Respuesta :
Answer:
Time till the 99% of the iodine is out of the system is 5.82 hours.
Explanation:
Initial amount of Iodine-134 =[tex]N_o=10.0 mg[/tex]
Final amount of iodine-134 left = N = [tex](100\%-99\%) of 10.0 mg = 1\% of 10 mg=0.1 mg[/tex]
Half life of iodine-134 = [tex]t_{\frac{1}{2}}=52.6 min[/tex]
Time till the 99% of the iodine is out of the system = t
Decay constant =[tex]\lambda [/tex]
[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{52.6 min}=0.0131749 min^{-1}[/tex]
[tex]\log N=\log N_o-\frac{\lambda t}{2.303}[/tex]
[tex]\log\frac{N}{N_o}=\frac{-\lambda t}{2.303}[/tex]
[tex]\log\frac{0.1 mg}{10 mg}=-\frac{0.0131749 min ^{-1}t}{2.303}[/tex]
t = 349.60417 min =5.8267 hours
(1 hour = 60 min)
Time till the 99% of the iodine is out of the system is 5.82 hours.
