Why is wave theory of electromagnetic radiation not able to explain photo electric effect? How does photon picture resolve this problem?

It was experimentally observed that below a certain threshold frequency, no photoelectrons were emitted. It was also observed that the maximum kinetic energy of the electrons varied linearly with the frequency of radiation and was independent of intensity of incoming radiation. There was no time lag between when the photon is absorbed and when the photoelectron is emitted. Increasing the intensity increased the photocurrent.

The wave theory predicts that the electrons would absorb the energy continuously. The greater the intensity, the greater the energy per unit area. Thus, greater should be the kinetic energy of the electrons emitted. However, this is not the case. Moreover, after a period of time, enough energy should be absorbed to eject the electron. Thus, threshold frequency should not exist.

In the photon picture, each electron absorbs one photon. If the frequency is high enough, then the energy of the photon () is enough to eject the electron. By conservation of energy,

where W₀ is the minimum energy required to free the electron. We can see that as the frequency increases, the maximum kinetic energy increases, in agreement with experimental results. Also, as intensity increases, the number of photons per unit area increase and so does the emitted photoelectrons; this results into increase in photocurrent.

Thus, the wave theory of light fails to explain the photoelectric effect whereas the photon picture of light is able to explain this effect.