This illustrates how we could compute the dimensions of a unit cell from the shape in which a substance crystallizes.
(a) Recall that there are 6.022 × 1023 atoms in a mole (this is Avogadro's number). From that, and the fact that platinum has a mass of 195.08 grams per mole, calculate the mass of each atom.
(b) Platinum crystallizes in a face-centered cubic lattice with atoms at each lattice point, that is, it looks like the middle picture given above for the diamond crystal. Find the number of platinum's per unit cell (hint. sum the fractions of platinum's that are inside of a single cell).
(c) From that, find the mass of a unit cell.
(d) Platinum crystal has a density of 21.45 grams per cubic centimeter. From this, and the mass of a unit cell, calculate the volume of a unit cell.
(e) Find the length of each edge.
(f) Describe a natural three-dimensional basis.