In a relativistic collision between a photon and an electron, the recoiling electron has an energy of 40keV and the scattered photon an energy of 120keV. Find the energy of the photon before the collision, find the angles at which the photon and the electrons are scattered. The electron is initially at rest.
Conservation of energy dictates that E + Ee = E' + Ee'
where E is the photon's energy before impact, E' its energy after impact, Ee the electron's initial energy and Ee' the electron's energy after impact.
I should put the conservation of momentum, but my problem lies with the conservation of energy.
The Attempt at a Solution
So, Ee is the rest energy of the electron, therefore 511keV. When I plug these values in my function, I get that E is -351keV. This raises 2 questions: why is it negative, and why is it smaller than E' when the theory says that E' < E. When I find the corresponding wavelength of the initial photon, it's also negative of course.
Could someone help me in figuring out what I've done wrong.