What is the exact mathematical packing fraction of a body-centred cubic (BCC) unit cell? — Solid State Chemistry Question

💡 Solution & Explanation

For BCC, $Z=2$ and atoms touch along the body diagonal, so $4r=\sqrt{3}a$. Packing fraction $=\frac{2\cdot\frac43\pi r^3}{a^3}$. Substituting $r=\frac{\sqrt{3}a}{4}$ gives $\frac{\sqrt{3}\pi}{8}$.