Expected observation if one assumes that light is a wave instead of a particle in the photoelectric effect For the purpose of this question I am pretending that I have not conducted a photoelectric effect experiment yet and I don't know what the outcome of the experiment will be. My questions are about the expected consequences if one assumes that light is a wave and not a particle (which we all know was not the result of this experiment).

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*A sinusoidal wave is non-localised. A metal target that absorbs a light wave should absorb that energy over a non-zero time interval since the wave is spread out over a non-zero length of space. This suggests that you should be able to liberate electrons from a target if you shine a low-energy wavelength of light onto a target (with energy significantly below the work function) by simply waiting long enough until enough energy is absorbed by the target.


*Often it is stated that increasing the intensity of a low-energy wavelength light is sufficient to allow photoelectrons to be liberated from the metal if light is a wave.
My questions are:
Is my reasoning for 1. correct that you would expect that shining a low-energy color of light should allow electrons to be liberated from a metal if one simply waits long enough until enough energy is absorbed by the metal?
I don't understand the reasoning behind 2. Increasing the intensity of a source of light increases the number of light waves from your source (the lamp in the experiment), but shouldn't one can expect that each of these light waves will strike a different spot on the metal. Therefore increasing the intensity should liberate more electrons due to more spots on the metal receiving light, but I don't see why increasing the intensity should immediately cause photoelectrons to become liberated (unless all the additional light waves happen to strike the exact same spot on the metal when the intensity is increased).
 A: By assuming light is a wave and not a particle, are you assuming classical physics is correct? There are no photons?
If so, your point 1) is right. That was one of the mysteries of the photoelectric effect that was hard to explain classically. A light of low intensity absorbed by a metal should add energy to the metal slowly. Eventually there should be enough to eject electrons.
However, what was observed was the electrons were never ejected for low frequency light, or they were ejected within a nanosecond or so for higher frequency. Thinking classically, this mean that the energy that was deposited uniformly over the surface of the metal was somehow concentrated very quickly onto a single electron. It was difficult to imagine a process that would do this.
For 2), again thinking classically, a wave deposits energy in proportion to its intensity. If the wave is spread over the surface and is low intensity, energy should continuously be added to the metal. You might expect the energy to stay spread out. If so, the energy near any particular atom increases slowly. But eventually it does increase to a level that might eject an electron.
Of course, things did not turn out as classical thoughts would lead one to expect.
A: We could make an analogy with sound waves to understand what is the classical outcome. If we are hit by a very loud noise, we can damage our ears, no mater it has low (like an explosion) or high pitch.
But being exposed to a low intensity sound for a long time is not dangerous. It is what we experience in our normal life.
So I think that the picture described in (2) is the correct one for a classical description.
