Solid $\text{Ba}({\text{NO}}_3{)}_2$ is gradually dissolved in a $1.0\times 10^{-4}\text{M}$ ${\text{Na}}_2{\text{CO}}_3$ solution. At what concentration of ${\text{Ba}}^{2+}$ will a precipitate begin to form? ($K_{sp}$ for ${\text{BaCO}}_3=5.1\times 10^{-9}$).

1. A
   $4.1\times 10^{-5}\text{M}$
2. B
   $5.1\times 10^{-5}\text{M}$
3. C
   $8.1\times 10^{-8}\text{M}$
4. D
   $8.1\times 10^{-7}\text{M}$