The wave theory of light could not explain the phenomenon of

The correct answer is Option (4) → photoelectric effect of radiation

According to the wave theory, light energy is spread continuously over the wavefront. For the photoelectric effect this predicts that the kinetic energy of the electrons should grow with intensity, that light of any frequency should eject electrons if it is intense enough, and that there should be a time lag in weak light. Experiment shows the opposite: there is a threshold frequency, the maximum kinetic energy depends only on the frequency, and emission is instantaneous. The effect is explained only by the photon picture, in which each photon of energy \( h\nu \) is absorbed by a single electron. Interference, diffraction and rectilinear propagation are all explained by the wave theory.

Note: A similar question was also asked in CUET (UG) 2025 on 16-05-2025 (Slot 1), and in CUET (UG) 2023 on 07-06-2023 (Slot 3).

NCERT (2026-27):
Photoelectric Effect and Wave Theory of Light – “The wave nature of light was well established by the end of the nineteenth century. The phenomena of interference, diffraction and polarisation were explained in a natural and satisfactory way by the wave picture of light.”

Photoelectric Effect and Wave Theory of Light – “… In short, the wave picture is unable to explain the most basic features of photoelectric emission.”