Question

(a) Write the important properties of photons which are used to establish Einstein's photoelectric equation.
(b) Use this equation to explain the concept of (i) threshold frequency and (ii) stopping potential.

Answer 1

(a)The important properties of photons which are used to establish Einstein’s photoelectric equation is that in interaction of radiation with matter, radiation behaves as if it is made up of particles called photons.
All photons of light of a particular frequency $\lambda$ or wavelength $A$ have the same energy
$E=hf$ and momentum $p=\frac{hf}{c}$
whatever the intensity of radiation may be.

(b) Einstein's photoelectric equation states that:

$E_{max}=hf-\varphi$

(i) If $E_{max}>0$ then $hf-\varphi >0$

or $hf-h{f}_0>0$

Here, $f_0$ is the threshold frequency.

For a given material, there exist a certain minimum frequency of the incident radiation, below which no emission of photoelectron takes place. This frequency is called threshold frequency. Above this threshold frequency, the maximum kinetic energy of the emitted photoelectron or equivalent stopping potential is independent of the intensity of the incident light but depends only upon the frequency of the incident light.

(ii) Again, loss in KE = gain in electromagnetic PE.

or $E_{max}=e{V}_s$

Where $V_s$ represents the stopping potential.

If the collecting plate in the photoelectric apparatus is kept at a high negative potential, then most of the high energetic electrons get repelled back along the same path and the photoelectric current in the circuit becomes zero. So, for a particular frequency of incident radiation, the minimum negative potential for which the electric current becomes zero is called cut-off or stopping potential.