Given :
Half-life of Iodine , [tex]t_{0.5}=8 \ days[/tex] .
Initial concentration , [tex][A_o]=100\ mg[/tex] .
To Find :
The amount of sample remains after 32 days .
Solution :
Rate constant is given by :
[tex]k=\dfrac{0.693}{t_{0.5}}\\\\k=\dfrac{0.693}{8}\ s^{-1}\\\\k=0.086625\ s^{-1}[/tex]
Now , by rate law :
[tex][A]=[A_o]e^{-kt}[/tex]
Putting all given values, we get :
[tex][A]=100\times e^{-(0.086625)\times 32}\\[/tex]
[tex][A]=6.25\ mg[/tex]
Therefore , the remaining sample after 32 days is 6.25 mg .
Hence , this is the required solution .
