Question

What is the energy, in keV, of 75 keV x-ray photons that are backscattered (i.e., scattered directly back toward the source) by the electrons in a target?

Short answer

Energy of the x-ray photons is 58 keV.

Step-by-step solution

Step 1. Given information is :75 keV x-ray photons are backscattered by the electrons in a target.

We need to find out the energy of the x-ray photons.

Step 2. Using the expression of Compton scattering.

$$\begin{gathered} ∆\lambda ={\lambda }_s-{\lambda }_i=\frac{h}{mc}(1-\cos \theta ) \\ E=\frac{hc}{\lambda } \\ \lambda =\frac{hc}{E} \\ \frac{hc}{E_s}-\frac{hc}{E_i}=\frac{h}{mc}(1-\cos \theta ) \\ \frac{c}{E_s}=\frac{1}{mc}(1-\cos \theta )+\frac{c}{E_i} \\ {E}_s=\frac{c}{\frac{1}{mc}(1-\cos \theta )+\frac{c}{E_i}} \\ {E}_s=\frac{3.0\times {10}^{8}m/s}{{\displaystyle \frac{1}{(9.11\times {10}^{-31}kg)(3\times {10}^{8}m/s)}}(1-\cos 180°)+{\displaystyle \frac{\left(3.0\times {10}^{8}m/s\right)}{75\times {10}^3\times 1.6\times {10}^{-19}V}}} \\ {E}_s=58keV \end{gathered}$$