Question

For bcc structure, the coordination number and packing are ______ respectively.

• A. $8,\frac{\pi \sqrt{3}}{8}$
• B. $6,\frac{\pi \sqrt{2}}{6}$
• C. $8,\frac{\pi \sqrt{2}}{6}$
• D. none of the above

Answer 1

The correct option is A $8,\frac{\pi \sqrt{3}}{8}$

For bcc structure, $4r=a\sqrt{3}\Rightarrow a=\frac{4r}{\sqrt{3}}$ (along body diagonal)

$\text{Packing Fraction}=\frac{2\times \frac{4}{3}\pi r^3}{a^3}=\frac{2\times \frac{4}{3}\pi r^3}{\frac{64r^3}{3\sqrt{3}}}=\frac{\pi \sqrt{3}}{8}$

Since, the body center atom is surrounded by $8$ other atoms. Therefore coordination number is $8$.