# Conceptually ok problem, but very difficult to solve

1. Jun 1, 2005

### Corneo

Hi, I was given this problem on a midterm regarding a photon colliding with a free electron. I need to find the angle of the scattered photon $\theta$, the new wavelength $\lambda'$, and its energy.

It states that the electron scatters at an angle of 60 degrees (relative and below the initial photon momentum) and at a velocity of 4 x 10^7 m/s.

I already set up the three equations given but I simply have no idea how to solve this systerm, substitution seems to be suicide due to the limited time on a midterm. I do not think matrices would help either. I just would like to know how to solve for the photon's scattered angle, because that seems like the most difficult part of this problem.

From conservation of momentum I can write.

$$x: \frac {h}{\lambda} = \gamma m u \cos \phi + \frac {h}{\lambda'} \cos \theta \qquad \phi = 60^\circ, u = 4 \times 10^7 m/s[/itex] [tex]y: 0 = \frac {h}{\lambda'} \sin \theta - \gamma m u \sin \phi$$

From conservation of energy I can write.

$$\frac {hc}{\lambda} + mc^2 = \frac {hc}{\lambda'} + \gamma m c^2$$

From here I simply do not know solve to solve this system. The unknowns are $\lambda, \lambda', \theta$

Last edited: Jun 1, 2005