How do you calculate the time to emission of an electron from a metal given the incident radiation?

Question

Here's the question:

A monochromatic point source of light radiates 25 W at a wavelength of 5000 angstroms. A plate of metal is placed 100 cm from the source. Atoms in the metal have a radius of 1 angstrom. Assume that the atom can continually absorb light. The work function of the metal is 4 eV. How long is it before an electron is emitted from the metal?

My attempt at an answer. I used the 100 cm placement away from the source for the radius and put that in to $4\pi r^2$ to get the total surface area. Divided the energy of the source by the total surface area. Multiplied that by the square of the atom spacing to get how much energy per sec was falling on that atom. I then used the work function of 4eV divided by the energy falling on that area per sec to find out how long it takes to reach the work function energy level.

My only issue is, is that the time they are looking for or is there some other concept I am missing. I know using the normal photo electric effect theory it is hf - work function= energy of emitted electron. If I stop timing at the point I reach the work function value then in theory would I not be emitting an electron with 0 energy. (tech impossible).

If its absorbing continuously would I add the time to allow for one more wave cycle above that of the energy and time needed to get to the work function.

Answer 1

Remember that you are dealing with a quantum phenomenon. As you said, you know that the quantum theory of the photoelectric effect tells you $hf - W = E_e$. So think about that: what does the term $hf$ represent the energy of? How is the energy of the incident radiation distributed? Is it possible for an electron in a metal to continuously absorb radiation?

Note that this is kind of a trick question, in the sense that the way it is worded may be a little misleading as to what sort of answer you are supposed to be getting.

Answer 2

I think it requires a single atom to absorb 2 photons at the same time(upto the frequency of the light particle) to emit the electron. Can you calculate this probability from the data given? Now this is the only reasonable conclusion I can make because otherwise as some one pointed out there is no emission of photo electrons.

Answer 3

I think the question is trying to get you to think about the differences between what you might think under the classical and intuitive model of the photoelectric effect and what actually happens.

Einstein won the Nobel Prize in 1921 for his work in precisely this area: he found, among other things, that no matter what the intensity, as long as there is enough energy to overcome the work function (i.e., as long as the frequency of incident light is greater than the cutoff frequency), photoelectrons will be emitted immediately.