⁴⁰K decays to ⁴⁰Ar with a half-life of 1.25 x 10⁹ yr.Assume that rocks contain no ⁴⁰Ar when they form, and that the only way ⁴⁰Ar can be present is through the decay of ⁴⁰K.If the ratio of ⁴⁰K to ⁴⁰Ar in a particular rock is found to be 1:3, what is the age of the rock?

Question

Quizplus · Accepted Answer

The ratio of 1:3 means that for every 1 part of ⁴⁰K, there are 3 parts of ⁴⁰Ar. This implies that 3 parts have decayed from the original 4 parts of ⁴⁰K, leaving 1 part. Therefore, 3/4 of the original ⁴⁰K has decayed. Using the decay formula, this corresponds to 2 half-lives, or 2.50 x 10⁹ years.

40K Decays to 40Ar with a Half-Life of 1

⁴⁰K Decays to ⁴⁰Ar with a Half-Life of 1