An element crystallises in a face-centred cubic (fcc) lattice with an edge length of 500 pm . If the density of the element is 4.0 g cm ⁻³ , the molar mass of the element is _____ g mol ⁻¹ . (Nearest integer) (Given: N_A = 6.0 10²³ mol ⁻¹ )

Step-by-step solution

For a face-centred cubic (fcc) lattice, the number of atoms per unit cell, Z = 4 . Edge length, a = 500 pm = 5 10⁻⁸ cm Density, d = Z M N_A a^3 Rearranging for molar mass, M = d N_A a^3 Z M = 4.0 6.0 10²³ (5 10⁻⁸)^3 4 M = 6.0 10²³ 125 10⁻²⁴ M = 6.0 12.5 = 75 g mol ⁻¹ Answer: 75