An element crystallises in a body-centred cubic (bcc) lattice with an edge length of 400 pm . If the density of the element is 10 g cm ⁻³ , the total number of atoms present in 256 g of the element is x 10²³ . The value of x is

Step-by-step solution

Volume of the given mass of the element: V = Mass Density = 256 g 10 g cm ⁻³ = 25.6 cm ³ Volume of one unit cell: a³ = (400 10⁻¹⁰ cm )³ = 64 10⁻²⁴ cm ³ Number of unit cells in the given mass: Number of unit cells = V a³ = 25.6 64 10⁻²⁴ = 0.4 10²⁴ = 4 10²³ Since the element crystallises in a bcc lattice, the number of atoms per unit cell ( Z ) is 2 . Total number of atoms = Z Number of unit cells Total number of atoms = 2 4 10²³ = 8 10²³ Thus, the value of x is 8 . Answer: 8