Question

A solid has a BCC structure. If the distance of closest approach between the two atoms is $1.73\stackrel{\circ }{A}$. The edge length of the cell is:
(Given, $\sqrt{3}=1.73$)

• A. $200\text{pm}$
• B. $\frac{\sqrt{3}}{\sqrt{2}}\text{pm}$
  
• C. $142.2\text{pm}$
• D. $\sqrt{2}\text{pm}$
  

Answer 1

The correct option is A $200\text{pm}$

For BCC, the relationship between radius and edge length is given by
$r=\frac{\sqrt{3}a}{4}$
Given $2r=1.73\stackrel{\circ }{\text{A}}$
Hence,
$1.73=\frac{\sqrt{3}}{2}\times a$
$\Rightarrow a=\frac{1.73}{\sqrt{3}}\times 2$
$\Rightarrow a=2\stackrel{\circ }{\text{A}}=200\text{pm}$