At what $\frac{\left[ Br ^{-}\right]}{\sqrt{\left[ CO _{3}^{2-}\right]}}$ does the following cell have its reaction at equilibrium?
$Ag ( s )\left| Ag _{2} CO _{3}( s )\right| Na _{2} CO _{3}( aq )|| KBr ( aq )| AgBr ( s )| Ag ( s )$
$K _{ gP }=8 \times 10^{-12}$ for $Ag _{2} CO _{3}$ and $K _{ gP }=4 \times 10^{-13}$ for $AgBr$
(A) $\sqrt{1} \times 10^{-7}$
(B) $\sqrt{2} \times 10^{-7}$
(C) $\sqrt{3} \times 10^{-7}$
(D) $\sqrt{4} \times 10^{-7}$
