# Electron velocity after Compton Scattering

1. Oct 2, 2012

### Inferniac

1. The problem statement, all variables and given/known data
In Compton scattering,how much energy must the photon have in order for
the scattered electron to achieve relativistic velocity?

2. Relevant equations
Compton scattering formula: $$λ'-λ=\frac{h}{mc}(1-cosθ)$$
$E=\frac{h}{λ}$,conservation of mass and momentum,possibly Lorentz transformations for velocity and kinetic energy?

3. The attempt at a solution
My train of thought goes like this:
Assume that θ=90°. That gives us $λ'-λ=\frac{h}{mc}$.
$λ'-λ$ can easily be turned into $E'-E$ using $E=\frac{h}{λ}$.
Using law of conservation of energy we solve for the kinetic energy of the scattered electron
Since we now know the electron's kinetic energy we can calculate its speed.

My problem lies with my first assumption.I don't know if it's correct. It was made after a hint that my professor made that we should use big angles.

Please note that I don't study physics in English so some things might require clarification.

2. Oct 2, 2012

### szynkasz

I think you should assume 180o so that energy trasferred from photon to electron is maximal.

3. Oct 2, 2012

### BruceW

Hi inferniac, welcome to physicsforums :)

The equation $E=\frac{h}{λ}$ is true in a natural system of units (where c=1), but in the rest of your post, it looks like you are keeping c not equal to 1. So maybe you forgot a c in the equation above?

Also, szynkasz has the right idea with the angle, although it is not usual in this forum to give the answer outright.

4. Oct 3, 2012

### Inferniac

Thank you for the welcome.

You are absolutely correct,I misstyped $E=\frac{h}{λ}$ instead of $E=\frac{hc}{λ}$ the first time and I copy-pasted again.
Yes,assuming a 180° angle makes more sense.I'll see were it goes from here.