Question

the half life of iodine - 131 is 8.10 days. how much of a 200 - gram sample would be left after 24.3 days?
a. 100 grams
b. 50 grams
c. 25 grams
d. 12.5 grams

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{t}{T_{1/2}}$, where $t = 24.3$ days is the time elapsed and $T_{1/2}=8.10$ days is the half - life. So $n=\frac{24.3}{8.10}=3$.

Step2: Use decay formula

The amount of substance remaining $N = N_0\times(\frac{1}{2})^n$, where $N_0 = 200$ grams is the initial amount and $n = 3$ is the number of half - lives. So $N=200\times(\frac{1}{2})^3$.

Step3: Compute the result

$N = 200\times\frac{1}{8}=25$ grams.

Answer:

C. 25 grams