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-

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

Answer 1

The correct option is A $200pm$

In a BCC structure atoms are present at corners and at body centre.
Distance of closest approach for two atoms is equal to the distance from the centre of corner particle to the centre of body centre particle, which is equal to half of the body diagonal in a unit cell
In BCC:
$\text{Body diagonal}=\sqrt{3}a$
$\text{Distance of closest approach}=\frac{\sqrt{3}a}{2}=1.73\stackrel{\circ }{A}$
$a=2\stackrel{\circ }{A}=200pm$