Cubic crystal structure FCC has closest packing of atoms.
An atom in this type of crystal have 12 nearest neighbours.
In FCC nearest neighbours are atoms at A and D.
The Distance AB is (square root of 2) a
So AD = Half of AB = [(square root of 2) a] / 2
So radius r = Half of the distance between nearest neighbours
i.e. radius r = [(square root of 2) a] / 4
So a (unit cell dimension) = 4r / (square root of 2)
