Question

Ratio of the total volume of $bcc$ to simple cubic structure is

• A. $3\sqrt{3}:8$
• B. $8:3\sqrt{3}$
• C. $24\sqrt{3}:1$
• D. $1:24\sqrt{3}$

Answer 1

Answer: (B)

Volume of unit cell $=a^3$

For $bcc,r=\frac{\sqrt{3}}{4}a$ or $a=\frac{4r}{\sqrt{3}}$

For simple cubic, $r=\frac{a}{2}$ or $a=2r$

Thus volume of simple cubic unit cell $=(2r{)}^3=8r^3$

$\frac{\text{ Volume of }bcc\text{ unit cell }}{\text{ Volume of simple cubic }}=\frac{64/3\sqrt{3}{r}^3}{8r^3}=\frac{64}{8\times 3\sqrt{3}}=\frac{8}{3\sqrt{3}}$