# Compton Scattering; Relation between scattering angles

Tags:
1. Mar 12, 2016

### watisphysics

1. The problem statement, all variables and given/known data
Show that the scatter angles of the photon (θ) and electron (Φ) in the Compton effect are related by
the relation:
$cot (θ/2 )=(1+\frac{hf}{mοC^2}) tan(Φ)$

Where f is the frequency of incident photon
2. The attempt at a solution
I wrote down the equations of conservation of linear momentum in x and y directions
$h/λ =h/λ' cos(θ) +Pe \ cos(Φ) \\ h/λ' sin(θ)=Pe \ sin(Φ)$
where Pe is the momentum of the electron after scattering.
Then we also have this equation;
$λ'-λ=\frac{h}{mοC} (1-cos(θ))$
Are these equations correct? Am I going in the right direction? How do I proceed from here? How can I solve these equations together to get the required?

2. Mar 12, 2016

### TSny

Welcome to PF!
Yes
Yes, you can get the answer from these equations.
The expression you want to derive contains tanΦ. From your first two equations, can you get tanΦ?

3. Mar 13, 2016

### watisphysics

Thank you!

Last edited: Mar 13, 2016