A monochromatic photon of wavelength $0.12$ nm collides elastically with a stationary electron at an angle of $150^{circ}$.

Step-by-step solution

1. Write the Compton formula: $Deltalambda={\lambda }_C(1-cos\theta )$, where ${\lambda }_C=\frac{h}{mc}=2.426\times 10^{-12},\text{m}=0.002426,\text{nm}$.
2. Compute $cos150^{\circ }=-cos30^{\circ }=-0.8660$; hence $1-cos\theta =1+0.8660=1.8660$.
3. Calculate the shift: $Deltalambda=0.002426,\text{nm}\times 1.8660=0.00453,\text{nm}$.
4. Add the shift to the initial wavelength to find the scattered wavelength: ${\lambda }^{\prime }=0.12,\text{nm}+0.00453,\text{nm}=0.12453,\text{nm}\approx 0.125,\text{nm}$.

Concept tested: Compton scattering, wavelength shift formula

Published 20 September 2026 · How this solution was prepared and checked