An element crystallises in a cubic close packed structure having a fcc unit cell of an edge 200 pm. Calculate the density if 200 g of this element contain 24 × 102324 × 1023 atoms.
We know the formula of density is: d = Z × Ma3 × N0d = Z × Ma3 × N0 We are given that the unit cell is FCC, and for FCC the number of atoms is 4 (Z = 4). We are given the edge length as 200 pm. This can be written as: a = 200 × 10-8cma = 200 × 10-8cm N0= 24 × 1023N0= 24 × 1023 M = 200g Putting the values, we get: d = 4 × 200/8 × 10-24 × 24 × 1023 d = 41.67 g/cm
