Nanowires are high aspect-ratio metal or semiconducting wires with diameters on the order of 1 to 100 nanometers and typical lengths of 1 to 100 microns. Nanowires likely will be used in the future to create high-density electronic circuits.
Nanowires can be fabricated from ZnO. ZnO has the wurtzite structure. The wurtzite structure is a hexagonal lattice with four atoms per lattice point at Zn(0, 0, 0), Zn(2/3, 1/3, 1/2), O(0, 0, 3/8), and O(2/3, 1/3, 7/8).
(a) How many atoms are there in the conventional unit cell?
(b) If the atoms were located instead at Zn(0, 0, 0), Zn(1/3, 2/3, 1/2), O(0, 0, 3/8), and O(1/3, 2/3, 7/8), would the structure be different? Please explain.
(c) For ZnO, the unit cell parameters are a = 3.24 Å and c = 5.19 Å.

This is not the ideal HCP c/a ratio.)
A typical ZnO nanowire is 20 nm in diameter and 5 mm long. Assume that the nanowires are cylindrical.
Approximately how many atoms are there in a single ZnO nanowire?