you have 8,640 grams of a radioactive kind of cesium. if its half - life is 30 years, how much will be left…

Explanation:

Step1: Calculate number of half - lives

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

Step2: Use the radioactive decay formula

The formula for radioactive decay is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives. Here, $A_0 = 8640$ grams and $n = 4$. So $A=8640\times(\frac{1}{2})^4$.

Step3: Calculate the remaining amount

First, $(\frac{1}{2})^4=\frac{1}{16}$. Then $A = 8640\times\frac{1}{16}=540$ grams.

Answer:

540