Energy relations in the β-ray type of radioactive disintegration

Abstract

The difficulties connected with the continuous β-disintegration are well known. The fact that a given isotope of any element has a definite atomic weight suggests that the energy of the normal state of any nucleus is quantized ; further evidence is afforded by the alternating intensities in band spectra. Evidence from the fine structure of α -rays and from the γ-rays, proves that nuclei are capable of existing in quantized excited states. In fact, in all transformations where α -particles, γ-radiation or protons are ejected from nuclei, the evidence suggests, (i) that the nuclear energy is quantized, and (ii) that energy is conserved. On the other hand, when a nucleus P transforms itself into a nucleus Q by emission of a β-particle, the β-particle has all energies between zero and a definite upper limit. One may either conclude that the energy either of P or of Q is not quantized, or that energy is not conserved in the transition. Since the a-transitions leading up to P , and starting from Q , show no sign of any indefiniteness in the energy, it is difficult to accept the former alternative ; and it is thus usual to suppose that energy is not conserved. In this paper we make the suggestion that the sharp upper limit of the β-rav spectrum is a significant parameter with which to classify a β-disintegration. We suggest the following hypotheses : two elements P , Q , such that P -> Q is a β-disintegration, both possess definite atomic weights, and hence definite binding energies. Following Heisenberg* we assume that β-disintegration can only take place if the energy E P of the nucleus P is higher than the energy E q of the nucleus Q. We make the new assumption that the energy difference E P — E q is equal to the upper limit of the i. e., to the maximum energy with which a β-particle can be expelled. According to our assumption, the β-particle may be expelled with less energy than the difference of the energies E P — E q , of the two nuclei, but not with more energy . We do not wish in this paper to dwell on what happens to the excess energy in those disintegrations in which the electron is emitted with less than the maximum energy. We may, however, point out that if the energy merely disappears, implying a breakdown of the principle of energy conservation, then in a β-ray decay energy is not even statistically conserved. Our hypothesis is, of course, also consistent with the suggestion of Pauli that the excess energy is carried off by particles of great penetrating power such as neutrons of electronic mass.