Question

the half - life of cesium - 137 is 30 years. if a rock contains 480 g of cesium - 137, how much of the original radioactive material will remain in 90 years?
a. 60.0 g
b. 120 g
c. 240 g
d. 390 g

Explanation:

Step1: Calculate number of half - lives

The half - life of cesium - 137 is 30 years and the time elapsed is 90 years. The number of half - lives $n=\frac{90}{30}=3$.

Step2: Use 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, $N_0 = 480$ g and $n = 3$. So $N=480\times(\frac{1}{2})^3$.

Step3: Calculate the remaining amount

$N = 480\times\frac{1}{8}=60$ g.

Answer:

A. 60.0 g