Modified expression for bulb-tracer depletion—Effect on argon dating standards

⁴⁰Ar/³⁹Ar geochronology depends critically on well-calibrated standards, often traceable to first-principles K-Ar age calibrations using bulb-tracer systems. Tracer systems also provide precise standards for noble-gas studies and interlaboratory calibration. The exponential expression long used for calculating isotope tracer concentrations in K-Ar age dating and calibration of ⁴⁰Ar/³⁹Ar age standards may provide a close approximation of those values, but is not correct. Appropriate equations are derived that accurately describe the depletion of tracer reservoirs and concentrations of sequential tracers. In the modified expression the depletion constant is not in the exponent, which only varies as integers by tracer-number. Evaluation of the expressions demonstrates that systematic error introduced through use of the original expression may be substantial where reservoir volumes are small and resulting depletion constants are large. Traditional use of large reservoir to tracer volumes and the resulting small depletion constants have kept errors well less than experimental uncertainties in most previous K-Ar and calibration studies. Use of the proper expression, however, permits use of volumes appropriate to the problems addressed.