A) \[1:1\]
B) \[3:2\]
C) \[\sqrt{2}:\sqrt{3}\]
D) \[2{{(\sqrt{2})}^{3}}:{{(\sqrt{3})}^{3}}\]
Correct Answer: D
Solution :
[d] Co. No. is 12 means it is f.c.c. lattice Co. No. is 8 means it is b.c.c. lattice f.e.c. \[{{\rho }_{1}}=\frac{4\times at.mass}{{{N}_{a}}\times a_{1}^{3}}\] b.c.c. \[{{\rho }_{2}}=\frac{2\times at.mass}{{{N}_{a}}\times a_{2}^{3}}\] \[\frac{{{\rho }_{1}}}{{{\rho }_{2}}}=\frac{4}{2}\times \frac{a_{2}^{3}}{a_{1}^{3}}=\frac{2\times {{\left( \frac{4r}{\sqrt{3}} \right)}^{3}}}{{{(2\sqrt{2}r)}^{3}}}\] \[=\frac{2\times 4\times 4\times 4}{2\times 2\times 2\times 2\times \sqrt{2}(3\sqrt{3})}\] \[=\frac{4\sqrt{2}}{3\sqrt{3}}=\frac{2{{(\sqrt{2})}^{3}}}{{{(\sqrt{3})}^{3}}}\]
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