Quantum Mechanics and Radioactive Disintegration

Application of quantum mechanics to a simple model of the nucleus gives the phenomenon of radioactive disintegration. The statistical nature of the quantum mechanics gives directly disintegration as a chance phenomenon without any special hypothesis. §1 contains a presentation of those features of quantum mechanics which are here used and gives a simple calculation of the disintegration constant. §2 discusses the qualitative application of the model to the nucleus. §3 presents quantitative calculations amounting to a theoretical interpretation of the Geiger-Nuttall relation between the rate of disintegration and the energy of the emitted $\alpha$-particle. In getting this relation one arrives at the rather remarkable conclusion that the law of force between emitted $\alpha$-particle and the rest of the nucleus is substantially the same in all the atoms even where the decay rates stand in the ratio ${10}^{22}$. §4 calls attention to the natural way in which the paradoxical results of Rutherford and Chadwick on the scattering of fast $\alpha$-particles by uranium receive explanation with the model here used. §5 discusses certain limitations inherent in the methods employed.