Maximum Kinetic Energy in Comton Scattering

[samuelyee]

Homework Statement

A photon of energy E is scattered off a stationary electron with rest mass m. What is the maximum kinetic energy of the recoiling electron?

Homework Equations

$$\lambda'-\lambda=\frac{h}{mc}(1-cos(\phi))$$
$$E=\frac{hc}{\lambda}$$

The Attempt at a Solution

The maximum kinetic energy gained is when $$\phi=180^{o}$$ , so
$$\lambda'-\lambda=\frac{2h}{mc}$$
After some manipulation, I finally get
$$K = \frac{2E^2}{2E+mc^2}$$
But the answer is supposed to be $$K = \frac{E^2}{E+mc^2}$$ , which would be the case if the cosine term is zero. Am I making the wrong assumption at the start?

Thanks for the help!

 

[sylas]

I am getting the same as you. I'm guessing a typo somewhere?

Cheers -- sylas