Derive Einstein's' photoelectric equation in terms of frequency.

Explanation

According to Einstein, energy of the radiations incident on a metal surface is used up in two ways:
(i) A part of this energy is used just to overcome the surface barrier so that electrons can come out of the metal surface.
(ii) Remaining part of energy of radiations incident on a metal surface provide the kinetic energy to the ejected electrons.
By Law of Conservation of energy :
Energy of radiation incident on a metal surface = Work function + Kinetic energy of electrons
`hv = hv_0 + 1/2 mv^2`
where `" "` v=frequency of incident light.
`" " v_0` = threshold frequency for a metal surface.
`" "` v= velocity of the ejected electron.
`1/2 mv^2 = hv - hv_0`
`1/2 mv^2 = h (v - v_0)`
which is the required Einstein.s photoelectric equation in terms of frequency.
Note : We know that
`v= dlambda`
and `v_0 = d lambda_0`
`lambda =` Wavelength of incident light
`lambda_0` =Threshold wavelength for a given metal surface.
`implies 1/2 mv^2 = h (c/(lambda) - c/(lambda_0))`
`1/2 mv^2 = hc (1/lambda - 1/(lambda_0))`
which is Einstein.s photoelectric equation in terms of wavelength.