The Radioactive Decay Constants of K 40 as Determined from the Accumulation of Ca 40 in Ancient Minerals

New measurements of the rate of emission of gamma-ray energy by ${\mathrm{K}}^{40}$ give 4.9\ifmmode\pm\else\textpm\fi{}0.1 Mev/sec. g K, in agreement with Gleditsch and Gr\'af. Thus the minimum value of the probability of electron capture in ${\mathrm{K}}^{40}$ is ${\ensuremath{\lambda}}_{e}=0.062\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{yr}.}^{\ensuremath{-}1}$. Spectrochemical analysis of 4 samples of lepidolite known to be 2.1\ifmmode\times\else\texttimes\fi{}${10}^{9}$ 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\ifmmode\times\else\texttimes\fi{}${10}^{9}$ 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 $\ensuremath{\beta}$-ray decay, ${\ensuremath{\lambda}}_{\ensuremath{\beta}}$, of ${\mathrm{K}}^{40}$ into ${\mathrm{Ca}}^{40}$, but also the probability of transformation by electron capture, ${\ensuremath{\lambda}}_{e}$, 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 $\ensuremath{\beta}$-decay alone. The decay constants ${\ensuremath{\lambda}}_{\ensuremath{\beta}}$ and ${\ensuremath{\lambda}}_{e}$ reported by Bleuler and Gabriel predict ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$=152, while M\"uhlhoff's ${\ensuremath{\lambda}}_{\ensuremath{\beta}}$ predicts ${\mathrm{Ca}}^{40}$/${\mathrm{K}}^{40}$=1.48 for a 2.1\ifmmode\times\else\texttimes\fi{}${10}^{9}$ year old mineral. We have therefore suggested approximate corrections for the effects of $\ensuremath{\beta}$-ray scattering in the observations by M\"uhlhoff and by Bleuler and Gabriel on the absolute rate of emission of $\ensuremath{\beta}$-rays by K. These corrections lead to a mean value of 34 $\ensuremath{\beta}$-rays/sec. g K, or ${\ensuremath{\lambda}}_{\ensuremath{\beta}}=(0.65\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{yr}.}^{\ensuremath{-}1}$. The observed value of ${\mathrm{C}}^{40}$/${\mathrm{K}}^{40}$=11 then leads to ${\ensuremath{\lambda}}_{e}=(0.9\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{yr}.}^{\ensuremath{-}1}$, and a total half-period of $T=(0.45\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{9}$ yr. for ${\mathrm{K}}^{40}$. Then approximately 42 percent of the disintegrations of ${\mathrm{K}}^{40}$ are by $\ensuremath{\beta}$-ray emission to the ground state of ${\mathrm{Ca}}^{40}$; 4 percent by electron capture to a 1.5-Mev excited state in ${\mathrm{A}}^{40}$, and 54 percent by electron capture to the ground state of ${\mathrm{A}}^{40}$. It is shown that these revised disintegration constants lead to a sufficiently smaller thermal output by K early in the earth's history to satisfy Birch's calculations on the possibility of an early solid terrestrial crust, and to remove arguments relating to the origin of species through gene mutations caused by intense ${\mathrm{K}}^{40}$ radiations early in the earth's history.