# What is the maximum energy that the electron can obtain?

1. Sep 28, 2014

### MrPunk44

1. The problem statement, all variables and given/known data
Problem 1) A photon having 44 keV scatters from a free electron at rest. What is the maximum energy that the electron can obtain?

I already used all of my attempts on this problem so I can't check whether or not any attempt on this forum is successful. Hopefully that's not a problem.

2. Relevant equations
1) $E = \frac{hc}{\lambda}$
2) $\delta \lambda = \frac{h}{mc} (1-cosx)$
3) $E_i = E_s + KE_e$

3. The attempt at a solution

In order to find the maximum energy the electron can obtain I first need to find the energy of the incident photon. In order to do that I must first find the wavelength of the scattered photon.

I use equation 1 for the wavelength of scattered photon. 1240ev*nm / 44000ev = .02818 nm. Then I maximize equation 2 by allowing x to equal pi. RHS equals 4.8488E-12 m. Since the incident photon has a higher energy I know it's wavelength must be smaller than .02818 nm. Therefore, I calculate .02818E-9 m - 4.8488E-12 m = .0233nm, which is the wavelength of the incident photon. Equation 1 gives me 53150ev as the energy of incident photon. Finally, equation 3 gives me 9150 ev as the maximum energy the electron can obtain.

Where'd I go wrong?

2. Sep 28, 2014

### Arjun Ar

KE=hvα(1-cosφ)/(1+α(1-cosφ)
α=8.1x10^-21v
KEmax=2hvα/(1+2α)