The experimental set-up used for the photoelectric effect is shown. It consists of an evacuated glass/quartz tube having a thin photosensitive plate C and another metal plate A. Light from the source S of sufficiently short wavelength passes through the quartz window and falls on the photosensitive plate C (emitter). The electrons emitted by the plate C are collected by the plate A (collector) by the electric field created by the battery. The battery maintains the potential difference between the plates C and A, which can be varied. Thus, the plate A can be maintained at a desired positive or negative potential with respect to the emitter C. When the collector plate A is positive with respect to the emitter plate C, the electrons are attracted to it. The emission of electrons causes a flow of electric current in the circuit, called the photoelectric current.
How does the stopping potential vary with the frequency of the incident radiation?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → linearly
The stopping potential \( V_0 \) stops the most energetic photoelectrons, so \( eV_0=K_{\mathrm{max}} \). With Einstein’s photoelectric equation \( K_{\mathrm{max}}=h\nu-\phi_0 \), this gives, for \( \nu\ge\nu_0 \),
\( \displaystyle V_0=\frac{h}{e}\,\nu-\frac{\phi_0}{e} \)
Option (1) linearly — Correct. \( V_0 \) against \( \nu \) is a straight line of slope \( h/e \), so above the threshold frequency the stopping potential rises linearly with the frequency.
Option (2) inversely — Incorrect. A higher frequency gives each photon more energy \( h\nu \). So the stopping potential increases with frequency.
Option (3) as its square — Incorrect. The photon energy \( h\nu \) is proportional to \( \nu \) itself, so \( V_0 \) has no \( \nu^{2} \) term.
Option (4) it does not depend on the frequency — Incorrect. The stopping potential does not depend on the intensity of the light. But it does depend on the frequency, and it grows with \( \nu \) above the threshold.
NCERT (2026-27):
Effect of Frequency of Incident Radiation on Stopping Potential – “The graph shows that (i) the stopping potential V0 varies linearly with the frequency of incident radiation for a given photosensitive material.”