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 110 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: Identify the decay formula

The formula for radioactive - decay after $n$ half - lives is $m = m_0\times(\frac{1}{2})^n$, where $m_0$ is the initial mass and $n$ is the number of half - lives.

Step2: Substitute the given values

Here, $m_0 = 110$ grams and $n = 3$. So, $m=110\times(\frac{1}{2})^3$.

Step3: Calculate the result

First, calculate $(\frac{1}{2})^3=\frac{1}{8}$. Then, $m = 110\times\frac{1}{8}=\frac{110}{8}=13.75$ grams.

Step4: Round the answer

Rounding $13.75$ to the nearest gram gives $14$ grams.