The atom ⁴⁰K decays radioactively to the gas ⁴⁰Ar.An ancient rock is found to contain enough ⁴⁰Ar gas to indicate that 77.0% of the ⁴⁰K in the rock has decayed to ⁴⁰Ar since the rock solidified.(Any previous argon would have boiled out of liquid rock. )How long ago did the rock solidify? The half-life of ⁴⁰K is 1.25 billion years.

Question

Quizplus · Accepted Answer

Given that 77.0% of the potassium (⁴⁰K) has decayed into argon (⁴⁰Ar), this means that 23.0% of the original potassium remains. Using the half-life formula, we can calculate the number of half-lives that have passed. The formula for the remaining amount of a substance after a certain number of half-lives is: remaining amount = initial amount * (1/2)^(time/half-life). Solving for the number of half-lives gives us approximately 2.1 half-lives. Multiplying 2.1 half-lives by the half-life duration of 1.25 billion years gives an age of approximately 2.65 billion years.

The Atom 40K Decays Radioactively to the Gas 40Ar

The Atom ⁴⁰K Decays Radioactively to the Gas ⁴⁰Ar