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 145 grams of a radioactive isotope, how much will be left after 5 half - lives? use the calculator provided and round your answer to the nearest gram.
Answer
Explanation:
Step1: Identify 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 values
Given $m_0 = 145$ grams and $n = 5$. So, $m=145\times(\frac{1}{2})^5$.
Step3: Calculate $(\frac{1}{2})^5$
$(\frac{1}{2})^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}$.
Step4: Calculate final mass
$m = 145\times\frac{1}{32}=\frac{145}{32}=4.53125$ grams.
Step5: Round the answer
Rounding $4.53125$ to the nearest gram gives $5$ grams.
Answer:
5