Compton Scattering: K, Wavelength Calculation

[Benlaww]

Homework Statement

A photon with wavelength 0.1365 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is 8.20×106 m/s?

Relevant Equations

K=1/2 *m*v^2
E=hc/(wl)
(wl)' = (wl) + (h/mc)(1-cos(theta))

K= 1/2 (9.11*10^-31)(8.2*^6)^2
(wl)' = hc/k = 6.5 nm
(wl)' - (wl) = 6.36 nm
cos(theta) = 1- (((6.36nm)(9.11*10^-31)(3*10^8))/(6.63*10^-34)) = -2620.7

theta = error

 

[TSny]

(wl)' = hc/k

This is not the correct relation between the final wavelength of the photon and the final kinetic energy of the electron. Let E = initial energy of the photon, E' = the final energy of the photon, and K = the final kinetic energy of the electron. How are E, E', and K related?

 

[Benlaww]

E = E' + K
Ahh I've figured it out now, I got my final wavelength as 1.39*10^-10 m. Thank you!