The unit cell of aluminium is a cube with an edge length of $405 \mathrm{pm}$. The density of aluminium is $2.70 \mathrm{gm} {\mathrm{cm}}^{-3}$. What is the type of unit cell of aluminium crystals ?

The quantities provided in the question are:

$a=405 \mathrm{pm}, \rho =2.70 gm/c{m}^3 , M=27$

We know that the density of a cubic unit call is given by the formula, $\rho =\frac{Z\times M}{N_A\times a^3}$

Rearranging the formula we get: $Z=\frac{\rho \times N_A\times a^3}{M}$

Substituting the given values and simplifying:

$Z=\frac{2.70\times 6.023\times {10}^{23}\times {\left(4.05\times {10}^{-8}\right)}^3}{27}$

$Z\simeq 4$
Hence, it is a face-centered cubic (FCC) unit cell.