Question

$\text{X}$- rays of wavelength $0.140\text{nm}$ are scattered from a very thin slice of carbon. What will be the wavelength of $\text{X}$- rays scattered at ${180}^{\circ }$.

• A. $0.144\text{nm}$
• B. $0.142\text{nm}$
• C. $0.148\text{nm}$
• D. $0.142\text{nm}$

Answer 1

The correct option is A $0.144\text{nm}$

Given, $\lambda =0.140\text{nm};\theta ={180}^{\circ }$

From Compton experiment,

The change in wavelength after collision $\left(\Delta \lambda \right)$ is,

$\Delta \lambda ={\lambda }^{\prime }-\lambda =\frac{h}{m_{0}c}(1-\cos \theta )$

$\Rightarrow {\lambda }^{\prime }=\lambda +\frac{h}{m_{0}c}\left(\cos \theta \right)$

$=0.140\times {10}^{-9}+\frac{6.63{\times }^{-34}(1-(-1\left)\right)}{9.11\times {10}^{-31}\times 3\times {10}^8}$

$=0.140\times {10}^{-9}+0.48\times {10}^{-11}$

$=0.140\times {10}^{-9}+0.0048\times {10}^{-9}$

$\therefore {\lambda }^{\prime }=0.144\text{nm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.