Compton effect: Scattering angle of electron

[vetgirl1990]

Homework Statement

A 0.7MeV (E°) photon scatters off a free electron such that the scattering angle of the photon is twice the scattering angle of the electron (θ=2φ). Determine the scattering angle for the electron.

Homework Equations

λ' - λ° = h/(m_ec)(1-cosθ)
E = hc/λ

ρ_electron = m_ev / √(1-v²/c²)

The Attempt at a Solution

The initial wavelength of the photon (λ°) = hc/E° = 5.92x10^-13m

Honestly, I'm not sure at all where to go from here. I know it's a conservation of momentum problem, but based on the equation above, I need the velocity of the electron in order to find it's momentum.

 

[Hiranya Pasan]

why do you need to find momentum?