The Half-Life of Actinouranium and the Problem of Geologic Time

Abstract

The actinium series arises from an isotope ${\mathrm{U}}^{235}$, or from two such isotopes ${\mathrm{U}}^{239}$ and ${\mathrm{U}}^{235}$, genetically connected. From work of Hahn and Meitner, the first possibility is almost certainly right. Assuming as a working hypothesis that ${\mathrm{U}}^{235}$ is the only long-lived uranium isotope, equations are developed for determining its decay constant ${\lambda }_4$ from data concerning radioactive minerals and substances. These equations also give the decay constant ${\lambda }_1$ of ${\mathrm{U}}^{238}$ and mineral ages. The results depend on the value of the actinium "branching" ratio, which lies between 0.03 and 0.04. Computations are carried out using both of these extreme values. Four minerals are discussed but only two, Karlshus bröggerite and Wilberforce uraninite, yield reliable results. The mean values from these are: The best value for the half-life of ${\mathrm{U}}^{238}$ is (4.58±0.09) ${10}^9$ yr. If ${\mathrm{U}}^{239}$ exists and has a half-life long compared with that of ${\mathrm{U}}^{235}$, the values for ${\lambda }_4$ would apply to ${\mathrm{U}}^{239}$. The ages, insensitive to the value of the branching ratio, are: Karlshus bröggerite, 0.81×${10}^9$ yr.; Wilberforce uraninite, 1.04×${10}^9$ yr. Since quantitative study of chemical alteration may throw light on the process and prove helpful in determining decay constants and mineral ages, equations are developed to show the effect of uniform leaching. Rates of removal or addition of Pb, U and Th are assumed different, but each of them is supposed constant in time. The resulting equations are applied to Katanga pitch-blende, to illustrate the method.