# Momentum conservation in photoelectric effect

• Reshma
In summary, 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. If momentum conservation is taken into account, the equation becomes: hf = hf0 + 1/2mv2 where f is the frequency of the incident wave and f0 is the threshold frequency. The qualitative changes introduced in the emerging electron are due to the recoil momentum of the outgoing electrons.
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?

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

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

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

Reshma said:
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.

jaysriramroy
The photoelectric effect causes the nucleus to recoil

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

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

## 1. How does momentum conservation apply to the photoelectric effect?

Momentum conservation is a fundamental law of physics that states that the total momentum of a closed system remains constant. In the photoelectric effect, this means that the total momentum of the incident photon and the ejected electron must be equal to the momentum of the absorbed photon.

## 2. Why is momentum conservation important in understanding the photoelectric effect?

Momentum conservation helps us to understand how energy is transferred in the photoelectric effect. It allows us to calculate the energy of the ejected electron and determine the characteristics of the incident photon, such as its frequency and wavelength.

## 3. Does the photoelectric effect violate momentum conservation?

No, the photoelectric effect does not violate momentum conservation. The conservation of momentum still applies, but the energy of the incident photon is transferred to the ejected electron instead of being conserved as kinetic energy.

## 4. How does the mass of the ejected electron affect momentum conservation in the photoelectric effect?

The mass of the ejected electron does not affect momentum conservation in the photoelectric effect. This is because the mass of the electron is very small compared to the energy of the incident photon, so its momentum is negligible in the overall conservation equation.

## 5. Can momentum conservation be applied to all forms of the photoelectric effect?

Yes, momentum conservation can be applied to all forms of the photoelectric effect, including the direct and inverse photoelectric effects. In both cases, the total momentum of the system remains constant, but the direction of the momentum may change depending on the specific conditions of the experiment.

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