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 220 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 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: Substitute the given values
Here, $A_0 = 220$ grams and $n = 5$. So, $A=220\times(\frac{1}{2})^5$.
## Step3: Calculate the value of $(\frac{1}{2})^5$
$(\frac{1}{2})^5=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}$.
## Step4: Calculate the remaining amount
$A = 220\times\frac{1}{32}=\frac{220}{32}=6.875$ grams.
## Step5: Round the answer
Rounding $6.875$ to the nearest gram gives $7$ grams.
# Answer:
7 grams