Compton Scattering; Relation between scattering angles

[watisphysics]

Homework Statement

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?

 

[TSny]

Welcome to PF!

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?

Yes

Am I going in the right direction?

Yes, you can get the answer from these equations.

How do I proceed from here? How can I solve these equations together to get the required?

The expression you want to derive contains tanΦ. From your first two equations, can you get tanΦ?

 

[watisphysics]

Thank you!