Question

there are 976 grams of a radioactive substance. how much substance will remain after 120 seconds if its half - life is 30 seconds? 30.5 grams 61 grams 122 grams 91.5 grams

Explanation:

Step1: Calculate the number of half - lives

The half - life is 30 seconds and the time elapsed is 120 seconds. The number of half - lives $n=\frac{120}{30}=4$.

Step2: Use the radioactive decay 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. Here, $N_0 = 976$ grams and $n = 4$. So $N=976\times(\frac{1}{2})^4$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^4=\frac{1}{16}$, and $N = 976\times\frac{1}{16}=61$ grams.

Answer:

61 grams