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

Light is an electromagnetic wave.

According to wave theory,  electrons on the surface of metal continuously absorbs the radiant energy. Greater the intensity greater is the amplitude of the electric and magnetic field of the wave. So the maximum kinetic energy of photoelectron is expected to increase with an increase in the intensity. Whatever the frequency of the incident wave, if the wave has sufficient intensity to impart enough energy for electron emission from the metal surface the electron should come out of the metal. This contradicts the observation that a minimum frequency is required for the photoelectric effect.

In the wave picture, the absorption of energy by electron takes place continuously over the entire wavefront of radiation. Since a large number of electrons absorbs the energy, the energy absorbed by an electron per unit time is small and it takes hours to pick up energy to overcome the work function of the metal. This is in contradiction to the observation that the photoelectric emission is instantaneous. So the wave theory fails to explain the photoelectric effect.

According to the photon picture of light if the energy of the photon exceeds the threshold frequency required to emit the electron from the metal surface, then the electron is emitted instantaneously with maximum kinetic energy.

$\\K_{max}=h\nu-\phi_{0}\\$

$\nu$ is the frequency of incident light and

$\phi_{0}$ is the work function.

This shows that there is a minimum frequency for which photoelectric emission takes place and the emission is instantaneous at this frequency. And also kinetic energy is proportional to the frequency of incident radiation. This is true according to the experimental observation of the photoelectric effect.

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