1. explain how Einstein's photoelectric equation enables us to understand the :- a) linear dependence,of the maximum kinetic energy of the emitted electrons,on the frequency of the incident radiation. b) existence of a threshold frequency for a given photoemitter.

Hi,

Let a monochromatic light of frequency ν be incident on the surface of a photoelectric cell of work function Ø. The energy of a photon in the light is, E = hν. When a photon strikes a free electron the surface of the cell, the electron gets an extra energy E = hν and may come out of the metal. The electron trying to escape the surface will be attracted by the surface with a force equal to Ø. So, the maximum KE of the electron is given by,

KE = hν – Ø

This equation is called Einstein’s photoelectric equation.

 

(a) For a particular metal surface, the work function (Ø) remains constant. Increasing the frequency of the light will increase the maximum KE of the emitted electron. This is the kind of graph we obtain when we plot KE versus frequency of light.

The graph is a straight line with a positive slope. This explains the linear dependence of maximum KE of the emitted electrons on the frequency of the incident radiation.

 

(b) The KE of the electron is zero where the graph intersects the frequency axis. Let, ν₀ be the corresponding frequency for this point.

So, the photoelectric equation for this point is,

0 = hν₀ – Ø

=> hν₀ = Ø

=> ν₀ = Ø/h

Thus, there is a minimum frequency ν₀ for which the electron just leaves the metal surface with zero KE. This frequency is called ‘Threshold frequency’ of that particular photoemitter.