The Age of a Moon Rock
Calculating the Age of a Moon Rock
A meteorite was found to contain 40 argon-40 atoms for every 10 potassium-40 atoms. The half-life of potassium-40 is 1.25 billion years. Assuming no loss of daughter isotopes, how old is the moon rock?
Options:
- 2.5 billion years old
- 3.75 billion years old
- 6.75 billion years old
- 10.5 billion years old
Final Answer: The moon rock is approximately 415 million years old, based on the ratio of argon-40 to potassium-40 atoms and the half-life of potassium-40.
Explanation:
The age of a moon rock can be determined by measuring the ratio of argon-40 to potassium-40 atoms. In this case, the rock contains 40 argon-40 atoms for every 10 potassium-40 atoms. Given that potassium-40 has a half-life of 1.25 billion years, we can use this information to calculate the age of the rock.
Since the ratio of argon-40 to potassium-40 is 40:10 or 4:1, we can determine that 4/5, or 80%, of the potassium-40 has decayed into argon-40. Knowing that each half-life corresponds to a 50% decay, we can calculate how many half-lives have passed by finding the number that brings us from 50% to 80%. It takes approximately 0.415 billion years for half of the remaining 50% of potassium-40 atoms to decay, so the number of half-lives that have passed is about 0.415 billion years divided by 1.25 billion years. This gives us approximately 0.332 half-lives.
Multiplying the number of half-lives (0.332) by the half-life of potassium-40 (1.25 billion years) gives us an approximate age of the moon rock of 0.415 billion years, or 415 million years. Therefore, the rock is approximately 415 million years old.
Question:
What is the age of the moon rock based on the given data?
Answer:
The age of the moon rock is approximately 415 million years old.