A) \[\frac{1}{2}a\,\, & :\frac{\sqrt{3}}{4}a\,\,:\frac{1}{2\sqrt{2}}a\]
B) \[\frac{1}{2}a\,\, & :\,\sqrt{3}a:\frac{1}{\sqrt{2}}a\]
C) \[\frac{1}{2}a\,\, & :\,\frac{\sqrt{3}}{2}a\,\,:\frac{\sqrt{3}}{2}a\]
D) \[1a:\sqrt{3}a:\sqrt{2}a\]
Correct Answer: A
Solution :
[a] Following generalization can be easily derived for various types of lattice arrangements in cubic cells between the edge length [a] of the cell and r the radius of the sphere. For simple cubic: \[a=2r\]or\[r=\frac{a}{2}\] For body centred cubic: \[a=\frac{4}{\sqrt{3}}r\] or \[r=\frac{\sqrt{3}}{4}a\] For face centred cubic: \[a=2\sqrt{2}r\]or \[r=\frac{1}{2\sqrt{2}}a\] Thus the ratio of radii of spheres for these will be simple : bcc : fcc \[=\frac{a}{2}:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a\] i.e. option [a] is correct answer.
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