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 165 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: Determine the decay formula

The formula for radioactive - decay 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 the values of $A_0$ and $n$

Given that $A_0 = 165$ grams and $n = 3$.

Step3: Substitute the values into the formula

$A=165\times(\frac{1}{2})^3$. Since $(\frac{1}{2})^3=\frac{1}{8}$, then $A = 165\times\frac{1}{8}=\frac{165}{8}=20.625$.

Step4: Round the result

Rounding $20.625$ to the nearest gram gives $21$ grams.