On the radioactivity of potassium and rubidium

Abstract

According to Fermi's theory of the β -disintegration the probability of the transition of a nuclear neutron into a proton depends largely on the energy difference involved, and therefore the lifetime of a β -emitting radioactive element and the upper velocity limit of its β -spectrum are connected by certain relations. From the experimental standpoint a connection of this nature is known from a paper of Sargent who, plotting the logarithms of the decay constants of the β -emitting radioactive bodies against the logarithms of maximum β -energies, found that they lie approximately on two straight lines. For our purpose we may write here for these lines the following equations: log λ = A + B log V. (1) If we measure the decay constant λ in sec -1 and the energy V in electron-kilovolts, we find for the constants A and B for the two lines: A 1 = –14 and A 2 = -24 B 1 = +3.7 B 2 = +5.8.