• # question_answer Which of the following expression is correct for packing fraction of $NaCl$ if the ions along the face are diagonally removed? 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) $\frac{\frac{4}{3}\pi \operatorname{r}_{-}^{3}+\frac{13}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}+{{\operatorname{r}}_{-}} \right)}^{3}}}$

 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 $=\frac{Occupied\,vol}{Total\,vol}$ $=\frac{\frac{13}{4}\times \frac{4}{3}\pi \operatorname{r}_{-}^{3}+4\times \frac{4}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}-{{\operatorname{r}}_{-}} \right)}^{3}}}$ $=\frac{\frac{13}{3}\pi \operatorname{r}_{-}^{3}+\frac{16}{3}\pi \operatorname{r}_{+}^{3}}{8{{\left( {{\operatorname{r}}_{+}}-{{\operatorname{r}}_{-}} \right)}^{3}}}$