$4-3$ Prove that the $\frac{c}{a}$ ratio for an ideal hcp structure is $\sqrt[\phantom{2}]{\frac{8}{3}}.$

$4-4$ How many atoms per square millimeter are there on a $(100)$ face of a copper crystal?

$(a_0=3\mathrm{.}60=0\mathrm{.}36(nm).)$ Answer $=1\mathrm{.}54$ x $10^13$ atoms$/$mm$^2$