Final answer:
Argon-argon dating is based on measuring the ratio of Ar-40 to K-40 in a rock sample to determine its age, with a K-40 half-life of about 1.25 billion years, making it useful for dating geological materials that are beyond the range of carbon-14 dating.
Step-by-step explanation:
Argon-argon dating is a radiometric dating method that is used to determine the age of rocks and minerals. The key isotope involved in this dating technique is Potassium-40 (K-40), which decays into Argon-40 (Ar-40) over time. By measuring the ratio of Ar-40 to K-40, scientists can calculate the age of a rock sample. The half-life of K-40 is approximately 1.25 billion years. This makes it a valuable tool for dating geological events that are older, as carbon-14 dating is limited to objects that are no more than about 50,000 to 60,000 years old.
Usually, if a rock sample is crushed, any Ar-40 gas that escapes can be measured, which allows for the determination of the Ar-40:K-40 ratio, thus yielding the age of the rock. This method is based on the assumption that the rocks did not contain any argon when they formed and that all the argon present comes solely from the decay of potassium-40. Potassium-argon dating can be used to date materials ranging from a few thousand years to billions of years old, allowing for a view into the early history of the Earth, which is older than the oldest known rocks and minerals. This dating technique is a cornerstone of geological studies and has applications in understanding the history of the Earth's crust and mantle.