A metal crystallizes with a face-centered cubic (FCC) lattice. The edge of the unit cell is $408\text{pm}$. The diameter of the metal atom is:

For a face-centered cubic (FCC) lattice, the relationship between the edge length ($a$) and the atomic radius ($r$) is:
$$4r=\sqrt{2}a$$
Given $a=408\text{pm}$.The diameter ($d$) is $2r$:
$$d=2r=\frac{\sqrt{2}a}{2}=\frac{a}{\sqrt{2}}$$
$$d=\frac{408}{1.414}\approx 288.5\text{pm}$$
The closest option is $288\text{pm}$.