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## Homework Statement

An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

## Homework Equations

p=γmv

E

_{γ}=pc=h/λ

λ'-λ = (h/m

_{e}c)(1-cosθ)

## The Attempt at a Solution

*Defining left as positive*

I have the following expressions for the initial and final momentum of the system, and I set them equal to each other.

P

_{initial}= p

_{e}+ p

_{γ}

Pi = -γ

_{i}m

_{e}v

_{ei}+ E

_{γi}/c

P

_{f}= γ

_{f}m

_{e}v

_{ef}- E

_{f}/c

given Ei/c = h/λ

h/λ - γ

_{i}m

_{e}v

_{ei}= γ

_{f}m

_{e}v

_{ef}- h/λ'

h(1/λ + 1/λ') = γ

_{f}m

_{e}v

_{ef}+ γ

_{i}m

_{e}v

_{ei}

I can plug in all the values for the electron and get some number, but I am still left with λ and λ'. I'm not sure if my approach is correct, but if it is, I don't see how I can find just λ (the initial wavelength).