the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to…

the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 130 grams of a radioactive isotope, how much will be left after 3 half - lives? use the calculator provided and round your answer to the nearest gram.

Answer

Explanation:

Step1: Recall half - life formula

The formula for the remaining amount of a radioactive substance after $n$ half - lives is $A = A_0\times(\frac{1}{2})^n$, where $A_0$ is the initial amount and $n$ is the number of half - lives.

Step2: Identify values

Here, $A_0 = 130$ grams and $n = 3$.

Step3: Calculate remaining amount

$A=130\times(\frac{1}{2})^3=130\times\frac{1}{8}=\frac{130}{8}=16.25$ grams.

Step4: Round to nearest gram

Rounding $16.25$ to the nearest gram gives $16$ grams.