Question

Gold crystallizes in CCP structure. The total number of voids present In $197\mathrm{gms}$ of Gold will be

Answer 1

Step 1: Number of atoms of gold

The molecular mass of Gold $\left(\mathrm{Au}\right)=197\mathrm{gms}$

Number of atoms of Gold

$$\begin{gathered} \mathrm{Au}=\frac{\mathrm{Weight}\mathrm{of}\mathrm{Gold}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{Gold}}\times {\mathrm{N}}_{\mathrm{A}} \\ \Rightarrow \mathrm{Au}=\frac{197}{197}\times {\mathrm{N}}_{\mathrm{A}} \\ \Rightarrow \mathrm{Au}={\mathrm{N}}_{\mathrm{A}} \end{gathered}$$

Step 2: Total number of voids

In CCP, there are $2\mathrm{n}$tetrahedral void and $\mathrm{n}$ Octahedral void

So, the total number of voids of Gold $\left(\mathrm{Au}\right)=2\mathrm{n}+\mathrm{n}$

$$\begin{gathered} =3\mathrm{n} \\ =3{\mathrm{N}}_{\mathrm{A}} \end{gathered}$$

Therefore the total number of voids present in $197\mathrm{gms}$ of Gold $\left(\mathrm{Au}\right)$ is $3{\mathrm{N}}_{\mathrm{A}}$.