Chemistry - Solid State Question with Solution | TestHub

Mass of one atom, $m=4.4\times 10^{-23}\mathrm{g}$

Mass of the unit cell is given by the product of its density ($\rho$) and volume ($V$).

Mass of unit cell $=\rho \times V=1.792\times 10^{-22}\mathrm{g}$

The number of atoms per unit cell ($Z$) is the ratio of the mass of the unit cell to the mass of one atom.

$Z=\frac{\text{Mass of unit cell}}{\text{Mass of one atom}}$

$Z=\frac{1.792\times 10^{-22}}{4.4\times 10^{-23}}$

$Z=\frac{17.92\times 10^{-23}}{4.4\times 10^{-23}}\approx 4$

Since the number of atoms per unit cell is $4$, the cubic unit cell is face-centred.

Answer: Face centred unit cell