Question

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

• A. $1.1513\times {10}^{24}$
• B. $3.472\times {10}^{24}$
• C. $10.416\times {10}^{24}$
• D. None of the above

Answer 1

The correct option is B $3.472\times {10}^{24}$

We know,

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$ $⟹7.2=\frac{\text{Mass}}{24\times {10}^{-24}}$
$\text{Mass}=1.72\times {10}^{-22}$
This is the mass of one unit cell.
Number of atoms per unit cell $=8\times \frac{1}{8}+2\times 1=1+2=3$
Mass of one atom $=\frac{1.72\times {10}^{-22}}{3}=5.76\times {10}^{-23}$
The number of atoms present in $200$ g of element $=\frac{200}{5.76\times {10}^{-23}}=3.472\times {10}^{24}$