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
hυ0 = 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