Read the following passage and answer the questions.
A student studies a photocell. It is an evacuated glass tube with a quartz window. Inside the tube are an emitter plate C and a collector plate A. Plate C is coated with a metal that gives out electrons even in red light. A battery and a commutator let her make plate A positive or negative with respect to C. A microammeter reads the photocurrent.
In the first run, she shines a red laser pointer on plate C. The light has a wavelength of 620 nm, and the pointer gives out a power of 2.4 mW. She records the photocurrent as she changes the potential of A from positive to negative values. In the second run, she uses a red laser of the same wavelength but twice the power. In the third run, she uses a violet laser of wavelength 410 nm. She adjusts it so that the same number of photons reach plate C each second as in the first run.
(Take \(hc = 1240\ \mathrm{eV\,nm}\) and \(1\ \mathrm{eV} = 1.6\times10^{-19}\ \mathrm{J}\).)
How does the graph of photocurrent against collector potential in the third run compare with that in the first run?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → The stopping potential is more negative, and the saturation current is the same.
Violet light of wavelength 410 nm has a higher frequency than red light of 620 nm. In the third run only the frequency changes. The same number of photons reaches plate C each second as in the first run.
Option (1) The stopping potential is the same, but the saturation current is larger. — Incorrect. The stopping potential depends on the frequency of the light, and the frequency has changed. The same number of photons each second gives the same number of photoelectrons, so the saturation current does not grow either.
Option (2) The stopping potential is more negative, and the saturation current is the same. — Correct. Each violet photon has more energy, so the fastest photoelectrons leave C with more kinetic energy. A larger retarding potential is needed to stop them. The same number of photons each second frees the same number of photoelectrons. So the saturation current stays the same, as the curves below show.
Option (3) The stopping potential is less negative, and the saturation current is the same. — Incorrect. A less negative stopping potential would need light of a lower frequency, that is, a wavelength longer than 620 nm.
Option (4) Both the stopping potential and the saturation current are the same. — Incorrect. Only the saturation current stays the same. The violet curve meets the potential axis farther on the negative side.
NCERT (2026-27):
Effect of frequency of incident radiation on stopping potential – “… We obtain different values of stopping potential but the same value of the saturation current for incident radiation of different frequencies. The energy of the emitted electrons depends on the frequency of the incident radiations. The stopping potential is more negative for higher frequencies of incident radiation.”
