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 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

Correct option (c)
Explanation:
For Simple cubic \(=r^{+}+r^{-}=a / 2\)
For Body centred \(=r^{+}+r^{-}=a \sqrt{3} / 4\)
where \(a=\) edge length, \(r^{+}+r^{-}=\)interatomic distance .
For Face centered
$$
r^{+}+r^{-}=\frac{a}{2 \sqrt{2}}
$$
Ratio of radii of the three will be
$$
\frac{a}{2}: \frac{a \sqrt{3}}{4}: \frac{a}{2 \sqrt{2}}
$$

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