Question

radioactive iodine - 131 has a half life of eight days. the amount of a 200.0 gram sample left after 32 days would be
50.00 g
25.00 g
12.50 g
6.250 g

Explanation:

Step1: Calculate number of half - lives

The half - life of iodine - 131 is 8 days and the time elapsed is 32 days. The number of half - lives $n=\frac{32}{8}=4$.

Step2: Use the half - life formula

The formula for the remaining amount of a radioactive substance is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount and $n$ is the number of half - lives. Here, $N_0 = 200.0$ g and $n = 4$. So $N=200\times(\frac{1}{2})^4$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^4=\frac{1}{16}$, and $N = 200\times\frac{1}{16}=12.5$ g.

Answer:

12.50 g