In a Compton scattering experiment, an X-ray photon of wavelength $\lambda =0.05\text{ nm}$ is scattered at an angle of $\theta =90^{\circ }$. What is the change in wavelength $\Delta \lambda$?

Solution

1. The Compton shift formula is $\Delta \lambda ={\lambda }_c(1-\cos \theta )$, where ${\lambda }_c=h/(m_{e}c)$.
2. The Compton wavelength of the electron is ${\lambda }_c\approx 0.00243\text{ nm}$.
3. For $\theta =90^{\circ }$, $\cos 90^{\circ }=0$, so $$\begin{array}{rl}\Delta \lambda & ={\lambda }_c(1-0)\\ & ={\lambda }_c\end{array}$$.
4. Thus, $\Delta \lambda =0.00243\text{ nm}$.
5. Hence the answer is (A).