Radiochemical techniques are useful in estimating the solubility product of
many compounds. In one experiment, \(50.0 \mathrm{~mL}\) of a \(0.010 \mathrm{M}
\mathrm{AgNO}_{3}\) solution containing a silver isotope with a radioactivity
of 74,025 counts per min per \(\mathrm{mL}\) were mixed with \(100 \mathrm{~mL}\)
of a \(0.030 \mathrm{M} \mathrm{NaIO}_{3}\) solution. The mixed solution was
diluted to \(500 \mathrm{~mL}\) and filtered to remove all of the AgIO
precipitate. The remaining solution was found to have a radioactivity of 44.4
counts per min per \(\mathrm{mL}\). What is the \(K_{\mathrm{sp}}\) of
\(\mathrm{AgIO}_{3} ?\)