Question

The retarding potential for having zero photo-electron current
A. Is proportional to the wavelength of incident light
B. Increases uniformly with the increase in the wavelength of incident light
C. Is proportional to the frequency of incident light
D. Increases uniformly with the increase in the frequency of incident light

Answer 1

Hint: Retarding potential or stopping potential is the potential that is applied in the photoelectric circuit to stop the ejection of electrons from the metal. The direction of retarding potential is opposite to the direction of the flow of current and reduces the kinetic energy of electrons to a point where they can’t leave the metal surface.

Formula used:
The expression of kinetic energy of the emitted electron is,
\[K.E = E - W\]
Here, $E$ is the energy of the incident radiation and $W$ is the work function of a metal.
The expression of stopping potential is,
\[e{V_0} = h\left( {\nu - {\nu _0}} \right)\]
Here, ${V_0}$ is the stopping potential, $\nu _0$ is the threshold frequency and $\nu$ is the frequency of incident radiation.

Complete step by step solution:
As we know that the kinetic energy of the emitted electron is,
\[K.E = E - W\]
Work function is a constant for a given material.
We can write the above equation as,
\[K.E = h\nu - h{\nu _0}\]
\[\Rightarrow K.E = h\left( {\nu - {\nu _0}} \right)\]

Suppose if we provide the negative potential, then the kinetic energy will become zero and the photo-electron will stop leading to zero current. Then,
\[e{V_0} = h\left( {\nu - {\nu _0}} \right)\]
Here, \[{V_0}\] is the retarding potential.
\[{V_0} = \dfrac{{h\left( {\nu - {\nu _0}} \right)}}{e}\]
So, this is the equation of the retarding potential. If we can see the above equation, as the frequency changes uniformly the retarding potential also varies. Since the wavelength and frequency are inversely proportional, the other three options are not applicable.

Hence, Option D is the correct answer.

Note:The kinetic energy of the electrons becomes zero at the stopping potential. Therefore, at this potential, the electron with the highest value of Kinetic energy will also stop, which is used to calculate the maximum kinetic energy of a photoelectron.