A crystalline solid of a 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 × 10 24 . The value of N is

Step-by-step solution

Formula of density = Z × M N A × a 3 For FCC unit cell Z , = 4 Edge length, a = 4 × 10 - 8   cm M = d × N A × a 3 Z = 8 × 6 × 10 23 × 64 × 10 - 24 4   g / mol Number of atoms = wt g molar   mass × N A = 256 × 10 × 6 × 10 23 8 × 6 × 16 = 2 × 10 24 Hence, the required value of N   =   2