An elemental metal crystallizes in a face-centred cubic (fcc) lattice. The atomic mass of the metal is 60 g mol ⁻¹ and its density is 6.25 g cm ⁻³ . The atomic radius of the metal is: (Use Avogadro's constant N_A = 6 10²³ mol ⁻¹ )

Step-by-step solution

For an fcc lattice, the number of atoms per unit cell is Z = 4 . The density d is given by: d = Z M N_A a^3 Substituting the given values: 6.25 = 4 60 6 10²³ a^3 a^3 = 240 6.25 6 10²³ = 240 37.5 10²³ = 2400 375 10⁻²³ = 6.4 10⁻²³ cm ^3 = 64 10⁻²⁴ cm ^3 Edge length a = (64 10⁻²⁴)^ 1/3 cm = 4 10⁻⁸ cm = 400 pm For an fcc unit cell, the relationship between atomic radius r and edge length a is: 4r = 2 a r = 2 400 4 = 100 2 pm Answer: 100 2 pm