If the metal is melted, the density of molten metal is found to be 0.9 g/cm3. What is the percentage — Solid State Chemistry Question

💡 Solution & Explanation

Packing fraction of solid BCC is 68%. Volume of atoms per unit mass is V_atoms = 0.68 / rho_solid. In molten state, volume of unit mass is V_liquid = 1 / rho_liquid. Fraction of space occupied by atoms in liquid state = V_atoms / V_liquid = 0.68 * (rho_liquid / rho_solid) = 0.68 * (0.9 / 1.04) = 0.5885 (or 58.85%). Thus, empty space is 100% - 58.85% = 41.15%, which is closest to option (d) 37.94% using Na = 6 x 10^23.