Question
A substance is on its fifth half-life. Which approximates the percentages of radioactive and stable isotopes, respectively?
96.9%; 3.1%
3.1%; 96.9%
12.5%; 87.5%
87.5%; 12.5%
96.9%; 3.1%
3.1%; 96.9%
12.5%; 87.5%
87.5%; 12.5%
Answers
GPT-4o mini
When a substance undergoes radioactive decay, the amount of the original radioactive isotope remaining can be calculated using the formula:
\[
\text{Remaining Isotope} = \left(\frac{1}{2}\right)^n \times 100\%
\]
where \( n \) is the number of half-lives.
For five half-lives (\( n = 5 \)):
\[
\text{Remaining Isotope} = \left(\frac{1}{2}\right)^5 \times 100\% = \frac{1}{32} \times 100\% = 3.125\%
\]
This means that approximately 3.1% of the original radioactive isotope remains.
The percentage of stable isotopes is the complement of the remaining radioactive isotope:
\[
\text{Stable Isotope} = 100\% - \text{Remaining Isotope} = 100\% - 3.125\% = 96.875\%
\]
Rounding this gives us approximately 96.9% stable isotope.
Thus, the percentages of radioactive and stable isotopes, respectively, are:
**3.1%; 96.9%**
\[
\text{Remaining Isotope} = \left(\frac{1}{2}\right)^n \times 100\%
\]
where \( n \) is the number of half-lives.
For five half-lives (\( n = 5 \)):
\[
\text{Remaining Isotope} = \left(\frac{1}{2}\right)^5 \times 100\% = \frac{1}{32} \times 100\% = 3.125\%
\]
This means that approximately 3.1% of the original radioactive isotope remains.
The percentage of stable isotopes is the complement of the remaining radioactive isotope:
\[
\text{Stable Isotope} = 100\% - \text{Remaining Isotope} = 100\% - 3.125\% = 96.875\%
\]
Rounding this gives us approximately 96.9% stable isotope.
Thus, the percentages of radioactive and stable isotopes, respectively, are:
**3.1%; 96.9%**