Question 40.4: Compton Scattering at 45° X-rays of wavelength λ0 = 0.200 00......
Compton Scattering at 45^{\circ}
X-rays of wavelength \lambda_{0}=0.200000 \mathrm{~nm} are scattered from a block of material. The scattered \mathrm{x}-rays are observed at an angle of 45.0^{\circ} to the incident beam. Calculate their wavelength.
Conceptualize Imagine the process in Figure 40.13 , with the photon scattered at 45^{\circ} to its original direction.
Categorize We evaluate the result using an equation developed in this section, so we categorize this example as a substitution problem.
Solve Equation 40.11
{{{\lambda}}}^{\prime}-\lambda_{0}={\frac{h}{m_{e}c}}({{{1-\cos\theta}}}) (40.11)
for the wavelength of the scattered x-ray:
\text { (1) } \lambda^{\prime}=\lambda_{0}+\frac{h(1-\cos \theta)}{m_{e} c}
Substitute numerical values:
\begin{aligned} \lambda^{\prime} & =0.200000 \times 10^{-9} \mathrm{~m}+\frac{\left(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(1-\cos 45.0^{\circ}\right)}{\left(9.11 \times 10^{-31} \mathrm{~kg}\right)\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)} \\ & =0.200000 \times 10^{-9} \mathrm{~m}+7.10 \times 10^{-13} \mathrm{~m}=0.200710 \mathrm{~nm} \end{aligned}
