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 :
[a] 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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