Match List-I with List-II in the context of the phenomenon of photoelectric effect. Frequency of incident radiation \( = \nu \) and threshold frequency \( = \nu_{0} \)
| LIST-I | LIST-II | ||
|---|---|---|---|
| A. | Maximum kinetic energy of photoelectrons | I. | Zero |
| B. | Photoelectric current for \( \nu \gt \nu_{0} \) | II. | proportional to \( \nu \) |
| C. | Momentum of a photon | III. | depends linearly on \( \nu \) |
| D. | Photoelectric current for \( \nu \lt \nu_{0} \) | IV. | proportional to intensity of incident radiation |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-III, B-IV, C-II, D-I
Use Einstein’s photoelectric equation \( K_{\max} = h\nu - h\nu_0 \) and the photon momentum \( p = h\nu/c \).
(A) Maximum kinetic energy of photoelectrons — this matches (III) depends linearly on \( \nu \). It is a straight line in \( \nu \) but not proportional to \( \nu \), being zero at \( \nu = \nu_0 \).
(B) Photoelectric current for \( \nu \gt \nu_0 \) — this matches (IV) proportional to intensity of incident radiation. Above the threshold, electrons emitted per second are proportional to photons arriving per second.
(C) Momentum of a photon — this matches (II) proportional to \( \nu \). \( p = E/c = h\nu/c \).
(D) Photoelectric current for \( \nu \lt \nu_0 \) — this matches (I) Zero. Below the threshold frequency no electron is emitted, however intense the radiation.
Note: In List-II, (III) “depends linearly on \( \nu \)” also fits (C), because a quantity proportional to \( \nu \) also depends linearly on \( \nu \); so (C) fits both (II) and (III). The question can still be solved because (A) fits only (III), as \( K_{\max} \) is not proportional to \( \nu \), and (D) fits only (I); Option (2) is the only option that contains both A-III and D-I.
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 – “… (iii) For a given photosensitive material, there exists a certain minimum cut-off frequency of the incident radiation, called the threshold frequency, below which no emission of photoelectrons takes place, no matter how intense the incident light is. 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).”
Wave Nature of Matter – “… For a photon, as we have seen,
\( \displaystyle p = h\nu/c \qquad (11.6) \)”