1) Radioactivity is produced when unstable nuclei break apart. In radioacitvity an atom of an element loses its identity with the loss of energy and release of sub atomic particles as the binding energy of the parent nucleus is very low and it is unstable and can break easily.
2) Radiometric dating is possible because the rates of decay of radioactive isotopes are constant. As the rate of decay of nucleus of an element follows first order kinetics with a constant specific rate constant. It decays over a period of time with the same rate irrespective of its source and other conditions.
3) Radiocarbon dating is used to date or know the age of a substance containing carbon or organic material.
Radiocarbon dating is used to date recent geologic events up to 75,000 years ago