Question
How many milligrams of a 6.5×10-2kg sample of the x parent isotope will remain at the end of 13.5 billion years?
Answers
GPT-4o mini
To determine how much of a parent isotope remains after a certain period, we need to know the half-life of the isotope. However, since you did not provide the half-life, I will describe the general approach to calculate this:
1. **Convert the mass to milligrams**: Since you provided the mass in kilograms, first convert it to milligrams.
\[
6.5 \times 10^{-2} \, \text{kg} = 6.5 \times 10^{-2} \times 10^6 \, \text{mg} = 6.5 \times 10^4 \, \text{mg} = 65000 \, \text{mg}
\]
2. **Determine the number of half-lives**: If you know the half-life of the isotope, you can calculate how many half-lives fit into the time period of 13.5 billion years (13.5 x 10^9 years).
\[
\text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}}
\]
3. **Calculate the remaining amount using the remaining fraction formula**:
The remaining quantity after \( n \) half-lives is given by:
\[
N = N_0 \left( \frac{1}{2} \right)^n
\]
where \( N_0 \) is the initial quantity, and \( N \) is the remaining quantity.
Using these steps, you can calculate the remaining amount of the isotope once you have the half-life. Please provide the half-life if you need a specific numeric answer.
1. **Convert the mass to milligrams**: Since you provided the mass in kilograms, first convert it to milligrams.
\[
6.5 \times 10^{-2} \, \text{kg} = 6.5 \times 10^{-2} \times 10^6 \, \text{mg} = 6.5 \times 10^4 \, \text{mg} = 65000 \, \text{mg}
\]
2. **Determine the number of half-lives**: If you know the half-life of the isotope, you can calculate how many half-lives fit into the time period of 13.5 billion years (13.5 x 10^9 years).
\[
\text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}}
\]
3. **Calculate the remaining amount using the remaining fraction formula**:
The remaining quantity after \( n \) half-lives is given by:
\[
N = N_0 \left( \frac{1}{2} \right)^n
\]
where \( N_0 \) is the initial quantity, and \( N \) is the remaining quantity.
Using these steps, you can calculate the remaining amount of the isotope once you have the half-life. Please provide the half-life if you need a specific numeric answer.