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What is the maximum energy that the electron can obtain?

  1. Sep 28, 2014 #1
    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. jcsd
  3. Sep 28, 2014 #2
    KE=hvα(1-cosφ)/(1+α(1-cosφ)
    α=8.1x10^-21v
    KEmax=2hvα/(1+2α)
     
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