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 α-particle. In getting this relation one arrives at the rather remarkable conclusion that the law of force between emitted α-particle and the rest of the nucleus is substantially the same in all the atoms even where the decay rates stand in the ratio 1022. §4 calls attention to the natural way in which the paradoxical results of Rutherford and Chadwick on the scattering of fast α-particles by uranium receive explanation with the model here used. §5 discusses certain limitations inherent in the methods employed.