Conservation of momentum photoelectric effect

[Gavroy]

hi

i was thinking about the photoelectric effect, that we discussed in school:

we said that, when a photon enters, it has an energy and this energy is used for electron binding energy and kinetic energy. so far so good.

but how is it possible, that the electron is emitted in the opposite direction of the incoming photon? this is totally against my understanding of conservation of momentum?

at first, i thought that it might be possible, that the metal layer itself would absorb twice the amount of momentum in the direction of the incoming photon. but this is also impossible, as this would need a huge amount of energy too, so there could not be any emitted electrons with the full kinetic energy.
therefore, my question is: where am i wrong?

 

[ZapperZ]

hi

i was thinking about the photoelectric effect, that we discussed in school:

we said that, when a photon enters, it has an energy and this energy is used for electron binding energy and kinetic energy. so far so good.

but how is it possible, that the electron is emitted in the opposite direction of the incoming photon? this is totally against my understanding of conservation of momentum?

at first, i thought that it might be possible, that the metal layer itself would absorb twice the amount of momentum in the direction of the incoming photon. but this is also impossible, as this would need a huge amount of energy too, so there could not be any emitted electrons with the full kinetic energy.
therefore, my question is: where am i wrong?

It's a very good question, and why photoelectric effect cannot occur on a volume of free electron gas.

What is going on here is that the "free electrons" in the conduction band in a metal still has a weak "potential" that couples it to the material's lattice ions. So while they can hop, skip, and jump between these ions, they still "see" these ions as a serious of weak, periodic potential.

Consequently, these lattice can act to take up the recoil momentum when the electrons are emitted from the solid. Since the lattice ions are prohibitively massive when compared to the electrons, you don't see much of an effect on them (very much like throwing a ball at a wall). But that's enough to save the conservation of momentum.

Zz.

 

[edpell]

Likewise on the absorption side the massive lattice takes up the incoming momentum not the electron.

 

[Gavroy]

but does this not mean, that not all the energy is used to bring up the kinetic energy of the electron and the binding energy? i mean, if some amount is used to transport momentum to the metal layer, it might be possible to measure a different maximum kinetic energy if you do this experiment by using a different angle of incidence?

 

[ZapperZ]

but does this not mean, that not all the energy is used to bring up the kinetic energy of the electron and the binding energy? i mean, if some amount is used to transport momentum to the metal layer, it might be possible to measure a different maximum kinetic energy if you do this experiment by using a different angle of incidence?

The energy that is taken up by the lattice is part (a rather small part, I might add) of the "work function" that has to be overcome.

Zz.

 

[Gavroy]

okay, but is it true, that the absorbed momentum of the metal is:

p=h/λ+mv

where lambda is the wavelength of the photon and v the velocity of the electron?

 

[ZapperZ]

okay, but is it true, that the absorbed momentum of the metal is:

p=h/λ+mv

where lambda is the wavelength of the photon and v the velocity of the electron?

But you can do your own calculation, because it is "trivial". It is the momentum of the emitted electron plus the miniscule momentum of the original incoming photon.

Now, I said "trivial" because we are talking about the simple photoelectric effect. In reality, the detailed momentum depends on the band structure of the material. This is because the in-plane momentum (momentum parallel to the surface of the material) is conserved with respect to the original momentum of the electron in the material, but out-of-plane momentum isn't, due to the recoil lattice. So it isn't as simple as what we have discussed here, but it should be sufficient to settle your question.

Zz.