Show that wave theory cannot explain fundamental characteristics of photoelectric effect.

(N/A) Light is an electromagnetic wave consisting of oscillating electric and magnetic fields. Phenomena like interference,diffraction,and polarization are explained well by the wave theory.
According to the wave theory,when light is incident on a metal surface,free electrons absorb radiant energy continuously. As the intensity of incident radiation increases,the amplitude of the electric and magnetic fields increases,leading to more energy absorption by the electrons.
Consequently,the wave theory predicts that the maximum kinetic energy of emitted electrons should increase with the intensity of light. Furthermore,it suggests that a sufficiently intense beam of any frequency should be able to eject electrons,implying that no threshold frequency should exist.
These predictions contradict experimental results. Experiments show that maximum kinetic energy is independent of intensity and that a threshold frequency is required for emission.
Additionally,the wave theory suggests that energy absorption occurs continuously over the wavefront. Since energy is spread over a large number of electrons,the energy absorbed per electron is very small. Calculations estimate that it would take hours for an electron to accumulate enough energy to escape. However,experiments show that electron emission is instantaneous,occurring within $10^{-9} \,s$.
Thus,the wave theory fails to explain the fundamental characteristics of the photoelectric effect.