Question

carbon dating makes use of the principle of

Answer 1

Carbon dating is the method to determine the age of an object. It uses the principle of atomic masses  to determine the isotopes, so carbon can be dated back according to these isotopes 
Other principles involved in this are
Gas proportional counting
liquid scintillation counting
accelerator mass spectrometry

Answer 2

Carbon dating uses the principle of atomic masses.
 It uses atomic mass to determine the isotopes(isotopes have the same no. of protons and electrons in the atom, but they have a different no. of neutrons in the nucleus, so they have different atomic masses), so carbon can be dated back according to these isotopes .C-14 is radioactive and decays over time. We can measure the amount of C-14 left in the dead plant or animal (fossils) to determine the age.