Question

$CaF_{2}(s) \rightleftharpoons \underset{S_{1}M}{Ca^{2 +}} + \underset{2S_{1}\text{ M}}{2F^{-}}$

Now, $K_{sp} = S_{1}.\left( 2S_{1} \right)^{2} \Rightarrow S_{1} = \left( \frac{K_{sp}}{4} \right)^{1/3} = \left( \frac{3.2 \times 10^{- 11}}{4} \right)^{1/3} = 2 \times 10^{- 4}\text{ M}$

Now, in KF solution,

$S_{2} = \frac{K_{sp}}{\left\lbrack F^{-} \right\rbrack^{2}} = \frac{3.2 \times 10^{- 11}}{\left( 4 \times 10^{- 3} \right)^{2}} = 2 \times 10^{- 6}M$

Now, $\frac{S_{2}}{S_{1}} = \frac{2 \times 10^{- 6}}{2 \times 10^{- 4}} = \frac{1}{100}$