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 geochemistry usually is given as a multiple of the present atmospheric ratio (Ra). Common values for R/Ra: He/He isotope chemistry is being used to date groundwaters, estimate groundwater flow rates, track water pollution, and provide insights into hydrothermal processes, igneous geology and ore genesis. U-series isotopes are unique amongst radiogenic isotopes because, being in the U-series decay chains, they are both radiogenic and radioactive. Because their abundances are normally quoted as activity ratios rather than atomic ratios, they are best considered separately from the other radiogenic isotope systems. Uranium is well mixed in the ocean, and its decay produces Pa and