Question

An element has a body centered cubic (bcc) structure with a cell edge length of $288\text{pm}$. The shortest interatomic distance is

• A. $\frac{4}{\sqrt{2}}\times 288\text{pm}$
• B. $\frac{\sqrt{2}}{4}\times 288\text{pm}$
• C. $\frac{\sqrt{3}}{2}\times 288\text{pm}$
• D. $\sqrt{3}\times 288\text{pm}$

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}\times 288\text{pm}$

(i) In BCC unit cell, atoms are present at corners and centre of unit cell.
(ii) Shortest interatomic distance in BCC unit cell
$=\frac{\text{Body diagonal}}{2}$
$=\frac{\sqrt{3}a}{2}=\frac{\sqrt{3}}{2}\times 288\text{pm}$