Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell.

For a face-centred unit cell:

$a=2 \sqrt{2} r$

It is given that the atomic radius, r = 0.144 nm

So, $a=2 \sqrt{2} \times 0.144 \mathrm{~nm}$

= 0.407 nm

Hence, length of a side of the cell = 0.407 nm