Q175 / 200 · TS EAMCET 2002 · Physics
In compton scattering process, the incident $X$-radiation is scattered at an angle $60^{\circ}$. The wavelength of the scattered radiation is $0.22 Å$. The wavelength of the incident $X$-radiation in $Å$ units is
- A$0.508$
- B$0.408$
- C$0.232$
- Correct answerD$0.208$
Solution
For Compton effect we have the relation
$\lambda_2-\lambda_1=\frac{h}{m_0 c}(1-\cos \theta)$
$\lambda_1=$ wavelength of incident radiation
$\lambda_2=$ wavelength of scattered radiation
$\begin{aligned}<br />\therefore 0.22-\lambda_1 & =0.024(1-\cos 60) \\<br />0.22-\lambda_1 & =0.024\left(1-\frac{1}{2}\right) \\<br />0.22-\lambda_1 & =0.024 \times \frac{1}{2} \\<br />\lambda_1 & =0.22-0.012=0.208 Å<br />\end{aligned}$
$\lambda_2-\lambda_1=\frac{h}{m_0 c}(1-\cos \theta)$
$\lambda_1=$ wavelength of incident radiation
$\lambda_2=$ wavelength of scattered radiation
$\begin{aligned}<br />\therefore 0.22-\lambda_1 & =0.024(1-\cos 60) \\<br />0.22-\lambda_1 & =0.024\left(1-\frac{1}{2}\right) \\<br />0.22-\lambda_1 & =0.024 \times \frac{1}{2} \\<br />\lambda_1 & =0.22-0.012=0.208 Å<br />\end{aligned}$
Hence, the correct answer is option: 'D'.