Compton Scattering Homework: Find Energy & Angles

[Jukai]

Homework Statement

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.

Homework Equations

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.

 

[vela]

How did you get E=-351 KeV?

 

[Jukai]

E + mec² = 120keV + 40keV

==> E = -351keV no? (I assume E'=120keV and Ee'=40keV, and that mec² = 511keV)

 

[sgd37]

right so the electron has suddenly lost over 90% of it's mass after it was supposed to gain energy from the photon. I'm guessing that that energy is referring to the kinetic term only

 

[Jukai]

I see, that would make more sense. Then E is 160keV, which is bigger than E' as expected. Thank you

 

[sgd37]

I trust you are referring to the initial energy of the photon being bigger than the final one rather than the electron which your post suggests

 

[Jukai]

Yes, I didn't mean to write Ee