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. $1a:\sqrt{3}a:\sqrt{2}a$
• 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, $r=\frac{a}{2\sqrt{2}}.$