Question

An element crystallizes in a structure which is a cubic type of unit cell having one atom in each corner of the cube and $2$ atoms on one of its diagonals. If the volume of the unit cell is $24\times {10}^{-24}$ cm${}^3$ and the density of element is $7.2$ g cm${}^{-3}$, the number of atoms present in $200$ g of element is:

• A. $3.47\times {10}^{24}$
• B. $2.65\times {10}^{21}$
• C. $8.47\times {10}^{22}$
• D. none of the above

Answer 1

The correct option is A $3.47\times {10}^{24}$

Total number of atoms in the given unit cell = $(\frac{1}{8}\times 8)+2=3$
density $=\frac{zM}{N_a\times V}$

$7.2=\frac{3\times M}{6\times {10}^{23}\times 24\times {10}^{-24}}$

$M=345.6\times {10}^{-1}$

Number of atoms in $200g$ of element is $\frac{200}{34.5}\times 6.023\times {10}^{23}=3.47\times {10}^{24}$