the half - life of a radioactive isotope is t...
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 135 grams of a radioactive isotope, how much will be left after 4 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, $m_0 = 135$ grams and $n = 4$. So, $m=135\times(\frac{1}{2})^4$.
## Step3: Calculate the value
First, calculate $(\frac{1}{2})^4=\frac{1}{16}$. Then, $m = 135\times\frac{1}{16}=\frac{135}{16}=8.4375$ grams.
## Step4: Round the answer
Rounding $8.4375$ to the nearest gram gives $8$ grams.
# Answer:
8