In a photoelectric experiment, the collector plate is made more and more negative with respect to the emitter plate. The photocurrent becomes zero when this potential reaches a value \(V\). If \(K\) is the maximum kinetic energy of the emitted photoelectrons and \(e\) is the electronic charge, which of the following is correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(K = eV\)
When the collector is negative, it repels the photoelectrons. Only the electrons with enough kinetic energy can still reach it. In moving against a potential \( V \), an electron loses kinetic energy \( eV \). The current falls to zero when even the fastest electron is just stopped.
Option (1) \(K \gt eV\) — Incorrect. The fastest electrons would still have energy left at the collector. They would reach it, and the current would not be zero at \( V \).
Option (2) \(K \lt eV\) — Incorrect. Then all electrons would already be stopped at a smaller potential. The current would become zero before the potential reaches \( V \).
Option (3) \(K = eV\) — Correct. At the stopping potential the most energetic electron just fails to reach the collector. Its whole kinetic energy is used up against the field, so \( K=eV \).
Option (4) \(0 \lt K \lt eV\) — Incorrect. Every value in this range is below \( eV \). With such energies, the current would stop at a retarding potential lower than \( V \).
NCERT (2026-27):
Effect of potential on photoelectric current – “Photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons, with the maximum kinetic energy (Kmax), so that”
\( K_{max}=eV_0 \)\( \qquad (11.1) \)