An element with a molar mass 27g mol ⁻¹ forms a cubic unit cell. Calculate the number of atoms present in a unit cell if the density of metal is 2.7g cm ⁻³ . [a^3 N_A = 40 cm ^3 mol ⁻¹]

Step-by-step solution

The density of a cubic unit cell is given by the formula: d = Z M a^3 N_A where Z is the number of atoms per unit cell, M is the molar mass, a is the edge length, and N_A is Avogadro's number. Rearranging the formula to solve for Z : Z = d (a^3 N_A) M Substituting the given values d = 2.7 g cm ⁻³ , M = 27 g mol ⁻¹ , and a^3 N_A = 40 cm ^3 mol ⁻¹ : Z = 2.7 40 27 Z = 108 27 = 4 The number of atoms present in the unit cell is 4 .