JEE Physics 2023 Question with Solution

Given: Two statements about the photoelectric effect are to be checked.

Find: Which option correctly identifies the truth values of Statement I and Statement II.

For photoelectric effect, the stopping potential is related to the maximum kinetic energy by

Also, for a given metal,

where $\lambda$ is the wavelength of incident light and $\phi$ is the work function.

From these relations, stopping potential depends on $KE_{\text{max}}$ and hence on the frequency or wavelength of the incident light, not on the intensity or power of the light source. Therefore, Statement I is correct.

Since

the maximum kinetic energy clearly depends on the wavelength of the incident light for a given metal. Therefore, Statement II is also correct.

Hence, both Statement I and Statement II are correct. The correct option is D.

The solution shows one approach incorrectly labels the option as C, but the working and the second approach both conclude that both statements are true. Therefore the defensible answer is D.

Given: The question asks whether stopping potential depends on power of source and whether maximum kinetic energy depends on wavelength.

Find: The correct combination of truth values.

Einstein photoelectric equation is

The stopping potential is defined through

so that

Thus, $V_s$ depends on the energy of incident photons, that is on $\nu$ or equivalently on $\lambda$. Changing intensity or power changes the number of emitted electrons, not the maximum kinetic energy. So Statement I is true.

For a fixed metal, $\phi$ is constant. Therefore changing $\lambda$ changes

and hence changes $KE_{\text{max}}$. So Statement II is true.

Therefore, both statements are true, so the correct option is D.