A metal crystallizes in a face-centred cubic (fcc) lattice. A 160 g sample of the metal contains 2 10²⁴ atoms. If the density of the metal is 5.0 g cm ⁻³ , the edge length of the unit cell is:

Step-by-step solution

Total volume of the sample V = Mass Density = 160 5.0 = 32 cm ^3 Since the metal crystallizes in an fcc lattice, the number of atoms per unit cell is Z = 4 . Total number of unit cells in the sample = Total number of atoms Z = 2 10²⁴ 4 = 5 10²³ Volume of one unit cell a^3 = Total volume Total number of unit cells = 32 5 10²³ = 6.4 10⁻²³ cm ^3 = 64 10⁻²⁴ cm ^3 Edge length a = (64 10⁻²⁴)^ 1/3 cm = 4 10⁻⁸ cm Converting to picometers: a = 4 10⁻⁸ 10¹⁰ pm = 400 pm Answer: 400 pm