Question

The stopping potential of a metal surface is independent of:
(A). Frequency of incident radiation
(B). Intensity of incident radiation
(C). The nature of the metal surface
(D). Velocity of the electrons emitted

Answer 1

Hint – In this question use the Einstein’s equation of photoelectric effect that is K.E =$h\nu - W$, then use the concept that kinetic energy is given as $K.E = e{v_o}$ where ${v_o}$ is the stopping potential. Separate terms to get stopping potential solemnly at the left-hand side and thus check for the factors onto which the stopping potential depends, this will help approaching the problem.

Formula used: K.E. =$h\nu - W$, $K.E = e{v_o}$

Complete step-by-step solution -
As we all know the Einstein’s equation of photoelectric effect which is given as,
K.E =$h\nu - W$.............. (1)
Kinetic energy of any particle is half times the multiplication of the mass of the particle and the square of the velocity of the particle.
Therefore, $\dfrac{1}{2}mv_{\max }^2 = h\nu - W$................ (2), [$\because $K.E = $\dfrac{1}{2}mv_{\max }^2$]
Where, K.E = kinetic energy of the electrons.
               m = mass of the electrons
                v = maximum velocity of the emitted electrons
                $\nu $ = frequency of the incident radiation
                h = Plank’s constant
                W = work function of the metal.
Now the stopping potential kinetic energy is given as
$K.E = e{v_o}$.................... (3), where e = charge on an electron = 1.6$ \times {10^{ - 19}}eV$ and ${v_o}$ = stopping potential.
Now from equation (1) and (3) we have,
$ \Rightarrow e{v_o} = h\nu - W$
Now divide by e throughout we have,
\[ \Rightarrow {v_o} = \dfrac{{h\nu - W}}{e}\]...................... (4)
Now from equation (2) and (4)
Stopping potential is dependent on
$\left( i \right)$ Frequency of the incident radiation i.e. $\nu $
$\left( {ii} \right)$ Nature of the metal surface i.e. work function of the metal W.
$\left( {iii} \right)$ Velocity of the electrons emitted i.e. ${v_{\max }}$
Stopping potential is independent of
$\left( i \right)$ Intensity of the incident radiation.
So this is the required answer.
Hence option (B) is the required answer.

Note – When light or photons are incident over a metallic surface electrons are emitted out, but however this emission depends upon the intensity of the photons bombarding the metal's work function is defined as the minimum energy that is required to eject an electron from the metal surface, moreover stopping potential refers to the difference in the potential that is required to stop the electrons moving between the plates of the metal, and thus preventing current flow in metals.