What Is the Wavelength of the Incident X-ray Photon in Compton Scattering?

[amani96]

Homework Statement

An X-ray photon is scattered at an angle of θ = 180.0° from an electron that is initially at rest. After scattering, the electron has a speed of 4.67 x 106m/s. Find the wavelength of the incident X-ray photon.

Homework Equations

hc/λ = hc/λ′ + KE

λ′ = λ + h/mc (1-cosθ)

The Attempt at a Solution

Ok, I solved the first equation for λ′and set both equal to each other:


hc/λ = hc/λ′ + KE
λ′= λ + (λ/hc)KE (hopefully my algebra isn't off...could somebody check?)

λ + (λ/hc)KE = λ + h/mc (1-cosθ) (subtract λ from both sides)

(λ/hc)KE = h/mc (1-cosθ) (multiply both sides 1/KE)

λ/hc = [h/mc (1-cosθ)]/KE (multiply both sides by hc/1)

λ = [h∧2/m(1-cosθ)]/KE

then plug in numbers...
But, do I have it right so far?

 

[mgb_phys]

Momentum is conserved, so all the new momentum of the electron came from the photon.
momentum of the electron = m v
momentum of the photon = h f = h c / wavelength.