Metallic gold crystallizes in face centered cubic lattice with edge-length $4.070\text{Å}$. Closest distance between gold atoms is :

In an FCC crystal, the nearest neighbor of the corner atom is the face center atom and the distance between them is

$\frac{\text{ face diagonal length }}{2}=\frac{\sqrt{2}a}{2}$

$\therefore$ Nearest neighbor distance $=\frac{\mathrm{a}\sqrt{2}}{2}=\frac{4.070\times \sqrt{2}}{2}\stackrel{0}{\mathrm{A}}=2.878\text{Å}$