If the half-life of iodine-131 is 8 days, how much of a 5-g sample is left after 32 days?

1 Answer

$0.3125 \setminus$g

Explanation:

The half life ${T}_{\setminus \textrm{\frac{1}{2}}}$ is the period of time after which the amount of radioactive element becomes half of its original amount

The amount left $N$ after $n$ half lives of a radioactive element with original amount ${N}_{0}$ is

$N = {N}_{0} {\left(\frac{1}{2}\right)}^{n}$

Given that half life of Iodine-131 is $8$ days hence the amount left $N$ after 32 days i.e. $n = \frac{32}{8} = 4$ half lives taking initial amount ${N}_{0} = 5$g

$N = 5 {\left(\frac{1}{2}\right)}^{4} = \frac{5}{16} = 0.3125 \setminus$g