Question

you have 1,312 grams of a radioactive kind of lanthanum. if its half - life is 93 minutes, how much will be left after 279 minutes?

Explanation:

Step1: Calculate number of half - lives

The half - life is 93 minutes and the time elapsed is 279 minutes. The number of half - lives $n=\frac{279}{93}=3$.

Step2: Use half - life 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 final amount. Here, $N_0 = 1312$ grams and $n = 3$. So $N=1312\times(\frac{1}{2})^3$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^3=\frac{1}{8}$, and $N = 1312\times\frac{1}{8}=164$ grams.

Answer:

164 grams