Consider a crystal with a face$-$centered cubic $($FCC$)$ structure, and assume that $1\%$ of the lattice sites are vacant due to vacancies. The density of the crystal is $4\mathrm{.}0$g$/$cm$3,$ and the molar mass of the atoms in the crystal is $60$g$/$mol$.$

a$)$ Calculate the number of vacant lattice sites per unit volume.

b$)$ Determine the total number of vacancies in a crystal with a volume of

$2\mathrm{.}0\backslash$times $106$ cm$3$

c$)$ If each vacancy is associated with a missing atom, calculate the percentage of

missing atoms in the crystal.