Photons of frequency \( \nu \) fall on a metal surface for which the threshold frequency is \( \nu_0 \). Then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → the ejected electrons have a distribution of kinetic energy from zero to \( h(\nu-\nu_0) \)
By Einstein’s photoelectric equation, an electron that absorbs a photon \( h\nu \) leaves with at most \( K_{\mathrm{max}}=h\nu-\phi_0 \). Since the work function is \( \phi_0=h\nu_0 \), this maximum is \( h(\nu-\nu_0) \).
Option (1) all the ejected electrons have the same kinetic energy \( h(\nu-\nu_0) \) — Incorrect. \( h(\nu-\nu_0) \) is only the maximum. Electrons that are more tightly bound lose more energy in escaping and come out slower.
Option (2) the ejected electrons have a distribution of kinetic energy from zero to \( h(\nu-\nu_0) \) — Correct. The least tightly bound electrons come out with the maximum kinetic energy \( h(\nu-\nu_0) \). More tightly bound electrons come out with less, down to almost zero. So the kinetic energies are spread over this whole range.
Option (3) the most energetic electrons have kinetic energy \( h\nu \) — Incorrect. \( h\nu \) is the whole photon energy. At least \( \phi_0=h\nu_0 \) of it is used up in escaping, so even the fastest electrons have only \( h(\nu-\nu_0) \).
Option (4) the average kinetic energy of the ejected electrons is \( h\nu_0 \) — Incorrect. \( h\nu_0 \) is the work function, the energy needed to escape from the surface. It is not the kinetic energy of the emitted electrons. Their average lies below \( h(\nu-\nu_0) \).
NCERT (2026-27):
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… If this quantum of energy absorbed exceeds the minimum energy needed for the electron to escape from the metal surface (work function φ0), the electron is emitted with maximum kinetic energy
\( K_{\mathrm{max}}=h\nu-\phi_0 \qquad (11.2) \)
More tightly bound electrons will emerge with kinetic energies less than the maximum value.”
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… Thus, there exists a threshold frequency ν0 (= φ0/h) for the metal surface, below which no photoelectric emission is possible, no matter how intense the incident radiation may be or how long it falls on the surface.”