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

[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?

Please help.

 

[e.bar.goum]

Photons always have momentum.

 

[kranav]

Photons always have momentum.

Ok, sorry.
then for a photon at rest p = m₀c
from the relation E² = p^2c2 + m0²c₄
here E = 0, if its at rest, will it?

 

[e.bar.goum]

Well, photons aren't ever at rest either.

To be more helpful,

$p= \hbar k$

 

[my_wan]

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.

 

[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 + m_ev (1)

the photoelectic equation is

1/2mv² = h/λ1 - h/λ2 (2)

would proving 2 with 1 help?

 

[Stonebridge]

Read this thread
https://www.physicsforums.com/showthread.php?t=73979