In a saturated solution of the sparingly soluble strong electrolyte $AgIO_3$ (molecular mass $= 283$),the equilibrium which sets in is $AgIO_{3(s)} \rightleftharpoons Ag^+_{(aq)} + IO^-_{3(aq)}$. If the solubility product constant $K_{sp}$ of $AgIO_3$ at a given temperature is $1.0 \times 10^{-8}$,what is the mass of $AgIO_3$ contained in $100 \ mL$ of its saturated solution?

• A
  $1.0 \times 10^{-4} \ g$
• B
  $28.3 \times 10^{-2} \ g$
• C
  $2.83 \times 10^{-3} \ g$
• D
  $1.0 \times 10^{-7} \ g$