A crystalline solid of a pure substance has a face-centred cubic...

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

For FCC unit cell $Z, = 4$

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

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

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

Hence, the required value of $N = 2$