Question

X-rays of 1.0$A^0$ are scattered from a carbon block. The wavelength of the scattered beam in a direction making ${90}^0$ with the incident beam is

• A. 1.024$A^0$
• B. 2.024$A^0$
• C. 3.024$A^0$
• D. 4.024$A^0$

Answer 1

The correct option is A 1.024$A^0$

Compton effect formula
$\Delta \lambda ={\lambda }_f-{\lambda }_i=\frac{h}{m_{e}C}(1-cos\theta )$
${\lambda }_f-1.0A^{\circ }=\frac{6.63\times {10}^{-34}}{9.1\times {10}^{-31}\times 3\times {10}^8}(1-cos{90}^{\circ })$
${\lambda }_f=1A^{\circ }+\frac{6.63\times {10}^{-34}}{9.1\times {10}^{-31}\times 3\times {10}^8}(1-0)$ $(\because cos{90}^{\circ }=0)$
$=1A^{\circ }+0.24\times {10}^{-11}m$
$=1A^{\circ }+0.024A^{\circ }(\because {10}^{-10}m=1A^{\circ })$
$=1.024A^{\circ }$

So, the answer is option (A).