An aqueous solution contains an unknown concentration of $Ba^{2+}$. When $50\; mL$ of the $1M$ solution of $Na_2SO_4$ is added, $BaSO_4$ just begins to precipitate. The final volume is $500\; mL$. The solubility product of $BaSO_4$ is $1 \times 10^{-10}$. What is the original concentration of $Ba^{2+}$.

Question

( A ) $1.0 \times 10^{-10}M$
( B ) $5 \times 10^{-9}M$
( C ) $2 \times 10^{-9}M$
( D ) $1.1 \times 10^{-9} M$