Question

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

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Solution

## 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,$\mathrm{D}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{unit}\mathrm{cell}}{\mathrm{Volume}\mathrm{of}\mathrm{unit}\mathrm{cell}}\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{Z}×\mathrm{M}}{{\mathrm{N}}_{\mathrm{a}}×{\mathrm{a}}^{3}}$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’$\mathrm{Unit}\mathrm{Cell}\mathrm{Mass}=\mathrm{m}×\mathrm{n}$Hence the density of a unit cell is the same as the density of the substance.

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