Can electrons "build up" energy? We're studying the photoelectric effect. My book says that according to the classical wave model, there is no reason for electron emissions to occur almost right after turning on the light source. It says the electron can "build up" energy until it has enough to leave. How does an electron build up energy? 
 A: In a classical model, the electromagnetic wave exerts an oscillating force on each electron. If the electrons can move freely along the surface of the metal, then they will simply oscillate too and fro and will not build up energy. However they also experience forces from the rest of the metal. At the frequencies concerned, these include slight restoring forces, so it is like a case of resonance. The size of the oscillation of the electrons can grow gradually, like the way the amplitude of a swing grows as you give it a little push on each oscillation. These oscillations are mostly along the surface, but they include a part in the in-out direction. The energy in the latter can thus build up and eventually a flow of electrons will come out, if the classical argument is right. What happens in practice is, of course, that this classical argument is largely wrong, because this is an experiment where the quantum nature of energy exchange is exhibited. The "energy build-up" I described is just an attempt to show what type of thing one might have expected in a classical treatment.
Usually such classical treatments are not completely wrong; they may for example capture the main facts about the 'classical limit.' The latter can occur when the discrete nature of energy exchange is not significant because the energy discreteness is small compared to other energies in the phenomenon.
The above was written purely based on my general knowledge of physics. Someone with expert knowledge of conductors and surface science might be able to give a better picture; I think the one I have given is roughly right. 
A: In the classical wave model of light, an electron can be considered of as being impacted by light wave. According to this model, the energy from the single light wave is not enough to cause an electron to emit from a metal surface. Instead, the electron must accumulate energy from many light waves over time in order to reach the threshold energy necessary to escape the metal's surface.
This buildup of energy is inconsistent with observed results and leads to the development of quantum mechanical theories of the photoelectric effect.
