If a high atomic weight is taken as evidence of a complicated structure of the atom, it might be expected that disintegration would occur more readily in heavy than in light atoms. At the same time, there is no reason to suppose that the elements of the highest atomic weight must be the most radio-active; in fact, radium is far more active than uranium, although its atomic weight is less. This is seen to be the case also in the radio-active products; for example, the radium emanation is enormously more active weight for weight than the radium itself, and there is every reason to believe that the emanation has an atom lighter than that of radium.
In order to explain the phenomena of radio-activity, Rutherford and Soddy have advanced the theory that the atoms of the radio-elements suffer spontaneous disintegration, and that each disintegrated atom passes through a succession of well-marked changes, accompanied in most cases by the emission of α rays.
A preliminary account of this hypothesis has already been given in [section 136], while the mathematical theory of successive changes, which is based upon it, has been discussed in [chapter IX]. The general theory has been utilized in chapters [X] and [XI] to account for the numerous active substances found in uranium, thorium, actinium and radium.
The theory supposes that, on an average, a definite small proportion of the atoms of each radio-active substance becomes unstable at a given time. As a result of this instability, the atoms break up. In most cases, the disintegration is explosive in violence and is accompanied by the ejection of an α particle with great velocity; in a few cases, α and β particles are expelled together, while in others a β particle alone escapes. In a few cases, the change in the atom appears to be less violent in character, and is not accompanied by the expulsion of either an α or β particle. The explanation of these rayless changes is considered in [section 259]. The expulsion of an α particle, of mass about twice that of the hydrogen atom, leaves behind it a new system lighter than the original one, and possessing chemical and physical properties quite different from those of the original element. This new system again becomes unstable, and expels another α particle. The process of disintegration, once started, proceeds from stage to stage at a definite measurable rate in each case.
At any time after the disintegration has commenced, there exists a proportion of the original matter, which is unchanged, mixed with the part which has undergone change. This is in accordance with the observed fact that the spectrum of radium, for example, does not change progressively with time. The radium breaks up so slowly that only a small fraction has been transformed in the course of a few years. The unchanged part still shows its characteristic spectrum, and will continue to do so as long as any radium exists. At the same time it is to be expected that, in old radium, the spectrum of those products which exist in any quantity should also appear.
The term metabolon has been suggested as a convenient expression for each of these changing atoms, derived from the successive disintegration of the atoms of the radio-elements. Each metabolon, on an average, exists only for a limited time. In a collection of metabolons of the same kind the number N, which are unchanged at a time t after production, is given by
where N₀ is the original number. Now dN/dt = -λN, or the fraction of the metabolons present, which change in unit time, is equal to λ. The value 1/λ may be taken as the average life of each metabolon.
This may be simply shown as follows:—At any time t after N₀ metabolons have been set aside, the number which change in the time dt is equal to λNdt or
