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Lets say we have a rock sample that we want to know the age of. Luckily,...

Lets say we have a rock sample that we want to know the age of. Luckily, there are radioactive isotopes and we can count them! Currently, there are 12 stable daughter isotopes and 4 unstable parent isotopes (16 total). The half-life of the unstable isotope is 10 years. How old is the rock? Please explain how you got your answer!

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Answer #1

There are total 16 isotopes with half-life of 10 years. It means that the number of parent isotopes would be reduced by half in every 10 years. Therefore starting with 16 isotopes, we have ratio of parent to daughter isotope since the formation of rock:

16:0 (0 year)

8:8 (10 years)

4:12 (20 years)

2:14 (30 years)

1:15 (40 years)

The number of parent isotopes decreases and number of daughter isotopes decreases, as time passes. However the rate of change is decreases with time.

For given 12 daughter isotopes and 4 parent isotopes, the rock will have the age of 20 years.

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