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) \[\frac{1}{2}a:\frac{\sqrt{3}}{2}a:\frac{\sqrt{2}}{2}a\]
D) \[1a:\sqrt{3}a:\sqrt{2}a\]
Correct Answer: A
Solution :
For simple cubic, a = 2r \[\therefore \]\[r=\frac{a}{2}\]For body centred cubic, \[a=\frac{4r}{\sqrt{3}}\] \[r=\frac{\sqrt{3}a}{4}\] For face centred cubic, \[a=2\sqrt{2}r\] \[r=\frac{a}{2\sqrt{2}}\] Hence, the ratio of radii in simple cubic, body centred cubic and face centred cubic is \[\frac{a}{2}:\frac{\sqrt{3}a}{4}:\frac{a}{2\sqrt{2}}\]
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