For a given photosensitive material, the stopping potential \( V_0 \) varies with the frequency of incident radiation as
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → linearly with frequency
Einstein's photoelectric equation gives the stopping potential in terms of the frequency \( \nu \) and the work function \( \phi_0 \):
\( \displaystyle eV_0 = h\nu - \phi_0 \;\Rightarrow\; V_0 = \frac{h}{e}\,\nu - \frac{\phi_0}{e} \)
This is a straight line of slope \( h/e \) (the same for every material), for frequencies above the threshold frequency.
Option (1) inversely proportional to frequency — Incorrect. \( V_0 \) increases as \( \nu \) increases.
Option (2) linearly with frequency — Correct. \( V_0 \) is a linear function of \( \nu \). It is not directly proportional, because the line does not pass through the origin.
Option (3) independent of frequency — Incorrect. \( V_0 \) depends on the frequency; it is the intensity of the radiation on which it does not depend.
Option (4) exponentially with frequency — Incorrect. The dependence is linear, not exponential.
NCERT (2026-27):
Effect of Frequency of Incident Radiation on Stopping Potential – “… Above the threshold frequency, the stopping potential or equivalently the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of its intensity (Fig. 11.5).”