Electronvolt

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The electronvolt (symbol eV) is a unit of energy that represents the change in energy experienced by an electron when moving from a point of potential Va to a point of potential Vb when the difference Vba = Vb-Va = 1 V, that is, when the potential difference of the electric field is 1 volt. Its value is 1.602176634 × 10⁻¹⁹ J.

It is one of the units accepted for use in the International System of Units, but does not strictly belong to it.

In high-energy physics, the electronvolt is a very small unit, so multiples such as the megaelectronvolt MeV or the gigaelectronvolt GeV are often used. At present, with the most powerful particle accelerators, energies of the order of teraelectronvolt TeV have been reached (an example is the Large Hadron Collider, LHC, which is prepared to operate with an energy of up to 14 teraelectronvolts). There are objects in our universe that are accelerators to even higher energies: gamma rays of tens of TeV and cosmic rays of petaelectronvolts (PeV, one thousand TeV), and even tens of exaelectronovolts (EeV, equivalent to one thousand PeV) have been detected.

Some typical multiples are:

1 keV = 10³ eV

1 MeV = 10³ keV = 10⁶ eV

1 GeV = 10³ MeV = 10⁹ eV

1 TeV = 10³ GeV = 10¹² eV

1 PeV = 10³ TeV = 10¹⁵ eV

1 EeV = 10³ PeV = 10¹⁸ eV

In particle physics it is used interchangeably as a unit of mass and energy, since in relativity both magnitudes refer to the same thing. Einstein's relationship, E = m c², gives rise to a unit of mass corresponding to eV (solving m from the equation) that is called eV/c².

1 eV/c2 = 1,783 × 10^{- 36} kg

1 keV/c2 = 1,783 × 10^-33 kg

1 MeV/c2 = 1,783 × 10^{- 30} kg

1 GeV/c2 = 1,783 × 10^-27 kg

History

The unit electronvolt, then still known as the "equivalent volt", was first used in 1912 in Philosophical Magazine in an article by Karel Taylor Compton and Owen Willans Richardson on The photoelectric effect.

In the US, with the development of particle physics, the unit BeV (or bev or Bev) began to be used, where B represented a trillion (from English " billion "). In 1948, however, the IUPAP rejected its use, preferring the use of the gig prefix for a billion electron volts, thus the unit is abbreviated GeV.

In some older publications, "ev" as an abbreviation for electronvolt.

The name of the Bevatron particle accelerator (in operation 1954-1993, Berkeley, USA) was derived from the BeV unit. The Tevatron accelerator (1983-2011, Illinois), which accelerated protons and antiprotons to energies up to 1 TeV, was named after the same key. The name Zevatron is sometimes used exaggeratedly for natural astrophysical sources of particles with energies up to 10²¹ eV (zetta prefix). The highest energy of a single particle has never been recorded before.

Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt to express temperatures. The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale:

{displaystyle {1eV over k_{text{B}}}={1.602 176 634times 10^{-19}{text{ J}} over 1.380 649times 10^{-23}{text{ J/K}}}=11 604.518 12{text{ K}}.}

Where k_B is Boltzmann's constant, K is Kelvin, J is Joules, eV is electronvolts.

For example, a typical fusion magnetic confinement plasma is 15 keV (kilo-electronvolts), which is equal to 174 MK (million kelvins).

Roughly: k_BT is 0.025 eV (≈ 290K/ 11604 K/eV) at a temperature of 20 °C.

Moment

In high-energy physics, the electronvolt is often used as the unit of momentum (momentum). A potential difference of 1 volt causes an electron to gain an amount of energy (or 1 eV). This results in the use of eV (and keV, MeV, GeV, or TeV) as momentum units, because the energy supplied results in the acceleration of the particle.

The dimensions of the units of moment are L¹ M¹ T^-1. The dimensions of energy units are L² M¹ T^-2. Therefore, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity L¹ T^-1, facilitates the conversion required to use units of energy to describe momentum. In the field of high-energy particle physics, the fundamental unit of speed is the speed of light in vacuum c.

If you divide the energy in eV by the speed of light, you can describe the momentum of an electron in units of eV/c.

The fundamental rate constant c is often set aside from units of momentum by defining units of length such as the value of c is unitary. For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS is done as:

{displaystyle p=1;{text{GeV}}/c={frac {(1times 10^{9})cdot (1.602 176 634times 10^{-19};{text{C}})cdot (1;{text{V}})}{2.99 792 458times 10^{8};{text{m}}/{text{s}}}}=5.344 286times 10^{-19};{text{kg}}cdot {text{m}}/{text{s}}.}

Distance

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 reported in units of the inverse of the particle masses.

