Final answer:
Radioactive decay, such as that from uranium to lead, allows scientists to date geological materials. Clair Patterson used this principle to determine the Earth's age, which is estimated at 4.55 billion years. The predictable pattern of decay defined by half-lives forms the basis for uranium-lead dating methods in geology.
Step-by-step explanation:
Sometimes changes in elements happen at a very steady rate, as observed in the case where uranium changes to lead. This process can be exploited to determine the age of materials by using radioactive decay series, where the parent element undergoes a series of decays until it becomes a stable daughter isotope. Clair Patterson used this principle of radioactive decay to determine the age of the Earth, which is approximately 4.55 billion years old. The U-238 decay series involves a mix of decay processes, eventually leading to the formation of stable lead isotopes like Pb-206. This is possible because of the constant ratio of formation and decay of these isotopes, allowing scientists to date geological samples accurately.
Radioactive decay uses the principles of first-order kinetics, which means that the decay process follows a predictable pattern described by the isotope's half-life—the time it takes for half the atoms in a sample to decay. Uranium-238, for example, undergoes a complex decay series consisting of both alpha (α) and beta (β) decays. By measuring the ratio of uranium to lead in a sample, scientists can calculate how much time has passed since the rock or material formed. This method of dating, known as uranium-lead dating, is a key tool in geology and the study of Earth's history.