Question

Two lines $A$ and $B$ of an X-ray give second order reflection maximum at a glancing angle of ${60}^{\circ }$ and third order reflection maximum at an angle of ${30}^{\circ }$ respectively from the face of the same crystal. If the wavelength of line $B$ is $0.25\text{nm}$, then the wavelength of line $A$ will be -

• A. $0.65\text{nm}$
• B. $0.35\text{nm}$
• C. $0.95\text{nm}$
• D. $0.15\text{nm}$

Answer 1

The correct option is A $0.65\text{nm}$

From Bragg's Law,

$2d\sin \varphi =n\lambda$

As crystal is same, $d=$ constant

$\therefore \frac{n\lambda }{\sin \varphi }=$ constant

So,

$\frac{n_1{\lambda }_1}{\sin {\varphi }_1}=\frac{n_2{\lambda }_2}{\sin {\varphi }_2}$

$\Rightarrow \frac{2\times {\lambda }_1}{\sin {60}^{\circ }}=\frac{3\times 0.25}{\sin {30}^{\circ }}$

​​​​​​​$\Rightarrow {\lambda }_1=0.65\text{nm}$

​​​​​​​​​​​​​​Hence, option $\left(A\right)$ is the correct answer.