Question about the Photoelectric Effect and the Work Function of a Metal

[ParsaEF]

TL;DR

A question about the quantum theory of the photoelectric effect

By the results of the photoelectric effect experiment, the photoelectric effect does not occur at all if the frequency of the light source is below a certain value.

We have the Work Function for a metal. Why when the energy of the photons of the light source is W/2, we don't have the photoelectric effect when two photons hit one electron? because I think that the energy of the photons will be absorbed by electrons anyway, no matter what is the Work Function. so when the photon's energy is less than the Work Function, it just absorbs the energy but they don't get emitted from the surface.

If it absorbes the photon of W/2, it just need W/2 more energy to get emitted. and this energy will be given to it by the next photon and then it has enough energy to get emitted.

 

[Vanadium 50]

A metal is not a bank. It does not store energy, waiting for the right moment where it finally has enough to eject an electron.

 

[PeterDonis]

I think that the energy of the photons will be absorbed by electrons anyway

You are assuming that there are available states for the electrons to go to when they absorb any amount of energy. But that's not correct. Bound states of electrons are quantized; there are only specific energies that are available. For the case of electrons in a metal, the electrons that the photoelectric effect ejects are in the conduction band, so there are no states of higher energy available that are still bound. So either an electron absorbs enough energy to be ejected from the metal (and the minimum energy for that to happen is the Work Funcfion energy), or it can't absorb any energy at all.

 

[Steve4Physics]

I believe that the two-photon photoelectric effect (PEE) is possible under the right conditions. But the probability is very low (typically several orders of magnitude smaller than single-photon PEE).

I don’t understand the details but this might help: https://chem.libretexts.org/Bookshe...Electronic_Spectroscopy/Two-photon_absorption

A similar process is used in two-photon photoelectron spectroscopy, e.g. see here.
EDIT: But, as noted by @PeterDonis in Post #5, in this case the photon absorptions are sequential rather than simultaneous.

 

[PeterDonis]

the two-photon photoelectric effect

As you note, the probability of this is very low. More pertinent to this discussion, however, is the fact that this process involves two photons being absorbed simultaneously, not sequentially. So it is not an example of the kind of process the OP is asking about.

 

[Steve4Physics]

As you note, the probability of this is very low. More pertinent to this discussion, however, is the fact that this process involves two photons being absorbed simultaneously, not sequentially. So it is not an example of the kind of process the OP is asking about.

Yes indeed. That's why I used the word 'similar'.