A) \[\frac{\frac{13}{3}\pi \operatorname{r}_{-}^{3}+\frac{16}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}+{{\operatorname{r}}_{-}} \right)}^{3}}}\]
B) \[\frac{\frac{13}{3}\pi \operatorname{r}_{-}^{3}+\frac{4}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}+{{\operatorname{r}}_{-}} \right)}^{3}}}\]
C) \[\frac{\frac{16}{3}\pi \operatorname{r}_{-}^{3}+\frac{13}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}+{{\operatorname{r}}_{-}} \right)}^{3}}}\]
D) \[\frac{\frac{4}{3}\pi \operatorname{r}_{-}^{3}+\frac{13}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}+{{\operatorname{r}}_{-}} \right)}^{3}}}\]
Correct Answer: A
Solution :
| Effective number of remaining \[{{\operatorname{Cl}}^{-}}\] |
| \[=4-\left[ 2\times \frac{1}{8}+\frac{1}{2} \right]=\frac{13}{4}\] |
| Effective number of \[N{{a}^{+}}=4\] |
| Packing Fraction \[=\frac{Occupied\,vol}{Total\,vol}\] |
| \[=\frac{\frac{13}{4}\times \frac{4}{3}\pi \operatorname{r}_{-}^{3}+4\times \frac{4}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}-{{\operatorname{r}}_{-}} \right)}^{3}}}\] |
| \[=\frac{\frac{13}{3}\pi \operatorname{r}_{-}^{3}+\frac{16}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}-{{\operatorname{r}}_{-}} \right)}^{3}}}\] |
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