X = 5 Å Y = 8 Å Molar mass of solid = 259.8 g mo l - 1 A solid crystallises in hexagonal lattice as shown in above figure. Density of the solid is 5 g/ml . How many molecules are their in the given unit cell? (Avagadro's number = 6.023 × 1 0 23 )

Step-by-step solution

Volume of unit cell = Area of base × height = X 2 sin ⁡ 6 0 ° × Y = 5 × 1 0 - 8 2 × 0.866 × 8 × 1 0 - 8 = 1.732 × 1 0 - 22 c m 3 Number of molecules in the unit cell = V o l u m e × D e n s i t y M o l a r mass × 6.023 × 1 0 23 = 1.732 × 1 0 - 22 × 5 259.8 × 6.023 × 1 0 23 ≈ 2 .