Question

the half - life of a radioactive isotope is 20.0 minutes. what is the total amount of a 12.00 g sample that will remain after an hour?
o 1.500 g
o 3.000 g
o 6.000 g
o 8.000 g

Explanation:

Step1: Convert 1 hour to minutes

1 hour = 60 minutes

Step2: Calculate number of half - lives

Number of half - lives $n=\frac{60}{20}=3$

Step3: Use radioactive decay formula

The formula for radioactive decay is $N = N_0(\frac{1}{2})^n$, where $N_0$ is the initial amount and $n$ is the number of half - lives. Here, $N_0 = 12$ g and $n = 3$. So $N=12\times(\frac{1}{2})^3$.

Step4: Calculate the remaining amount

$N = 12\times\frac{1}{8}=1.5$ g

Answer:

1.5 g