Question

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is $8gc{m}^{-3},$ then the number of atoms present in 256 g of the crystal is $N\times {10}^{24}$. The value of N is

Answer 1

$d=\frac{Z\times M}{N_A\times a^3}8=\frac{4\times M}{6.022\times {10}^{23}\times (400\times {10}^{-10}{)}^3}$
$M=76.8gmo{l}^{-1}$
76.8 g contain $=6\times {10}^{23}atoms$
$\therefore$ 256 g will contain $=20\times {10}^{23}atoms$
$=2\times {10}^{24}$ atoms
$\therefore N=2$