Question

Relationship between atomic radius and edge length $a$ of a body-centered cubic unit cell is :

• A. $r=a/2$
• B. $r=\frac{\sqrt{3}}{4}a$
• C. $r=\sqrt{a/2}$
• D. $r=\frac{3a}{2}$

Answer 1

The correct option is B $r=\frac{\sqrt{3}}{4}a$

In $bcc$, atoms on body diagonal are in contact with each other.

So, length of body diagonal = $r+2r+r=4r$

Also, body diagonal = $\sqrt{3}a$.

So, $4r=\sqrt{3}a$.

So, $r=\frac{\sqrt{3}}{4}a$.

Hence, Option "B" is the correct answer.