A crystalline solid of pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm⁻³, then the number of atoms present in 256 g of the crystal is N × 10²⁴. The value of N is?

The edge length a = 400 pm = 400 × 10⁻¹² cm
The formula for the density is D = ZM/N₀a³
8 g/cm³ = 4 atoms × M / (6.023 × 10²³ atoms/mol × (400 × 10⁻¹² cm)³)
The atomic mass M = 77 g/mol
The number of atoms in 256 g of pure substance = 256 g / 77 g/mol × 6.023 × 10²³ = 2 × 10²⁴
But it is equal to N × 10²⁴. Hence, the value of N is 2.