Question

An element crystallises 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 $24\times {10}^{-24}{\text{cm}}^3$ and density of element is $7.2{\text{g/cm}}^3$. Calculate the number of atoms present in $200\text{g}$ of the element.

Answer 1

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

$Z=\frac{l^3\times \rho \times N}{M}M=\frac{l^3\times \rho \times N}{Z}=\frac{24\times {10}^{-24}\times 7.2\times 6.023\times {10}^{23}}{3}=34.69\text{Number of atoms}=\frac{\text{Mass}}{\text{Molar mass}}\times 6.023\times {10}^{23}=\frac{200}{34.69}\times 6.023\times {10}^{23}=3.47\times {10}^{24}$