# Photoelectric emission in polychromatic light

Most of the literaure discusses the Photoelectric Effect in mocochromatic light. The only information I could get on polychromatic light is : https://arxiv.org/pdf/0904.1283.pdf

However, the specific quetions I am interested in are:

Given a mixed polychromatic light of $n$ wavelengths $\lambda_n$ , falling upon a target with threschhold wavelength $\lambda_t > max(\lambda_n)$, will we be possibly able to detect electrons that correspond to a particular wavelength appart from all others?

And since every wavelength in the mixed light cause emission, will we be able to detect the intensity as well ? Specifically, since highe intensity means larger number of photons, and thus larger number of collisions, will we be able to detect the intensity in this way?

Ignore the effect of depth of target, and asume uniform illumination.

Your problem is that even for monochromatic light the electrons are emitted with a range of kinetic energies from zero up to $h\nu$ minus the work function.

The photoelectric effect is far from a simple process. The incident photon transfers almost all its energy to a photoelectron with almost 100% yield, but that initial photoelectron is travelling in the same direction as the incident photon i.e. down into the bulk of the metal. We only see emission of a photo electron from the surface if the initial electron hits something and ricochets back, or if it scatters off and transfers its energy to some other electron and that travels back towards the surface. This rather haphazard process means that only one in about $10^5$ to $10^6$ photons ends up producing a photoelectron, and it means the energies of the emitted electrons are essentially randomly distributed.

So when you have a range of wavelengths there isn't going to be any clear distinction between the energies of photoelectrons ejected by the different wavelengths.

The exception to this is if we use an extremely thin metal foil. In that case most of the initial photoelectrons pass straight though the foil and out the other side, and the energy of the electron is approximately $h\nu-\phi$. In that case we can calculate the frequency of the incident photon from the energy of the photoelectron.

• and that way, if we have, e.g. a which detects electrons energy by means of Lorentz force (assuming all of this happens in vaccum), will we be able to group electrons corrsponding to different wavelength as that will cause a difference in energy? – Sean Aug 24 '17 at 17:17
• @Sean: Yes if you're using the thin film method, though there will still be some spread in the energies of photoelectrons emitted by any one wavelength. – John Rennie Aug 24 '17 at 17:20