Question
What is the age of a meteorite if potassium-40 decayed from 80 g to 10 g? The half-life of potassium-40 is 1.3 billion years.
1.3 billion years
2.6 billion years
3.9 billion years
5.2 billion years
1.3 billion years
2.6 billion years
3.9 billion years
5.2 billion years
Answers
GPT-4o mini
To determine the age of the meteorite based on the decay of potassium-40, we can use the concept of half-lives.
Given:
- Initial amount of potassium-40: 80 g
- Remaining amount of potassium-40: 10 g
- Half-life of potassium-40: 1.3 billion years
We can determine how many half-lives have passed by finding out how many times 10 g fits into 80 g through the half-life process:
1. After 1 half-life, 80 g would decay to 40 g.
2. After 2 half-lives, 40 g would decay to 20 g.
3. After 3 half-lives, 20 g would decay to 10 g.
So, it takes 3 half-lives to go from 80 g to 10 g.
Now, we calculate the total time:
- 3 half-lives × 1.3 billion years per half-life = 3.9 billion years.
Therefore, the age of the meteorite is **3.9 billion years**.
Given:
- Initial amount of potassium-40: 80 g
- Remaining amount of potassium-40: 10 g
- Half-life of potassium-40: 1.3 billion years
We can determine how many half-lives have passed by finding out how many times 10 g fits into 80 g through the half-life process:
1. After 1 half-life, 80 g would decay to 40 g.
2. After 2 half-lives, 40 g would decay to 20 g.
3. After 3 half-lives, 20 g would decay to 10 g.
So, it takes 3 half-lives to go from 80 g to 10 g.
Now, we calculate the total time:
- 3 half-lives × 1.3 billion years per half-life = 3.9 billion years.
Therefore, the age of the meteorite is **3.9 billion years**.