Question
Plutonium-239, a radioactive isotope often used as fuel in nuclear reactors, has a half-life of 24,100 years. Approximately how long would it take for 504 grams of plutonium-239 to decay to just 63 grams?(1 point)
Responses
48,200 years
48,200 years
72,300 years
72,300 years
96,400 years
96,400 years
24,100 years
Responses
48,200 years
48,200 years
72,300 years
72,300 years
96,400 years
96,400 years
24,100 years
Answers
GPT-4o mini
To determine how long it would take for 504 grams of plutonium-239 to decay to 63 grams, we can use the concept of half-lives.
1. **Calculate the number of half-lives needed**:
- The starting amount is 504 grams.
- We want to know how many half-lives it takes to reduce that to 63 grams.
The decay can be analyzed as follows:
- After 1 half-life: \( 504 \text{ grams} \to 252 \text{ grams} \)
- After 2 half-lives: \( 252 \text{ grams} \to 126 \text{ grams} \)
- After 3 half-lives: \( 126 \text{ grams} \to 63 \text{ grams} \)
Thus, it takes 3 half-lives to go from 504 grams to 63 grams.
2. **Calculate the total time**:
- Each half-life of plutonium-239 is 24,100 years.
- Therefore, for 3 half-lives, the total time is:
\[
3 \times 24,100 \text{ years} = 72,300 \text{ years}
\]
So, the answer is **72,300 years**.
1. **Calculate the number of half-lives needed**:
- The starting amount is 504 grams.
- We want to know how many half-lives it takes to reduce that to 63 grams.
The decay can be analyzed as follows:
- After 1 half-life: \( 504 \text{ grams} \to 252 \text{ grams} \)
- After 2 half-lives: \( 252 \text{ grams} \to 126 \text{ grams} \)
- After 3 half-lives: \( 126 \text{ grams} \to 63 \text{ grams} \)
Thus, it takes 3 half-lives to go from 504 grams to 63 grams.
2. **Calculate the total time**:
- Each half-life of plutonium-239 is 24,100 years.
- Therefore, for 3 half-lives, the total time is:
\[
3 \times 24,100 \text{ years} = 72,300 \text{ years}
\]
So, the answer is **72,300 years**.