Choose the correct statements among the following
(A) Photo electron emission from a photo-sensitive surface is possible only if the incident radiation has a frequency above the threshold frequency.
(B) The maximum kinetic energy of the photoelectrons in a photoelectric effect varies linearly with the intensity of incident radiation.
(C) An electron and a proton are accelerated through the same potential. The momentum associated with the electron is lesser as compared to the proton.
(D) An electron and a proton have the same de-Broglie wavelength. The proton has a higher kinetic energy than the electron.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (C) only
Use Einstein’s photoelectric equation, \( K_{\max} = h\nu - \phi_0 \), and the momentum–energy relation \( p = \sqrt{2mK} \).
(A) Photo electron emission from a photo-sensitive surface is possible only if the incident radiation has a frequency above the threshold frequency. — Correct. Below the threshold frequency a photon cannot free an electron, however intense the light.
(B) The maximum kinetic energy of the photoelectrons in a photoelectric effect varies linearly with the intensity of incident radiation. — Incorrect. \( K_{\max} \) depends on the frequency; intensity changes only the photocurrent.
(C) An electron and a proton are accelerated through the same potential. The momentum associated with the electron is lesser as compared to the proton. — Correct. Both gain the same energy eV, and \( p = \sqrt{2meV} \) is smaller for the lighter electron.
(D) An electron and a proton have the same de-Broglie wavelength. The proton has a higher kinetic energy than the electron. — Incorrect. Since \( \lambda = h/p \), equal wavelengths mean equal momenta, and \( K = p^{2}/2m \) is larger for the lighter particle, so the electron has the higher kinetic energy.
Note: Statements (A) and (B), and the de Broglie relation λ = h/p used in (D), are from the latest textbook (2026-27). The relation p = √(2mK) for a particle accelerated through a potential, needed for (C) and (D), is printed only in the pre-rationalised textbook (2022-23). It was removed from the latest book, but matter waves and the de Broglie relation are still in the CUET 2026 syllabus, so do not skip it.
NCERT (2026-27):
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 – “… De Broglie proposed that the wave length \( \lambda \) associated with a particle of momentum p is given as
\( \displaystyle \lambda = \frac{h}{p} = \frac{h}{mv} \qquad (11.5) \)”
NCERT (Pre-rationalised edition, 2022-23):
Wave Nature of Matter – “… Consider an electron (mass m, charge e) accelerated from rest through a potential V. The kinetic energy K of the electron equals the work done (eV) on it by the electric field:
\( \displaystyle K = eV \qquad (11.8) \)
Now,
\( \displaystyle K = \frac{1}{2}mv^{2} = \frac{p^{2}}{2m}, \text{ so that } p = \sqrt{2mK} = \sqrt{2meV} \qquad (11.9) \)”