Question

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

Answer 1

The edge length $a=400pm=400\times {10}^{-10}cm$
The formula for the density is
$D=\frac{ZM}{N_0{a}^3}$
$8g/c{m}^3=\frac{4atomsM}{6.023\times {10}^{23}atoms/mol\times (400\times {10}^{-10}cm{)}^3}$
The atomic mass $M=77g/mol$
The number of atoms in 256 g of pure substance $=\frac{256g}{77g/mol}\times 6.023\times {10}^{23}=2\times {10}^{24}$
But it is equal to $N\times {10}^{24}$.

Hence, the value of N is 2.