Photoelectric and summation of photons energy

[hokhani]

TL;DR

Why the photon energies don't get summed?

Classical electromagnetic field can't explain photoelectric effect since at any frequency, increasing the intensity only increases the photon number and don't increase the wave amplitude (as was thought in classical waves). Since photons don't have enough energy they can not excite electrons.
Here, I know that one photon can not excite an electron but how about a large number of photons radiating on one electron?

 

[PeroK]

There is no such thing as a photon in classical EM.

It's not just that the frequency of the light is the key factor. The dislocated electrons have a precise kinetic energy for each frequency. Where the KE is the difference between the photon energy (for a given frequency) and the energy to release the electron.

In the classical model, even if the electrons could be released by wave intensity, the KE would not be a precise value for a given frequency. The KE should depend on the intensity.

Both these factors (threshold energy and KE) show that the energy imparted to an electron depends only on the frequency of the light and not its intensity. This is not consistent with a classical wave model.

 

[hokhani]

show that the energy imparted to an electron depends only on the frequency of the light and not its intensity.

If I understood correctly, you mean that intensity is independent of frequency. Isn't it?