Kinetic isotope effect effects, while "k"/"k" ~ 1.15-1.3 are typical for β secondary kinetic isotope effect. For reactants containing several isotopically-substituted β-hydrogen atoms, the observed isotope effect is often the result of several H/D's at the β position acting in concert. In these cases, the effect of each isotopically-labeled atom is multiplicative, and cases where "k"/"k" > 2 are not uncommon. The following simple expressions relating deuterium and tritium kinetic isotope effects, which are also known as the Swain equation (or the Swain-Schaad-Stivers equations), can be derived from the general expression given above using some simplifications: i.e., In deriving these expressions, the reasonable
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