The substance gray tin is found to crystallize in a cubic lattice, with an edge length of 646.0 pm. if the density of solid gray tin is 5.850 g/cm3, how many sn atoms are there per unit cell?

First find the volume of the cubic lattice given edge length of 646 pm or 6.46x10^-8 cm.

volume = (6.46x10^-8 cm) ^3

volume = 2.7x10^-22 cm^3

The total mass of the lattice is:

mass = (5.850 g/cm^3) * 2.7x10^-22 cm^3

mass = 1.577x10^-21 grams

The molar mass of tin is 118.71 g/mol and the Avogadros number is 6.022 x 10^23 atoms/mol, hence:

Sn atoms = [1.577x10^-21 g / (118.71 g/mol) ] * 6.022 x 10^23 atoms/mol

Sn atoms = 8 atoms