An element crystallizes in a body-centered cubic (bcc) lattice with an edge length of 400 pm. If the density of the element is 5.0 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 bcc lattice, the effective number of atoms per unit cell, Z = 2 . Edge length, a = 400 pm = 400 10⁻¹² m = 4 10⁻⁸ cm. The density of the unit cell is given by: = Z M N_A a^3 Rearranging for molar mass M : M = N_A a^3 Z Substituting the given values: M = 5.0 6.0 10²³ (4 10⁻⁸)^3 2 M = 30.0 10²³ 64 10⁻²⁴ 2 M = 30.0 6.4 2 = 96 g mol ⁻¹ . Answer: 96