$2.$ ZrC has a rock salt structure $($NaCl$)$ which may be considered as two interpenetrating f$.$c$.$c$.$ lattices of two types

of atoms. Corners and faces of the unit cell are located by C ions, and Zr ions locate at the edges and inside of the

unit cell. $($radius of Zr is $0\mathrm{.}23$ nm and radius of C is $0\mathrm{.}17$ nm$)$

a$)$ Draw ZrC unit cell showing the Zr and C ions and determine number of atoms.

b$)$ The atomic weight of Zr is $91\mathrm{.}2$ g$/$mole and that of C is $12$ g$/$mole$.$ Calculate the theorical density of ZrC in

grams$/$cm$3$

$.$

c$)$ Calculate the ionic packing factor of ZrC