Question

If $′a′$ stands for the edge length of the cubic systems: simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these system 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)

For the different unit cells the relation between 'a' & 'r' is:
$sc \, 2r=a$
$fcc \, 4r=\sqrt{2}a$
$bcc \, 4r=\sqrt{3}a$