# Radiometric Dating: Calculating Rock Age Using Potassium-40 and Argon-40

Radiometric dating is a method used to determine the age of rocks by analyzing the relative proportions of certain isotopes in the rock. In this case, we are dating rocks based on the proportions of potassium-40 and argon-40 isotopes. Potassium-40 is a parent isotope with a half-life of 1.25 billion years, meaning it takes 1.25 billion years for half of the potassium-40 in the rock to decay into argon-40.

When analyzing the ratios of argon-40 to potassium-40 in a rock, we can calculate the age of the rock. For example, if a rock contains 3 times as much argon-40 as potassium-40, it means that 3/4 of the original potassium-40 has decayed into argon-40. This ratio covers 1.5 half-lives of potassium-40.

To calculate the age of the rock in this scenario, we need to multiply the half-life of potassium-40 (1.25 billion years) by the number of half-lives covered by the ratio, which is 1.5. The result would be approximately 1.875 billion years, indicating the age of the rock.