The Radioactive Decay Constants ofK40as Determined from the Accumulation ofCa40in Ancient Minerals

New measurements of the rate of emission of gamma-ray energy by ${\mathrm{K}}^{40}$ give 4.9±0.1 Mev/sec. g K, in agreement with Gleditsch and Gráf. Thus the minimum value of the probability of electron capture in ${\mathrm{K}}^{40}$ is ${\lambda }_e=0.062\mathrm{}\times {10}^{-9\mathrm{}}$ ${\mathrm{yr}.\mathrm{}}^{-1\mathrm{}}$. Spectrochemical analysis of 4 samples of lepidolite known to be 2.1×${10}^9$ years old, as well as 22 younger lepidolites, gives a maximum value of 22, and a most probable value of 11 for the ratio of radiogenic ${\mathrm{Ca}}^{40}$ to residual ${\mathrm{K}}^{40}$ in the 2.1×${10}^9$ year old minerals. In such an ancient mineral, the ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$ ratio is a function not only of the probability of $\beta$-ray decay, ${\lambda }_{\beta }$, of ${\mathrm{K}}^{40}$ into ${\mathrm{Ca}}^{40}$, but also the probability of transformation by electron capture, ${\lambda }_e$, of ${\mathrm{K}}^{40}$ into ${\mathrm{A}}^{40}$. This is because the electron capture process may significantly deplete the ${\mathrm{K}}^{40}$, thus tending to produce larger ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$ ratios than would result from $\beta$-decay alone. The decay constants ${\lambda }_{\beta }$ and ${\lambda }_e$ reported by Bleuler and Gabriel predict ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$=152, while Mühlhoff's ${\lambda }_{\beta }$ predicts ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$=1.48 for a 2.1×${10}^9$ year old mineral. We have therefore suggested approximate corrections for the effects of $\beta$-ray scattering in the observations by Mühlhoff and by Bleuler and Gabriel on the absolute rate of emission of