Solve Conservation of Energy & Momentum: Photon & Electron Collision

[Minus1]

A photon of energy E traveling in the +ve x direction collides elastically with an electron of mass m, moving in the opposite direction. After the collision the photon travels back along the -ve x direction with the same energy E.

Use the conservation of energy and momentum to demonstrate that the initial and final momenta of the electron are equal and opposite and of magnitude E/c.

This question is worth 10 marks and I am kinda lost on what to do soany help at all would be greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hi Minus1! Welcome to PF!

The photon has energy E, so what is its momentum?

Now suppose the electron has momentum p before, and momentum q after …

what is the energy of the electron before and after?

 

[Altabeh]

A photon of energy E traveling in the +ve x direction collides elastically with an electron of mass m, moving in the opposite direction. After the collision the photon travels back along the -ve x direction with the same energy E.

Use the conservation of energy and momentum to demonstrate that the initial and final momenta of the electron are equal and opposite and of magnitude E/c.

This question is worth 10 marks and I am kinda lost on what to do soany help at all would be greatly appreciated.

In an elastic collision, the total kinetic energy of the colliding bodies won't change. So the conservation law of momentum gives
P_1+P_2 = P'_1+ P'_2,
that is, for the collision of an electron [with all specifications indexed by 1] and a photon [with all quantities indexed by 2]. Since the direction of motion of photon has been reversed, so
P'_2 = -P_2
which its insertion into the preceding equation gives
P_1-P'_1 = -2P_2.
Now we switch to the conservation law of energy that, assuming electron is moving at low speed, says
P^2_1/2m + |P_2|c =P'^2_1/2m + |P'_2|c.
By assumption, |P_2|c = |P'_2|c. Thus from the above equation we can get P'_1 = +- P_1. From this point I'll leave the remainder for you ro gain the required result.

AB

 

[Minus1]

Thanks guys, I wish I could take you in the exam but I don't think they'd allow it, lol

 

[Minus1]

Hi Minus1! Welcome to PF!

The photon has energy E, so what is its momentum?

Now suppose the electron has momentum p before, and momentum q after …

what is the energy of the electron before and after?

Thanks for the warm welcome, I feel at home already