Two ionic solids $AB$ and $CB$ crystallize in the same lattice. If $\frac{r_{A^{+}}}{r_{B^{-}}}$ and $\frac{r_{C^{+}}}{r_{B^{-}}}$ are $0.50$ and $0.70$, respectively, then the ratio of edge length of $AB$ and $CB$ is

The correct option is C 0.88
$\frac{r_{A^{⨁}}}{r_{B^{\ominus }}}=0.50$ and $\frac{r_{C^{⨁}}}{r_{B^{\ominus }}}=0.70$
$\Rightarrow \frac{r_{A^{⨁}}+r_{B^{⨁}}}{r_{B^{\ominus }}}=1+0.5=1.5$
Similarly, $\frac{r_{C^{⨁}}+r_{B^{\ominus }}}{r_{B^{\ominus }}}=1.70$
$\therefore \frac{r_{A^{⨁}}+r_{B^{\ominus }}}{r_{C^{⨁}}+r_{B^{\ominus }}}=\frac{1.5}{1.7}=0.88$
Also, $a_{AB}=2(r_{A^{⨁}}+r_{B^{\ominus }})$ and $a_{CB}=2(r_{C^{⨁}}+r_{B^{\ominus }})$
$\therefore \frac{a_{AB}}{a_{CB}}=\frac{2\times 1.5}{2\times 1.7}=0.88$