Question

the half - life of indium - 111 is 67.2 hours. how many milligrams of indium - 111 would remain after 14 days if the initial amount was 50.0 mg

25.0 mg
1.56 mg
0.781 mg
3.13 mg

Explanation:

Step1: Convert days to hours

14 days $\times$ 24 hours/day = 336 hours

Step2: Calculate number of half - lives

$n=\frac{336}{67.2}=5$

Step3: Use half - life formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount and $n$ is the number of half - lives. Given $N_0 = 50.0$ mg and $n = 5$. So $N=50\times(\frac{1}{2})^5$
$N = 50\times\frac{1}{32}=1.5625\approx1.56$ mg

Answer:

1.56 mg