Momentum conservation in photoelectric effect

[Reshma]

The photoelectric equation is given by:
hf = hf₀ + 1/2mv² where f is the frequency of the incident wave and f₀ is the threshold frequency.

HERE, only the conservation of energy is taken into consideration and momentum conservation is neglected. Why is this approach justified? Suppose we take momentum conservation into consideration--how will the photoelectric equation be modified?

What qualitative changes will be introduced in the emerging electron?

 

[nishant]

see according to me definitely mommentum conservation has been taken into account,a photon having a definite momentum usese all its momentum to give an impulse to the the electron.infact momentum and energy here point to the same thing

 

[Reshma]

That doesn't completely answer my question. How can you call the energy and momentum here as the same thing?

 

[nishant]

here the energy to the electron is provided by the momentum of the photon

 

[ZapperZ]

The photoelectric equation is given by:
hf = hf₀ + 1/2mv² where f is the frequency of the incident wave and f₀ is the threshold frequency.

HERE, only the conservation of energy is taken into consideration and momentum conservation is neglected. Why is this approach justified? Suppose we take momentum conservation into consideration--how will the photoelectric equation be modified?

What qualitative changes will be introduced in the emerging electron?

No, conservation of momentum is not neglected if you go beyond the naive treatment of photoelectric/photoemission phenomenon.

Note one important thing: the photoelectric effect is the emission of electrons from a SOLID surface, such as a metal. This is crucial. In the Spicer 3-step model of photoemission, the momentum of both the photon and the outgoing electrons are explicitly considered. In this model, the in-plane momentum (momentum parallel to the surface of the cathode) is conserved. However, since the momentum of the photon is miniscule with respect to the in plane momentum of the outgoing electron, one doesn't detect the momentum of the photon by looking at the outgoing electron.

The perpendicular momentum is something else. The existence of the solid, or more specifically, the lattice ions, is NECESSARY to take up the recoil momentum of the outgoing electrons (this means that photoemission as we know it doesn't occur in gasses - photoIONIZATION that occurs in gasses are of a different nature). Furthermore, since the electrons can come out from different energy within a band, there are no conservation of energy and momentum in the perpendicular direction.

So yes, these considerations ARE already studied and taken care of in a photoemission phenomenon.

Zz.

 

[Jayse_83]

The photoelectric effect causes the nucleus to recoil

 

[Reshma]

Thank you very much, ZapperZ. I completely got it now.

 

[kranav]

Hello! thanks for the information.
could you please suggest me a book or some other resource regarding this? I need more.
many thanks!