Kinetic isotope effect approximation that reduced masses are approximately equal to the masses of the hydrogen, deuterium, or tritium was used. In addition, the vibrational motion was assumed to be approximated by a harmonic oscillator, so that formula_19 (X = H, D, or T). The subscript ""s"" refers to these "semi-classical" kinetic isotope effects, which disregard quantum tunneling. Tunneling contributions must be treated separately as a correction factor. For isotope effects involving elements other than hydrogen, many of these simplifications are not valid, and the magnitude of the isotope effect may depend strongly on some or all of the neglected factors. Thus, kinetic
Isotope persisted down to the present because their rate of decay is so slow (e.g. uranium-238 and potassium-40). Post-primordial isotopes were created by cosmic ray bombardment as cosmogenic nuclides (e.g., tritium, carbon-14), or by the decay of a radioactive primordial isotope to a radioactive radiogenic nuclide daughter (e.g. uranium to radium). A few isotopes are naturally synthesized as nucleogenic nuclides, by some other natural nuclear reaction, such as when neutrons from natural nuclear fission are absorbed by another atom. As discussed above, only 80 elements have any stable isotopes, and 26 of these have only one stable isotope. Thus, about two-thirds