Identify the correct statement according to Einstein's picture of photoelectric effect:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Maximum Kinetic Energy of electrons depends linearly on frequency of incident radiation.
Einstein's photoelectric equation says that one photon gives all its energy to one electron, and part of it is used to overcome the work function \( \phi_{0} \):
\( \displaystyle K_{\max} = h\nu - \phi_{0} \)
This is a straight line in \( \nu \) with slope \( h \), so \( K_{\max} \) depends linearly on frequency. The intensity only decides how many photons arrive per second.
Option (1) Maximum Kinetic Energy of electrons depends linearly on frequency of incident radiation. — Correct. \( K_{\max} = h\nu - \phi_{0} \) is a linear function of \( \nu \).
Option (2) Maximum Kinetic Energy of electrons depends linearly on intensity of incident radiation. — Incorrect. \( K_{\max} \) does not depend on intensity at all; more intensity means more photons, not more energy per photon.
Option (3) The photoelectric current is independent of intensity of incident radiation. — Incorrect. More photons per second release more electrons per second, so the photoelectric current is proportional to the intensity.
Option (4) Intensity of incident radiation is directly proportional to the frequency of radiation. — Incorrect. Intensity and frequency are independent; intensity depends on the number of photons per second per unit area, and frequency on the energy of each photon.
NCERT (2026-27):
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… In photoelectric effect, an electron absorbs a quantum of energy (hν) 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
\( \displaystyle K_{max} = h\nu - \phi_0 \qquad (11.2) \)”
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… According to Eq. (11.2), Kmax depends linearly on ν, and is independent of intensity of radiation, in agreement with observation.”