Argthtjtr

I got this question on a test and the answer key states that the answer is 'Yes'. According to what I understand electrons are emmitted with different kinetic energies based upon their depth from the metal surface i.e. an electron would come out with a lesser kinetic energy if it was situated deeper as it would have to go through more collisions. This reasoning contradicts the given answer. I would like to know if my reasoning is correct.

It is somewhat matter of what precisely one would refer to as photoelectric effect.

As far as the radiation-electron mechanism of transfer of energy, there is no direct role played by surface. However, referring to the Einsten's formula;
$$
h f = Phi + K,
$$
where $K$ is the maximum kinetic energy of the photoelectron, $f$ the frequency of the incoming radiation, and $Phi$ the work-function of the metal, it is true that the latter term is depending on the surface and its detailed structure, presence of impurities and so on. In this sense, there is a clear surface effect.

I would say that photoemission is not a surface effect, not normally. Your understanding is correct.

That said, there is also "surface photoemission" due to the $vec{p} cdot vec{A}$ term in the Hamiltonian and symmetry breaking at the surface. As an example, see this paper about silver.

If there is a sizable probability that a photon frees an electron, Notably a conduction electron, then it is implied that there is a sizeable extinction coefficient or imaginary part of the refractive index. Thus means that the photon cannot penetrant deep into the material and is emitted from near the surface. To call it a surface effect however implies that the characteristics of the surface, such as surface states, are enabling. I don't believe that this is the case. In principle a photon could travel into the bulk, set an electron free and this could escape from the bulk. It is not likely but nothing prevents this. I would therefore not qualify photo emission as a surface effect.

There is a concept of free electrons which says that the electrons in outer most shell are under very weak influence of the nucleus and move freely across the metal surface, whereas those near the nucleus are bound by strong nuclear force(higher than the detaching ability of photons) inhibiting them to be able to freely move across the surface. This is how surface phenomenon comes into picture.

With, frequency of light being capable of causing electron emission, the other factor for emission of electron count is the intensity of light. More the intensity of light, more the number of photons striking the metal surface and higher is the electron emission.