# Electron Volt

The electron volt is not a frequently used unit, but it plays a vital role in electricity and magnetism, nuclear physics, etc. Now the question that arises is what is an electron volt? Basically, the electron volt is a unit of energy and is abbreviated as eV.

An electron volt is a small unit of energy. When we want to move the charge having a value of 1efrom lower potential to higher potential, then the charge will accelerate with some kinetic energy of 1eV. The electron volt (eV) is defined as: an electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV.

## Value of 1eV

• We know that energy or the work done is also measured in terms of joules, abbreviated as J.

• The electron volt (eV) and Joules (J) both are units of energy. We use both units depending upon the need for calculations.

• An electron volt is a unit of energy and the Joule is the SI unit of energy. Both Joules and eV can be interpreted in terms of one another.

• Joule is most commonly used in the measurement of energy and eV is mostly used in calculating the energy of atomic energy levels.

• Now, the value of 1eV is given by:

We know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

⇒ W = qΔV = 1e⁻ C(1V) J/C

⇒ W = 1eV = 1.6 x 10⁻¹⁹ Joules

• Therefore, 1 electron volt is equal to 1.6 x 10⁻¹⁹ Joules.

### Relation Between 1eV and Joules

Both electron volt and the joules can be related by unit conversions. One should always keep in my mind that, unit conversion can be done if and only if both measuring units are of the same scale. Here, both electron volt and joules are the units of energy and hence they are interchangeable.

So, the electron volt and joules have a relation given by:

⇒ 1ev = 1.6 x 10⁻¹⁹ J

Therefore the value of one electron volt is equal to 1.6 x 10⁻¹⁹ J.

### Examples:

1: A Particle Carrying Charge of 4e Falls through a Potential Difference of 4V. Calculate the Energy Acquired by the Particle.

Sol:

We know that whenever an object falls from a higher level to a lower level the potential energy stored will release in the form of kinetic energy. Thus the energy acquired by the particle will be kinetic energy.

Given,

Charge of the particle = q = 4e

The potential difference between two levels = ΔV = 4V

We need to calculate the kinetic energy, then:

⇒ K.E = qΔV

⇒ K.E = (4e)(4)

⇒ K.E = 16e

⇒ K.E = 16 x 1.6 x 10⁻¹⁹ eV

⇒ K.E = 25.6 eV

Therefore, the energy acquired by a charge of 4e when it falls through a potential difference of 4V is 25.6eV.

2: Define Electron Volt and Prove that 1eV = 1.6 x 10⁻¹⁹

Sol:

Electron Volt definition: An electron volt is the amount of energy required to move a charge equal to 1e⁻ across a potential difference of 1eV. This is how we define one electron volt.

Now, to prove that the value of 1eV is 1.6 x 10⁻¹⁹ we will use the unit conversions for a better understanding.

Now, we know that in order to move an electron with a potential difference of 1V, then the amount of work done is,

⇒ W = qΔV = 1e⁻ C(1V) J/C

⇒ W = 1eV = 1.6 x 10⁻¹⁹ Joules

Therefore, 1 electron volt is equal to 1.6 x 10⁻¹⁹ Joules.

3: What is the Value of One Mega Electron Volt?

Sol:

1 mega unit = 10⁶

Then, 1 mega electron volt is given by,

⇒  1MeV = 10⁶ x 1.6 x 10⁻¹⁹

⇒  1MeV = 1.6 x 10⁻¹³ eV

Therefore, the value of one mega electron volt is 1.6 x 10⁻¹³ eV.