Solid $Ba(NO_3)_2$ is gradually dissolved in a $1.0 \times 10^{-4} M\; Na_2CO_3$ solution. At what concentration of $Ba^{2+}$ will a precipitate begin to form ? ($K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9} $ ).

Question

( A ) $5.1 \times 10^{-5}$ M
( B ) $4.1 \times 10^{-5}$ M
( C ) $8.1 \times 10^{-8}$ M
( D ) $8.1 \times 10^{-7}$ M