Question

Ga (atomic mass $70\mathrm{u}$) crystallizes in a hexagonal close-packed structure. The total number of voids in $0.581\mathrm{g}$ of $\mathrm{Ga}$ is ________ $\times {10}^{21}$. (Round off to the nearest integer). [Given: ${\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}$].

Answer 1

The above question can be solved as:

Step 1: Number of moles of $\mathrm{Ga}=0.581/70$

Step 2: Number of atoms of $\mathrm{Ga}=0.581/70\times {\mathrm{N}}_{\mathrm{A}}$

Step 3:

Total number of voids $$\begin{gathered} =0.581/70\times {\mathrm{N}}_{\mathrm{A}}\times 3 \\ =0.0249\times 6.023\times {10}^{23} \\ \cong 15\times {10}^{21} \end{gathered}$$

In hexagonal close packing, there are one octahedral void and two tetrahedral voids and the total number of voids is equal to $15\times {10}^{21}$.

Therefore, Ga (atomic mass $70\mathrm{u}$) crystallizes in a hexagonal close-packed structure. The total number of voids in $0.581\mathrm{g}$ of $\mathrm{Ga}$ is $15\times {10}^{21}$.