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Q.
Ratio of the total volume of $b c c$ to simple cubic structure is
The Solid State
Solution:
Volume of unit cell $=a^{3}$
For $b c c, r=\frac{\sqrt{3}}{4} a$ or $a=\frac{4 r}{\sqrt{3}}$
For simple cubic, $r=\frac{a}{2}$ or $a=2 r$
Thus volume of simple cubic unit cell $=(2 r)^{3}=8 r^{3}$
$\frac{\text { Volume of } b c c \text { unit cell }}{\text { Volume of simple cubic }}=\frac{64 / 3 \sqrt{3} r^{3}}{8 r^{3}}=\frac{64}{8 \times 3 \sqrt{3}}=\frac{8}{3 \sqrt{3}}$