To determine the age of the sample based on the remaining amount of radioactive parent isotope, we can use the concept of half-lives.
If the half-life of the isotope is 10,000 years, we can establish how many half-lives have passed based on the remaining amount.
Starting with a quantity of 1 (100% of the parent isotope):
- After 1 half-life (10,000 years), 1/2 remains.
- After 2 half-lives (20,000 years), 1/4 remains.
- After 3 half-lives (30,000 years), 1/8 remains.
Since only 1/8 of the radioactive parent remains, this means 3 half-lives have passed.
Therefore, the age of the sample is: 3 half-lives × 10,000 years/half-life = 30,000 years.
So, the sample is 30,000 years old.
1 answer