Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell. What is the length of a side of the cell?

Solution: Given, atomic radius = 0.144 nm

Type of unit cell = face centered

We know that side (a) in fcc =2√2

Thus, a = 2√2  × 0.144 nm

 a = 2 × 1.414 × 0.144 = 407 nm.

Thus the side of the given cell = 407 nm.