An element crystallises in fcc unit cell with cell edge length of 3.608 10⁻⁸ cm, the density of element is 8.92 gcm ⁻³ . Calculate the atomic mass of element ( N _A = 6.022 10²³ ).

Step-by-step solution

For an fcc unit cell, the number of atoms per unit cell is Z = 4 . The formula for the density of a unit cell is given by: d = Z M N_A a^3 Rearranging the formula to solve for the atomic mass M : M = d N_A a^3 Z Given values: d = 8.92 g cm ⁻³ N_A = 6.022 10²³ mol ⁻¹ a = 3.608 10⁻⁸ cm Substituting the values into the formula: M = 8.92 6.022 10²³ (3.608 10⁻⁸)^3 4 M = 8.92 6.022 10²³ 46.97 10⁻²⁴ 4 M = 252.3 4 M 63.07 g/mol Rounding to the nearest integer, the atomic mass of the element is 63 g/mol . Answer: 63 g/mol