Certain characteristics of photoelectric effect cannot be explained by classical wave theory.
Photoelectrons are emitted only when irradiated by light waves of certain frequency. The greater the frequency of light wave used, the greater the kinetic energy of the photoelectrons. But according to classical wave theory, photoelectrons can be emitted by a light wave of any frequency as the energy of the light wave is independent of its frequency.
A minimum frequency called threshold frequency is needed to emit photoelectrons from a certain metal surface. Different metals have different values of threshold frequency. Classical wave theory cannot explain why photoelectrons are not emitted for low frequency light waves.
Kinetic energy of the photoelectrons is not affected by the intensity of light wave used. But according to classical wave theory, light wave of greater intensity has greater energy, hence can emit photoelectrons with higher kinetic energy.
The emission of photoelectrons is instantaneous when metal surface is irradiated by a light wave of frequency higher than the threshold frequency. But according to classical wave theory, electrons take time to absorb energy from the light wave, hence there is a time interval between irradiation and emission.