Compton Scattering Angle - CM FRAME

[unscientific]

Homework Statement

Given incoming photon has energy 10Mev and scatters at angle 25 degrees, find the scattering angle in CM frame.

Homework Equations

The Attempt at a Solution

[/B]
In lab frame, let the energy of incoming photon be $E$. Total 4-vector would be $P + Q = (\frac{E}{c},\frac{E}{c}) + (mc,0)$.

Using compton scattering formulas, I solved the scattering angle of electron $\alpha = 35 ^o$, energy of scatted electron $E_e = 4.02 ~MeV$, energy of scattered photon $E' = 5.47~MeV$.Having solved this completely in the lab frame before/after scattering, how do I proceed in CM-frame?

In CM frame, total momentum is $0$, so 4-vector would be $P_{cm} + Q_{cm} = (\frac{E_{p,cm}+E_{e,cm}}{c},0)$.

Even when I assume that in CM frame they are both scattered along the same line it doesn't help.

 

[vela]

Did you mean $\alpha=35^\circ$ or is that a typo?

Since you know everything the lab frame, you can simply use the Lorentz transformation to find the four-vectors in the CM frame. Suppose the CM moves with speed $\beta=v/c$. Get expressions for the three-momentum of the photon and the electron in the CM frame. As you noted, their sum should be 0, which will allow you to determine $\beta$.

 

[unscientific]

Solved.