Question

If a the length of the side of $a$ cube, the distance between the body-centered atom and one corner atom in the cube will be:

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

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}a$

We know that for bcc structure, $r=\frac{\sqrt{3}}{4}a$
Hence, $2r=\frac{\sqrt{3}}{2}a$
$2r$ represents the distance between the body-centered atom and one corner atom.
Thus, if $a$ represents the length of the side of a cube, the distance between the body-centered atom and one corner atom in the cube will be $\frac{\sqrt{3}}{2}a$.