Question

First order X - ray reflection $(\lambda =154$ pm$)$ which is maximum from a set of $(2,0,0)$ planes of a bcc lattice was observed at ${16}^o{6}^{\prime }$. The edge length (in pm) of unit cell is: $(\text{sin}{16}^o{6}^{\prime }=0.2773)$

• A. $360$
• B. $420$
• C. $560$
• D. $180$

Answer 1

The correct option is C $560$

The Braggg's equation is as follows:

$n\lambda =2dsin\theta$ $...\left(i\right)$

Here, $n=1;\theta ={16}^0{6}^{\prime };\lambda =154$ pm

This is observed from $(2,0,0)$ planes of a bcc lattice.

$d=\frac{a}{\sqrt{2^2+0+0}}$ $...\left(ii\right)$

So, from these two equations, we get $a=555.36\approx 560$ pm (edge length of unit cell)