Question

Is the density of a unit cell the same as the density of the substance?

Answer 1

Unit cell:

• The mass of a unit cell is equal to the product of the number of atoms in a unit cell and the mass of each atom in the unit cell.
• For real crystals with defects, the density can be slightly different due to vaccancies, dislocations, grain boundaries,s, etc.

A unit cell will have a density of,

$$\begin{gathered} \mathrm{D}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{unit}\mathrm{cell}}{\mathrm{Volume}\mathrm{of}\mathrm{unit}\mathrm{cell}} \\ =\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{a}}\times {\mathrm{a}}^3} \end{gathered}$$

Depending on what sort of cell it is, the number of atoms will vary. The mass of a unit cell is calculated by multiplying the number of atoms (n) into the mass of each atom ‘m’

$\mathrm{Unit}\mathrm{Cell}\mathrm{Mass}=\mathrm{m}\times \mathrm{n}$

Hence the density of a unit cell is the same as the density of the substance.