A) \[\frac{3\sqrt{3}}{4\sqrt{2}}\]
B) \[\frac{4\sqrt{3}}{3\sqrt{2}}\]
C) \[\frac{\sqrt{3}}{\sqrt{2}}\]
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
| [a] For BCC lattice: \[Z=2,a=\frac{4r}{\sqrt{3}}\] |
| For FCC lattice: \[\text{Z=4, a=2}\sqrt{\text{2}}\text{r}\] |
| \[\therefore \frac{{{d}_{25{}^\circ C}}}{{{d}_{900{}^\circ C}}}=\frac{{{\left( \frac{ZM}{{{N}_{A}}{{a}^{3}}} \right)}_{BCC}}}{{{\left( \frac{ZM}{{{N}_{A}}{{a}^{3}}} \right)}_{FCC}}}\] |
| \[=\frac{2}{4}{{\left( \frac{2\sqrt{2}r}{\frac{4r}{\sqrt{3}}} \right)}^{3}}\] |
| \[=\left( \frac{3\sqrt{3}}{4\sqrt{2}} \right)\] |
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