Question
In the Compton scattering of a photon with energy $E_{1}$ from an electron at rest, show that the energy of the scattered photon $E_{2}$ is given by$$E_{2}=\frac{E_{1}}{\left(E_{1} / m c^{2}\right)(1-\cos \phi)+1}$$
Step 1
This can be rewritten in terms of the wavelength $\lambda$ as $E = \frac{hc}{\lambda}$, where $c$ is the speed of light. Show more…
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A photon of initial energy $E_{0}$ undergoes Compton scattering at an angle $\theta$ from a free electron (mass $m_{e} )$ initially at rest. Using relativistic equations for energy and momentum conservation, derive the following relationship for the final energy $E^{\prime}$ of the scattered photon: $$E^{\prime}=\frac{E_{0}}{1+\left(\frac{E_{0}}{m_{e} c^{2}}\right)(1-\cos \theta)}$$
A photon of initial energy $E_{0}$ undergoes Compton scattering at an angle $\theta$ from a free electron (mass $m_{e} )$ initially at rest. Derive the following relationship for the final energy $E^{\prime}$ of the scattered photon: $$E^{\prime}=\frac{E_{0}}{1+\left(\frac{E_{0}}{m_{e} c^{2}}\right)(1-\cos \theta)}$$
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