Question

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

Answer 1

Number of atoms in a unit cell $\left(Z\right)=1+2=3$

$Z=\frac{l^3\times \rho \times N}{M}$

$M=\frac{l^3\times \rho \times N}{Z}$

$=\frac{24\times {10}^{-23}\times 7.2\times 6.023\times {10}^{23}}{3}=34.69$

Number of atoms $=\frac{\text{Mass}}{\text{Molar mass}}\times 6.023\times {10}^{23}$

$=\frac{200}{34.69}\times 6.023\times {10}^{23}=3.47\times {10}^{24}$.

Thus, the number of atoms $3.47\times {10}^{24}$