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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
12a:32a:22a
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B
1a:3a:2a
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C
12a:34a:122a
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D
12a:3a:12a
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Solution

The correct option is C $$\dfrac {1}{2}a : \dfrac {\sqrt {3}}{4} a : \dfrac {1}{2\sqrt {2}}a$$
Simple cubic unit cell, $$r = a/2$$
Body-centred cubic unit cell, $$r = \dfrac {a\sqrt {3}}{4}$$
Face-centred cubic unit cell, $$r = \dfrac {a}{2\sqrt {2}}$$.

Chemistry

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