For a photoelectric effect
(A) the photoelectric current is directly proportional to the intensity of the incident radiation.
(B) the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation.
(C) for a given frequency of the incident radiation, the stopping potential increases linearly with the intensity of the incident radiation.
(D) the photoelectric emission is an instantaneous process without any apparent time lag.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
For radiation above the threshold frequency, the number of photoelectrons per second is proportional to the number of photons per second, that is to the intensity. The maximum energy of each electron is fixed by the frequency (Einstein's photoelectric equation).
\( \displaystyle K_{\max} = h\nu - \phi_0, \qquad V_0 = \frac{h\nu - \phi_0}{e} \)
(A) the photoelectric current is directly proportional to the intensity of the incident radiation. — Correct. For a given frequency above the threshold, the saturation current is proportional to the intensity.
(B) the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation. — Correct. \( K_{\max} = h\nu - \phi_0 \) is a straight line in \( \nu \), with slope \( h \).
(C) for a given frequency of the incident radiation, the stopping potential increases linearly with the intensity of the incident radiation. — Incorrect. The stopping potential depends on the frequency and not on the intensity.
(D) the photoelectric emission is an instantaneous process without any apparent time lag. — Correct. The delay is about \( 10^{-9}\,\mathrm{s} \) or less, even for very dim light.
Statements (A), (B) and (D) are correct, which is Option (1).
NCERT (2026-27):
Effect of Frequency of Incident Radiation on Stopping Potential – “… (i) For a given photosensitive material and frequency of incident radiation (above the threshold frequency), the photoelectric current is directly proportional to the intensity of incident light (Fig. 11.2).”
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).”
Effect of Frequency of Incident Radiation on Stopping Potential – “… (iv) The photoelectric emission is an instantaneous process without any apparent time lag (~10–9s or less), even when the incident radiation is made exceedingly dim.”