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 _N_₀ 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 2_T_, one quarter remain; and so forth. [Illustration: uncaptioned] 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.