How can we prove that Conservation of Momentum exists in Photoeectric Effect

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Discussion Overview

The discussion revolves around the application of conservation of momentum in the context of the photoelectric effect. Participants explore the relationship between the momentum of photons and electrons during the photoelectric interaction, questioning how to effectively demonstrate this conservation principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in applying the photoelectric equation to demonstrate conservation of momentum, noting that initial and final momentum of the electron and photon seem to be zero.
  • Another participant asserts that photons always possess momentum, challenging the assumption that they can be at rest.
  • A subsequent reply emphasizes that photons cannot be at rest and provides the relation p = ħk as a more relevant expression for photon momentum.
  • Further, a participant clarifies that the initial momentum of the electron and photon cannot be assumed to be zero, arguing that the conservation of momentum should be shown by comparing the relativistic momentum of both particles before and after the interaction.
  • Another participant shares their initial momentum conservation equation and the photoelectric equation, seeking guidance on how to connect these equations to prove conservation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the assumptions regarding the momentum of photons and electrons. There are competing views on how to approach the conservation of momentum in the context of the photoelectric effect, and the discussion remains unresolved.

Contextual Notes

Participants express uncertainty about the initial conditions of momentum for the photon and electron, and there are unresolved mathematical steps in connecting the conservation equations to the photoelectric effect.

Who May Find This Useful

This discussion may be of interest to students and researchers exploring the principles of momentum conservation in quantum mechanics, particularly in relation to the photoelectric effect.

kranav
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Hello!
As the title suggests

I tried to use the photoelectric equation and convert it into conservation of momentum equation but something's not fitting in.

We know that the initial momentum of the electron and the final momentum of the photon would be zero.

Is there any other way?

Please help.
 
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Photons always have momentum.
 
e.bar.goum said:
Photons always have momentum.

Ok, sorry.
then for a photon at rest p = m0c
from the relation E2 = p2c2 + m02c4
here E = 0, if its at rest, will it?
 
Well, photons aren't ever at rest either.

To be more helpful,

p= \hbar k
 
kranav said:
We know that the initial momentum of the electron and the final momentum of the photon would be zero.
No. Not only can you not assume they are zero a photon doesn't even exist without momentum. Also it can increase the momentum of the electron, which doesn't have to start at zero, by expending only part of the photons momentum. Hence the photon will be frequency shifted to a different momentum.

To show conservation then you need only show the initial relativistic momentum of the electron plus the initial relativistic momentum of the photon is the same before and after the interaction. That is 2+5=3+4. It's somewhat more complex than that in practice but nowhere do conservation require starting or ending with zero momentum for either particle.
 
Hell all!
thanks for the comments, really helped.
The problem is much more harder than I imagined.
Can someone help me start it, please ??

I have the basic momentum conservation equation but not sure how that will help.

h/λ1 + 0 = h/λ2 + mev (1)

the photoelectic equation is

1/2mv2 = h/λ1 - h/λ2 (2)

would proving 2 with 1 help?
 

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