CHAPTER IV The Law of Radioactive Decay A radioactive nucleus is one that will eventually disintegrate and release some energy. But when? One might imagine that a radioactive nucleus would begin to “age” from the moment of its birth, and that after the passage of a predetermined time, the disintegration process would take place. This is how radioactivity _might_ work in a deterministic universe. What actually happens to a radioactive nucleus, however, is much more interesting. At any instant of its life, the radioactive nucleus has some probability of disintegrating in the next second. This probability is unaffected by its age. No matter how long the nucleus has lived, its chance of disintegrating in the next second is always the same. It is as if a game of roulette were being played. The wheel spins, and if its number comes up, the nucleus disintegrates in the first second. If not, the wheel spins again. Each time the wheel spins there is some probability of its number coming up. The precise value of this probability is a characteristic of each particular radioactive species. The higher the probability, the more rapidly the nucleus may be expected to disintegrate. But a given nucleus need not do at any particular time what is expected of it. The notion of probability (or chance) has meaning only when applied to a large number of cases. To say that a given nucleus has one chance in a hundred of decaying in the next second means that out of some large number (say 100 million) of such radioactive nuclei, one per cent (one million) will decay in the next second. But it is absolutely impossible to say beforehand which nuclei will be the ones to decay. A particular nucleus may decay immediately or only after some very long time. The collection as a whole, however, will always do the expected thing. (This is the principle on which insurance companies operate.) The situation is best described in terms of a time span which is called the half-life of the radioactive species. The half-life is defined as the amount of time which is required for one half of a large number of identical radioactive nuclei to disintegrate. It makes no difference what this large number is, provided only that it is large enough.