Question

An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. The atomic radiusis:

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

Answer 1

Answer: (A)

$\frac{\sqrt{3}}{4}\times 288 \,pm$

Answer 2

In bcc unit cell, atoms lying along a body diagonal touch each other
Length of body diagonal $=\sqrt{3}a$
$\sqrt{3}a=4r$
$r=\frac{\sqrt{3}}{4}a$
As $a=288\,pm$
$\therefore r=\frac{\sqrt{3}}{4}\times288Pm$