Question

Using photon picture of light, show how Einstein's photoelectric equation can be established. Write two features of photoelectric effect which cannot be explained by wave theory.

Answer 1

Einstein explained the various laws of photoelectric emission on the basis of Planck's quantum theory. According to Planck's quantum theory, light radiations consist of tiny packets of energy called quanta. One quantum of light radiation is called a photon which travels with the speed of light.
The energy of a photon is given by,
$E=h\nu$
where h is Planck's constant and $\nu$ is the frequency of light radiation.
Einstein assumed that one photoelectron is ejected from a metal surface if one photon of suitable light radiation falls on it.
Consider a photon of light of frequency $\nu$, incident on a photosensitive metal surface. The energy of the photon (= h$\nu$) is spent in two ways :
(1) A part of the energy of the photon is used in liberating the electron from the metal surface which is equal to the work function ${\Phi }_0$ of the metal.
(2) The rest of the energy of the photon is used in imparting the maximum kinetic energy $K_{max}$. to the emitted photo electron.
If $v_{max}$ is the maximum velocity of the emitted photoelectron and m is its mass, then
Max. K.E. of the photoelectron,
$K_{max}=\frac{1}{2}m{v}_{max}^2$
$\therefore hv={\Phi }_0+\frac{1}{2}m{v}_{max}^2$
This equation is called Einstein's photoelectric equation.
Features of photoelecric effect which can not be explained by wave theory:
(i) The wave theory could not explain the instantaneous process of photoelectric effect.
(ii) It could not be explained why the photoelectric emission is independent of intensity.