Electron Volt

An electron volt is defined as the energy an electron acquires while accelerating through a potential difference of 1 volt in a vacuum. This unit is used when the calculation involves elementary particles like electrons, protons, photons, etc. 

History

Historically, the unit of electron volt was used in particle accelerators due to its usefulness in simplifying the value of the energy of the particles. The value of most of the charged particles was a multiple of the electronic charge of an electron. So, for calculation purposes, the value of the electronic charge is taken as a standard unit. Later on, the use of electron volts came in handy for many fields of physics, including particle physics, high energy physics, plasma physics, etc. 

Why is electron volt used in physics?

In particle physics, most charged particles have energy as multiple of the electron charge of an electron (due to ionisation).

So let e be the charge of an electron.

Let Q be the charge of a charged particle.

Since the charge of the particle will be an integral multiple of electrons charge, we write,

Q = ne

Here n is an integer.

To find the energy of the particle due to its charge, we multiply the value of its charge with the value of the potential difference ( V ) around the charged particle. Therefore, the value of energy E is,

E = QV

E = neV (since Q = ne)

Now, let V be equal to mx1, where m is the magnitude of the potential difference.

Therefore, E = ne x (m x 1)

E = (n x m)x(1 x e)

Both n and m are scalar quantities.1 and e has the dimensions of potential difference and electric charge respectively . If we multiplication 1 and e we will give the unit of energy since W = q x V where w is work, q is the charge and V is the potential difference. 

The value of e is, e = 1.602 x 10–19. Therefore, 1xe will give energy eV = 1.602 x 10-19 joules.

Since n and m are constant numbers, we can say that their product will also be a constant number. Therefore, let n x m = N. 

From the above calculation, we can say that the total energy of a charged particle can be expressed as a multiple of eV = 1.602 x 10-19. This value of eV is called an electron volt. 

The unit of electron volt is also used as a unit of mass, momentum, temperature, time and distance. 

Since electron volt can be used to express energy in any form, irrespective of its magnitude, we use a certain prefix to the symbol ‘eV’ of electron volt. For X-rays, the energy of the photons is expressed in terms of Kilo electron volt or ‘ KeV ’. For atomic mass units, the mass is expressed in terms of Mega electron volt or ‘ MeV ‘. 

The electron volt is also used to express the ionisation potential of atoms. For a Hydrogen atom, it is expressed as approximately -13.6 eV/n2. Here, n is the number of the discrete energy levels allowed according to Bohr’s model of the hydrogen atom. 

Note: In later studies, it was found that there are particles with charge which are not an integral multiple of e. For example, a quark with a charge of ⅔ e.  

Application of electron volt (eV)

1. As a unit of mass

In particle physics, the mass of a particle is expressed in the units of eV/c2. Mass is commonly expressed in terms of eV by using a natural system with c set to 1. This is possible as a result of the mass energy equivalence of Einstein’s formula E = mc2.

The value of 1 atomic mass unit expressed in terms of electron volt is,

1 u = 931.4941 MeV/c2 

2. As a unit of momentum

By dividing energy with the speed of light, one can get the momentum of a particle. In high energy physics, momentum is commonly expressed in terms of electron volt divided by the speed of light.

3. As a unit of distance

In particle physics, the particle scattering lengths are often expressed in inverse energy units, mainly electron volts. Also, wavelengths of photons are expressed in terms of electron volt with energy equivalent to the energy of the photon in terms of electron volts.

4. As a unit of temperature

In plasma physics, the temperature is expressed as an electron volt. Here, the electron volt is divided by the Boltzmann constant Kb to get the temperature in the kelvin scale. 1 eV divided by Boltzmann constant will give us a temperature of 11604.5182 K. On looking at the value of the temperature, we can see that for calculations involving high temperature, we can use the kelvin electron volt conversion to simplify the calculations.

5. As a unit of time 

On dividing Planck’s ‘ h ‘  constant with electron volt we get

h/(2xπxeV) = 6.582 x 10-16 s

This time eV relation will give us a constant, which is highly helpful in a calculation involving particles with a short half-life. 

Conclusion 

An electron volt is a unit of energy that has a significant application in mainly particle physics and high energy physics. It helps in simplifying calculations and helps in giving us a better insight into the data that are hard to analyse in the common unit of energy (joules).

The value of 1 electron volt is 1eV = 1.602 x 10-19 joules.