An X‑ray photon of wavelength $0.10\text{nm}$ is scattered elastically by an electron at an angle of $120^{\circ }$. Calculate the wavelength of the scattered photon (in nm).

Step-by-step solution

1. Recall Compton shift formula $Deltalambda=\frac{h}{m_{e}c}(1-cos\theta )$, where $h/m_{e}c=2.4263\times 10^{-12}\text{m}$.
2. Compute $1-cos120^{circ}=1-(-0.5)=1.5$.
3. Calculate $Deltalambda=2.4263\times 10^{-12}\text{m}\times 1.5=3.6395\times 10^{-12}\text{m}$.
4. Convert to nanometres: $3.6395\times 10^{-12}\text{m}=3.6395\times 10^{-3}\text{nm}=0.00364\text{nm}$.
5. Add the shift to the initial wavelength: ${\lambda }_{\text{scattered}}=0.10+0.00364=0.10364\text{nm}$.
6. Round to four significant figures: $0.1036\text{nm}$.

Concept tested: Compton scattering

Published 13 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked