Derive the formula to determine the density of a unit cell.

(N/A) Let the edge length of a unit cell of a cubic crystal be $a$ determined by $X$-ray diffraction. Let the density of the solid be $d$ and the molar mass be $M$.
Volume of the unit cell $= a^3$
Mass of the unit cell $= z \times m$
Where,$z =$ number of atoms present in one unit cell and $m =$ mass of a single atom.
Mass of an atom in the unit cell is given by $m = \frac{M}{N_A}$,where $M$ is the molar mass and $N_A$ is the Avogadro constant.
Density of the unit cell $= \frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}$
$d = \frac{z \cdot m}{a^3}$
Substituting the value of $m$:
$d = \frac{z \cdot M}{a^3 \cdot N_A}$
The density of the unit cell is the same as the density of the substance.
Thus,the density of the solid can be determined using $z, M, a,$ and $N_A$.