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Obtain Einstein’s photoelectric equation with necessary explanation. Einstein’s explanation of photoelectric equation:

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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 Φ ) and the remaining energy as the kinetic energy of the ejected electron. From the law of conservation of energy,

hυ = Φ0 + \(\frac{1}{2}\)mv2 …… (1) 

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

3. If we reduce the frequency of the incident light, the speed or kinetic energy of photo electrons is also reduced. At some frequency V of incident radiation, the photo electrons are ejected with almost zero kinetic energy. Then the equation (1) becomes

0 = Φ0

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

hυ = hυ0 + \(\frac{1}{2}\)mv …… (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 Kmax. Then

Kmax=   \(\frac{1}{2}\)\(mv^2_{max}\)

where nmax is the maximum velocity of the electron ejected. 

The equation (1) is rearranged as follows:

Kmax = hυ – Φ0

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