Question

If ‘$a$’ stands for the edge length of the cubic systems : simple cubic, body centered cubic and face centered cubic, then the ratio of radii of the spheres in these systems will be respectively,

• A. $\frac{1}{2} a: \frac{\sqrt{3}}{2} a: \frac{\sqrt{2}}{2} a$
• B. $1 a: \sqrt{3} a: \sqrt{2} a$
• C. $\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
• D. $\frac{1}{2} a: \sqrt{3} a: \frac{1}{\sqrt{2}} a$

Answer 1

Answer: (C)

Simple cubic unit cell, $r=a / 2$
Body-centred cubic unit cell, $r =\frac{ a \sqrt{3}}{4}$
Face-centred cubic unit cell, $r =\frac{ a }{2 \sqrt{2}} .$