If the atoms/ions in the crystal are taken to be hard spheres touching each other in the unit cell, then the fraction of volume occupied in the body cantered cubic structure is
(a)$\sqrt{3} \pi$
(b)$\frac{\sqrt{2} \pi}{6}$
(c)$\pi$
(d)$\frac{2 \pi}{6}$
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed D; on checking, A is correct — see the explanation.
Printed D (2π/6 ≈ 1.05) is impossible; the bcc fraction is √3π/8.
Explanation
bcc: 2 atoms of radius √3a/4 per cell; packing fraction = 2 × (4/3)π(√3a/4)³/a³ = √3π/8 = 0.68.