Outside this system of units, the conversion factors between electronvolts, seconds, and nanometers are as follows:

{displaystyle hbar ={frac {h}{2pi }}=1.054 571 817 646times 10^{-34} {mbox{J s}}=6.582 119 569 509times 10^{-16} {mbox{eV s}}.}

These relationships also allow us to express the half-life τ of an unstable particle (in seconds) as a function of its resonance width Γ (in eV) by Γ = ħ/τ. For example, the B0 meson has a half-life of 1.530(9) picoseconds, mean resonance width is cτ = 459.7 μm, or a resonance width of 4.302 10^-4 eV.

In contrast, the minute differences in meson masses responsible for meson oscillations are often expressed in more convenient inverse unit picoseconds.

Energy expressed in electronvolts is sometimes expressed by the wavelength of light with photons of the same energy:

{displaystyle {frac {1;{text{eV}}}{hc}}={frac {1.602 176 634times 10^{-19};{text{J}}}{(2.99 792 458times 10^{10};{text{cm}}/{text{s}})cdot (6.62 607 015times 10^{-34};{text{J}}cdot {text{s}})}}thickapprox 8065.5439;{text{cm}}^{-1}.}

They are often presented in units of the reverse mass of the particle.

Unit size

The electron volt is an extremely small amount of energy on a common scale. The energy of a flying mosquito is about one trillion electron volts. Therefore, the unit is useful where typical energies are very small, i.e. in a world of particles. Here, too, 1 eV is often a relatively small energy, so larger multiples and prefixes are used: 1 keV is a thousand eV, 1 MeV is a million eV, 1 GeV is a billion eV, 1 TeV is a trillion eV. Sometimes the abbreviation is used as an acronym.

The largest particle accelerator (LHC) supplies each proton with 7 TeV. Breaking a single ²³⁵U uranium nucleus releases approximately 215 MeV. [8] By combining a nucleus of a deuterium atom with a nucleus of tritium, 17.6 MeV is released. On color television screens, electrons are accelerated by a high voltage of about 32,000 volts, so that the electrons acquire a kinetic energy of 32 keV. Electronvolts are well-suited for measuring the energy of chemical bonds, being on the order of units or tens of eV for a molecule. It takes 13.6 eV to remove an electron from a hydrogen atom (ionization). The order of eV also has energies of photons of visible light. In thermodynamics, energies less than electron volts are produced; for example, the average kinetic energy of air particles at room temperature is 38 meV (millielectronvolts).

The speed of an electron with a kinetic energy of 1 eV is approximately 593 km/s. The speed of a proton with the same kinetic energy is then only 13.8 km/s.

The magnitude of the electronvoltio in SI units is determined by measuring the electron charge. The most accurate of known methods is the measurement of the Josephson effect, which determines the value of Josephson's constant ${displaystyle K_{mathrm {J} }}$ . The magnitude of the elemental load is then determined from the relationship ${displaystyle e={frac {2}{left(R_{mathrm {K} }K_{mathrm {J} }right)}}}$ . Zde ${displaystyle R_{mathrm {K} }}$ . Here. ${displaystyle R_{mathrm {K} }}$ is the constant of von Klitzing that is measured more precisely than ${displaystyle K_{mathrm {J} }}$ . The relative standard deviation of Josephson's constant measurement is 2.5 × 10 −8 (2.5 millionths of percentage), and the conversion of an electron-volt in a July is equally accurate.

Measurement

Equipment to measure the photoelectric effect: K - M cathode - grid, A - anode P - potentiometer

In technical practice, it is advantageous that for elementary charged particles, the change in energy in electron volts corresponds directly to the electrical voltage in volts by which the particle is accelerated (or slowed down). An example is an apparatus for observing an external photoelectric effect, where a stopping electric field is used to determine the energy of the electrons.

Light (or other radiation) passes through a window into an empty flask and strikes a cathode to knock electrons off its surface. They fly through the grid, hitting the anode and creating an electrical current in the circuit, which we measure with a microammeter. To determine the energy of the flying electrons, we set using a potentiometer braking voltage between the cathode and the network. This electric field returns few energy electrons to the cathode and they do not participate in current conduction. However, if the electron has enough kinetic energy, it overcomes the braking field and continues towards the anode. The required kinetic energy in electron volts corresponds directly to the braking voltage in volts. Therefore, we can experimentally determine the extreme value of the voltage between the cathode and the grid at which a current still flows through the circuit, for example, 1.2 volts. This means that light supplies electrons with a kinetic energy of 1.2 electron volts.

In practice, therefore, we often compare the unknown value of the particle's energy directly with the electron-volt and not with the units of the SI system. This is one of the main reasons to set up this unit. The imprecision of the conversion factor between eV and J is usually completely negligible due to measurement errors under normal laboratory conditions. Furthermore, the electron volt can be calculated with much more precision than the joule by the SI definition.

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