Final answer:
The U-Pb (Uranium-Lead) isotopic system is most suitable for dating rocks from the Permian Period due to the long half-life of Uranium-238, which makes it capable of dating ancient rocks. Radiometric dating relies on the predictable decay rate from the parent isotope to the daughter isotope to estimate the age of the sample.
Step-by-step explanation:
To date a rock from the Permian Period, the appropriate parent/daughter isotopic system to use would be U-Pb (Uranium-Lead). The Permian Period is quite old, ranging from roughly 299 to 252 million years ago. Uranium-238 decays into lead-206 through a series of intermediate decay products and has a half-life of approximately 4.5 billion years. This long half-life makes U-238 ideal for dating ancient rocks because it allows us to date materials back to the formation of the Earth. Radiometric dating converts the measured amount of a radioactive element into an estimate of the sample's age by using the known decay rate of the parent isotope to the daughter isotope.
It's important to use an isotope system like U-Pb for the Permian Period because other systems, such as potassium-argon (K-Ar), have shorter half-lives which are more effective for dating younger geological materials. For instance, K-40 decays to Ar-40 and is useful for dating materials that are on the order of billions to tens of thousands of years old due to its half-life of 1.25 billion years. However, this is less effective than U-Pb for the Permian because some potassium-40 might have already decayed to undetectable levels.