A metal crystallises with a face-centred cubic (FCC) lattice. If the edge of the unit cell is exactl — Solid State Chemistry Question

💡 Solution & Explanation

In an FCC lattice, the face diagonal has a length of $\sqrt{2}a$ and is equal to $4r$ (where $r$ is the radius). The diameter of the atom is $D = 2r$. Therefore, $4r = \sqrt{2}a \implies 2D = \sqrt{2}a \implies D = \frac{a}{\sqrt{2}}$. Substituting $a = 408\text{ pm}$, $D = \frac{408}{1.414} \approx 288.5\text{ pm}$.