Question

Write Einstein's photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation.
Write the three salient features observed in photoelectric effect which can be explained using this equation.

Answer 1

Einstein’s photoelectric equation,

$K_{max}=h\nu -{\varphi }_0$ where

$K_{max}$ is the max kinetic energy of emitted electrons and ${\varphi }_0$ is the work function.

According to Planck’s quantum theory, light radiations consist of small packets of energy. Einstein postulated that a photon of energy hv is absorbed by the electron of the metal surface, then the energy is used to liberate electron from the surface and rest of the energybecomes the kinetic energy of the electron.

Energy of photon is,

$E=hv$

Where, h = Planck’s constant

v = frequency of light

The minimum energy required by the electron of a material to escape out of it, is work function.

The additional energy acquired by the electron appears as the maximum kinetic energy ‘K_max’ of the electron.

Einstein's photoelectric equation

$K_{max}=e{V}_o$

Salient features observed in photoelectric effect: —

The stopping potential and hence the maximum kinetic energy of emitted electrons varies linearly with the frequency of incident radiation.

There exists a minimum cut - off frequency, for which the stopping potential is zero.

Photoelectric emission is instantaneous.