Derive the expression for the density $(d)$ of a unit cell: $d = \frac{zM}{a^3 N_A}$.

(N/A) $1$. Let the edge length of the unit cell be $a \ cm$.
$2$. The volume of the unit cell is $V = a^3 \ cm^3$.
$3$. Let $z$ be the number of atoms per unit cell and $M$ be the molar mass of the substance.
$4$. The mass of one atom is $\frac{M}{N_A}$,where $N_A$ is Avogadro's number.
$5$. The total mass of the unit cell is $z \times \frac{M}{N_A}$.
$6$. Density $(d) = \frac{\text{Mass of unit cell}}{\text{Volume of unit cell}} = \frac{z \times M}{a^3 \times N_A}$.