Which expression gives the density ρ in terms of the number of atoms per unit cell n, atomic mass A, unit cell volume Vc, and Avogadro's number N_A?

• A. ρ = n A / Vc × N_A
• B. ρ = Vc / (n A) × N_A
• C. ρ = n / Vc × A × N_A
• D. ρ = n A / Vc

Answer: (A)

Mass density comes from mass per unit cell divided by the cell’s volume. The total mass in a unit cell is the number of atoms in the cell, n, times the mass of a single atom. A single atom’s mass is the molar mass A divided by Avogadro’s number N_A (because one mole, containing N_A atoms, weighs A grams). So mass per unit cell is nA/N_A. Dividing by the unit cell volume Vc gives the density: ρ = (nA/N_A)/Vc = nA/(N_A Vc). This form correctly ties together the number of atoms per cell, the atomic/molar mass, Avogadro’s number, and the cell volume. If A is given in atomic mass units, the same relation holds because 1 amu equals 1 g/mol divided by N_A, keeping the same structure.