A photon of wavelength $0.71\text{A˚}$ is scattered elastically by a stationary electron at an angle of $120^{\circ }$. Calculate the wavelength of the scattered photon.

Step-by-step solution

1. The Compton wavelength shift is given by $\Delta \lambda =\frac{h}{m_{e}c}(1-\cos \theta )$.
2. The Compton wavelength $\frac{h}{m_{e}c}=2.426\times 10^{-12}\text{m}=0.02426\text{A˚}$.
3. For $\theta =120^{\circ }$, $\cos 120^{\circ }=-0.5$, so $1-\cos \theta =1-(-0.5)=1.5$.
4. Thus $\Delta \lambda =0.02426\times 1.5=0.03639\text{A˚}$.
5. Initial wavelength ${\lambda }_i=0.71\text{A˚}$, so scattered wavelength ${\lambda }_f={\lambda }_i+\Delta \lambda =0.71+0.03639=0.74639\text{A˚}$.
6. Rounded to three significant figures, ${\lambda }_f=0.746\text{A˚}$.

Concept tested: Compton effect – wavelength shift

Published 8 September 2026 · How this solution was prepared and checked