ATeV and AMeV, depending on the energy scale.

In the  LHC , protons with an energy of 6.5 TeV and lead nuclei with 574 TeV are brought to collision. The energy of a single nucleus with approx. 1 µJ (for a proton) or 90 µJ (for lead) is still very low. However, if one takes into account the large number of particles (1.15 · 10 11 protons per particle package , in the ring of the LHC there are up to 2808 particle packages per direction), the total energy of the protons in the ring is 720 MJ, which roughly corresponds to kinetic energy of a large aircraft taking off and taking off.

## Conversion to joules per mole

In chemistry , the energy per particle is often not given, but per mole (with the unit J / mol), which is obtained by multiplying the energy of the individual particle by the Avogadro constant , for example: ${\ displaystyle N _ {\ mathrm {A}}}$

${\ displaystyle 1 \; \ mathrm {eV} \ cdot N _ {\ mathrm {A}} = 96 \, 485 \; {\ frac {\ mathrm {J}} {\ mathrm {mol}}} = F \ cdot 1 \; \ mathrm {V}}$,

where is Faraday's constant . ${\ displaystyle F = e \ cdot N _ {\ mathrm {A}}}$

## Individual evidence

1. a b Le Système international d'unités . 9e édition, 2019 (the so-called "SI brochure", French and English).
2. based on EU Directive 80/181 / EEC in the EU member states and Article 17 of the Unit Ordinance in Switzerland
3. "The electron volt is the energy that an electron gains when it passes through a potential difference of 1 volt in a vacuum."
4. DIN 1301 units. Part 1: Unit names, unit symbols. October 2010, p. 8.
5. DIN 66030 Information Technology - Representation of unit names in systems with a limited number of characters. May 2002, p. 5, table 1.
6. Event view of highest energy neutrino detected by IceCube - CERN Courier. Retrieved January 2, 2019 .
7. LHC Design Report ( Memento of the original from September 8, 2009 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.