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

1. Dec 12, 2011

### kranav

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?

2. Dec 12, 2011

### e.bar.goum

Photons always have momentum.

3. Dec 13, 2011

### kranav

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?

4. Dec 13, 2011

### e.bar.goum

Well, photons aren't ever at rest either.

$p= \hbar k$

5. Dec 13, 2011

### my_wan

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.

6. Dec 13, 2011

### kranav

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?

7. Dec 13, 2011