Why should the electron's energy knocked out be dependent on the intensity of the light? I know according to the photelectric effect this is not true , but the belief that it should be according to classical physics ? , could someone explain the approach of what classical physics 's hypothesis was ?
 A: The energy carried by the classical electromagnetic wave is given by the Poynting vector

Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric field E and the magnetic field B

This leads to the expression for the  Poynting vector

The higher the intensity in the classical wave description, the bigger the electric field depicting the wave, and the larger the energy transported by the wave. The lower the intensity the less energy the electron should get, if it were a classical scattering.
A: Exposure of a metallic surface by light knocks electrons out of the surface at an electric potential difference. The surprising thing was that the intensity of the photoelectric current periodically increased and decreased depending on the wavelength of the light. This was described as early as 1887 by Hertz and Hallwachs.
Einstein's hypothesis was now that light consists of quanta, later called photons. Light is not a wave, but a stream of photons, which have a periodically oscillating electric and a magnetic field component and transport energy in packets. The electrons can leave the atom that binds them only if they absorb photons of certain energy content.
Planck had unexpectedly come up with quantization of radiation in explaining blackbody radiation. He considered his results as pure calculation not relevant for Newton's hypothesis that light consists of corpuscles. At first, he was also skeptical of Einstein's hypothesis.
However, the quantum hypothesis turned out to be verifiable. Thus, the emission spectra of chemical elements could be recognized as the discrete emission of photons from excited electrons as they relax in the atom.
