Question

1. the half - life for cobalt - 60 is 5.272 years. how much of a 160 gram sample would remain after 15.816 years?

Explanation:

Step1: Calculate the number of half - lives

The formula to calculate the number of half - lives $n$ is $n=\frac{t}{T_{1/2}}$, where $t$ is the time elapsed and $T_{1/2}$ is the half - life. Given $t = 15.816$ years and $T_{1/2}=5.272$ years. So, $n=\frac{15.816}{5.272}=3$.

Step2: Calculate the remaining amount

The formula for the remaining amount $A$ of a radioactive substance is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount. Here, $A_0 = 160$ grams and $n = 3$. Then $A=160\times(\frac{1}{2})^3$. Since $(\frac{1}{2})^3=\frac{1}{8}$, $A = 160\times\frac{1}{8}=20$ grams.

Answer:

20 grams