Question

Obtain Einstein’s photoelectric equation with the necessary explanation.

Answer 1

Einstein’s explanation of photoelectric equation:

1. When a photon of energy hv is incident on a metal surface, it is completely absorbed by a single electron and the electron is ejected.

2. In this process, a part of the photon energy is used for the ejection of the electrons from the metal surface (photoelectric work function Φ₀) and the remaining energy as the kinetic energy of the ejected electron. From the law of conservation of energy,

hv = Φ₀ + `1/2` mv² ..........(1)

where m is the mass of the electron and u its velocity

          Emission of photoelectrons

3. If we reduce the frequency of the incident light, the speed or kinetic energy of photoelectrons is also reduced. At some frequency V₀ of incident radiation, the photoelectrons are ejected with almost zero kinetic energy.

Then the equation (1) becomes

hv₀ = Φ₀

where v₀ is the threshold frequency. By rewriting the equation (1), we get

hv = hv₀ + `1/2` mv² ……(2)

The equation (2) is known as Einstein’s Photoelectric equation.

If the electron does not lose energy by internal collisions, then it is emitted with maximum kinetic energy K_max. Then

K_max = `1/2 "mv"_"max"^2`

where v_max is the maximum velocity of the electron ejected.

The equation (1) is rearranged as follows:

K_max = hv – Φ₀