Calculate the number of atoms in 1 g metal if it forms fcc crystal structure [ ( density ) a ^3=1.728 10⁻²² ~g ]

Step-by-step solution

Atoms in 1 g of metal The density of a crystal is related to its structure by = Z M N_A a^3 , where Z is the number of atoms per unit cell, M is the molar mass, and N_A is Avogadro's number. Since the metal forms an FCC structure, Z = 4 . Given a^3 = 1.728 10⁻²² g, substitute the density formula: ( Z M N_A a^3 ) a^3 = 1.728 10⁻²² g Simplifying yields Z M N_A = 1.728 10⁻²² g. Substituting Z = 4 gives 4M N_A = 1.728 10⁻²² g, which represents the mass of 4 atoms. The mass of one atom is m_ atom = 1.728 10⁻²² 4 = 4.32