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.
If the number is not large enough, fluctuations will occur, and instead of 50 per cent of the nuclei decaying during the period of a half-life, it may be 40 per cent or 60 per cent. As a matter of fact the 40 per cent to 60 per cent limits correspond to a sample size of about 100 nuclei. For 10,000 nuclei, the limits will be 49 per cent to 51 per cent. The number of radioactive nuclei with which we customarily deal, is about 10²³ (100,000,000,000,000,000,000,000). This is the number, for example, of radioactive nuclei in about an ounce of radium. For such a large number of nuclei the deviation from 50-per-cent decay during a half-life will be utterly negligible. Thus we live in a universe which, on a macroscopic scale, appears ordered and subject to exact laws; while underlying these laws, on a microscopic scale, nature plays out a game of chance, full of randomness and uncertainty in the individual case.
We may draw a graph showing how N, the number of the remaining radioactive nuclei, varies with the time t. The graph shows that: in the first half-life T, half of the original number N₀ of radioactive nuclei decay. In the second half-life, half of those remaining decay, and so on. After the time T, one half of the original radioactive nuclei still remain; after 2T, one quarter remain; and so forth.
Different radioactive species have different half-lives. Many are only a small fraction of a second; some are billions of years. N¹⁶ decays to O¹⁶ (plus an electron and a neutrino) with a half-life of about eight seconds. A free neutron decays into a proton, an electron, and a neutrino with a half-life of 13 minutes. Strontium with weight 90 (Sr⁹⁰) undergoes a beta decay with a half-life of 28 years. (This is an isotope that is not found anywhere in nature, but is made in fairly large quantities in the fission process.) Potassium with weight 40 (K⁴⁰), which is present in the amount of 0.01 per cent in ordinary potassium, has a half-life of one billion years. It has presumably been left over from the time when the primordial elements were formed. Half-lives for gamma decay are extremely short by comparison to those for beta decay. They usually amount to a small fraction of a second.
Radioactivity is characterized by the kind of particle emitted from the nucleus (our examples, so far, have been of beta and gamma particles), by the energy possessed by this particle, and by the half-life in which the radioactive decay takes place.
The biological hazard from radioactivity depends on all three of these characteristics. No matter whether the radioactive nuclei are produced in an atomic explosion or in an atomic reactor, some time will in general elapse before a human population can become exposed. If this time is long compared to the half-life of the radioactive species, most of the nuclei will have disintegrated, and the hazard will thereby be reduced. If, on the other hand, the half-life is long compared to this time, as well as to the life-span of a human being, the rate at which disintegrations occur will be low, and again the hazard will be reduced.
In short the dangerous half-lives are the intermediate ones, not too long, not too short. Sr⁹⁰ is an example.
CHAPTER V
Breakup of the Nucleus
The positive electric charges within an atomic nucleus repel one another. In the most heavily charged nuclei this repulsion becomes so great that the nucleus can break into two parts, simultaneously releasing a considerable amount of energy. In the case of spontaneous nuclear fission the two parts are more or less equal in size. In the process of alpha decay one of the parts (the alpha particle) is much smaller than the other.