- #1
AbigailM
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Homework Statement
A photon with initial momentum p collides with a free electron having
a mass m that is initially at rest. If the electron and photon recoil in opposite
directions, what will be the change in the photon’ wavelength? (Hint: use
relativistic forms for energy and momentum.)
Homework Equations
Conservation of Energy:
[itex]hf_{i}+m_{e}c^{2}=hf_{f}+\sqrt{p_{e}^{2}c^{2}+m_{e}^{2}c^{4}}[/itex]
Conservation of Momentum:
[itex]\boldsymbol{p_{i}}=\boldsymbol{p_{f}}+\boldsymbol{p_{e}}[/itex]
The Attempt at a Solution
I won't go through the whole derivation as it's quite a bit of latex but:
If you square both equations above and introduce hf into the conservation of momentum equation, you can equate the two equations and rearrange. This will give you the compton scattering equation:
[itex]\lambda_{2}-\lambda_{1}=\frac{h}{m_{e}c}(1-cos\theta)[/itex]
If the recoiling electron and photon are to be in opposite directions this is an angle of 180°.
Plugging this into the compton scattering equation gives:
[itex]Δ\lambda=\frac{2h}{m_{e}c}[/itex]
,which is the change in wavelength.
Does this look ok? As always everyone, thanks for the help!