Answer: 71.72 days
Explanation:
This problem can be solved using the Radioactive Half Life Formula:
[tex]A=A_{o}.2^{\frac{-t}{h}}[/tex] (1)
Where:
[tex]A=0.12 g[/tex] is the final amount of Iodine-131
[tex]A_{o}=60 g[/tex] is the initial amount of Iodine-131
[tex]t[/tex] is the time elapsed
[tex]h=8 days[/tex] is the half life of Iodine-131
Knowing this, let's substitute the values and find [tex]t[/tex] from (1):
[tex]0.12 g=(60 g)2^{\frac{-t}{8 days}}[/tex] (2)
[tex]\frac{0.12 g}{60g}=2^{\frac{-t}{8 days}}[/tex] (3)
Applying natural logarithm in both sides:
[tex]ln(\frac{0.12 g}{60g})=ln(2^{\frac{-t}{8 days}})[/tex] (4)
[tex]-6.21=-\frac{t}{8 days}ln(2)[/tex] (5)
Finding [tex]t[/tex]:
[tex]t=71.72 days[/tex]
