A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400   pm…

Formula of density $=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}$

For FCC unit cell $\mathrm{Z},=4$

Edge length, $\mathrm{a}=4\times {10}^{-8}\mathrm{ }\mathrm{cm}$

$\mathrm{M}=\frac{\mathrm{d}\times {\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}{\mathrm{Z}}=\frac{8\times 6\times {10}^{23}\times 64\times {10}^{-24}}{4}\mathrm{ }\mathrm{g}/\mathrm{mol}$

Number of atoms $=\frac{\mathrm{wt}\left(\mathrm{g}\right)}{\mathrm{molar}\mathrm{ }\mathrm{mass}}\times {\mathrm{N}}_{\mathrm{A}}=\frac{256\times 10\times 6\times {10}^{23}}{8\times 6\times 16}=2\times {10}^{24}$ 

  Hence, the required value of  $\mathrm{N} = 2$