Obtain Einstein's photoelectric equation with necessary explanation.

Explanation

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.
In this process , a part of the photon energy is used for the ejection of the electrons from the metal surface (photoelectric work function `phi_0` ) and the remaining energy as the kinetic energy of the ejection electron. From the law of conservation of energy,
`hu=phi_0+1/2 mv^2` .........(1)
where m is the mass of the electron and v its velocity

If we reduce the frequency of the incident light the speed or kinetic energy of photo electrons is also reduced. at some frequency `v_0` incident rediation, the photo electrons are ejected with almost zero kinetic energy . Then the equation (1) becomes
`hu_0=phi_0`
where `v_0` is the thrshould frequency. By rewriting equation (1) , we get
`hu =hu_0 +1/2 mv^2` ..........(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 `u_("max")` is the maximum velocity of the electron ejected. The equation (1) is rearranged as follows :
`K_("max")=hu-phi_0`