Question

If $a$ stands for the edge length of the cubic system : simple cubic, body-centred cubic and face-centred 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

The correct option is C $\frac{1}{2}a:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$

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