Answer:
0.2774 grams of iodine-131 would remain at 39 days.
Explanation:
Initial concentration of iodine-131 = [tex][A_o]=8.0 g[/tex]
Final concentration of iodine-131 after time t = [A] = ?
Duration of time = t = 39 days
Half life of the iodine-131 = [tex]t_{1/2}=8.04 days[/tex]
Rate constant = [tex]k=?[/tex]
For the first order kinetics :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex][A]=[A_o]\times e^{-kt}[/tex]
[tex][A]=8.0\times e^{-\frac{0.693}{t_{1/2}\times t}[/tex]
[tex]=8.0\times e^{\frac{0.693}{8.04 day}\times 39 day}[/tex]
[A] = 0.2774 g
0.2774 grams of iodine-131 would remain at 39 days.
