Question

Two ionic solids AB & CB crystallize in the same lattice. If $\frac{r{A}^{+}}{r{B}^{-}}$ and $\frac{r{C}^{+}}{r{B}^{-}}$ are 0.6 and 0.8 respectively then the ratio of edge length of AB and CD is -

• A. 0.68
• B. 0.78
• C. 0.88
• D. 0.98

Answer 1

The correct option is C 0.88

$\frac{r_{A^{+}}}{r{B}^{-}}=0.60$ and $\frac{r_{C^{+}}}{r{B}^{-}}=0.80$
$\Rightarrow \frac{r_{A^{+}}+r_{B^{-}}}{r_{B^{-}}}=0.60+1=\frac{r_{A^{+}}}{r_{B^{-}}}+1-------\left(1\right)$
Similarly, $\frac{r_{C^{+}}}{r_{B^{-}}}+1\frac{r_{C^{+}}+r_{B^{-}}}{r_{B^{-}}}=1.080=1.80-----\left(2\right)$
Dividing $e{q}^n$ (1) & (2) we get,
$\frac{r_{A^{+}}+r_{B^{-}}}{r_{c^{+}}+r_{B^{-}}}=\frac{1.60}{1.80}=0.88$
Also, $a_{AB}=2(r_{A^{+}}+r_{B^{-}})and{a}_{CB}=2(r_{c^{+}}+r_{B^{+}})$
$\therefore \frac{a_{AB}}{a_{CB}}=\frac{1.60}{1.80}=0.88$