Which radioactive isotope and isotopes would you use to date a 4-billion-year-old piece of granite?

1) Would depend on what you were trying to date. It you were trying to date the crystallisation of the parental magma, most likely U-Pb dating on zircon or perhaps monazite if present. Both minerals occur commonly as igneous minerals in granite and are relatively resistant to metamorphism, so stand a reasonable chance of retaining the crystallization age. The U-Pb system is also a long-lived decay system, so is appropriate to the timescale.. If you were trying to date the age of the 'stuff' the granite was made from (i.e. when the 'stuff' was extracted from the mantle) Hf isotopes. If you were trying to date the cooling history of the granite, a combination of U-Pb (on minerals such as titanite), Ar-Ar and Rb-Sr dating. The Rb-Sr and K-Ar (which Ar-Ar dating is based upon) and the Lu-Hf system are also long-lived systems, which are appropriate to the timescalse but typically record different information from the U-Pb system in zircon. In the case of the Rb-Sr and K-Ar system, they are prone to disturbance by heating, which makes them useful for dating the cooling and uplift history of rocks. 

2) Is a tricky measurement. You could use Ar-Ar dating or U238-U234-Pb206 dating. But both are analytically difficult because both the U-Pb and K-Ar system are based on decays that are slower than is optimal for the age range. There is not really a better alternative though. Both methods, are however applicable to young igneous rocks, with care. 

3) C14 dating. The material is geologically young and organic, so if it has remained closed system, C14 is probably applicable. 

4) None. You would look for volcanic ash beds in the sedimentary sequence and do U-Pb dating on the contained zircons. With a few exceptions, fossils cannot be directly dated.

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