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

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

K^{40}

λ_{e} = 0.062 \times 10^{- 9}

{yr .}^{- 1}

. 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

{Ca}^{40}

to residual

K^{40}

in the 2.1×

10^{9}

year old minerals. In such an ancient mineral, the

{Ca}^{40}

K^{40}

ratio is a function not only of the probability of

β

-ray decay,

λ_{β}

, of

K^{40}

into

{Ca}^{40}

, but also the probability of transformation by electron capture,

λ_{e}

, of

K^{40}

into

A^{40}

. This is because the electron capture process may significantly deplete the

K^{40}

, thus tending to produce larger

{Ca}^{40}

K^{40}

ratios than would result from

β

-decay alone. The decay constants

λ_{β}

and

λ_{e}

reported by Bleuler and Gabriel predict

{Ca}^{40}

K^{40}

=152, while Mühlhoff's

λ_{β}

predicts

{Ca}^{40}

K^{40}

=1.48 for a 2.1×

10^{9}

year old mineral. We have therefore suggested approximate corrections for the effects of

β

-ray scattering in the observations by Mühlhoff and by Bleuler and Gabriel on the absolute rate of emission of

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