There are four radioactive chains. One of them starts with the abundant isotope of uranium, U²³⁸. This isotope undergoes a few alpha decays and a couple of beta decays to become radium, which has a charge of 88 and a weight of 226. All the radium in the world is produced in this manner as a daughter product in the fifth decay of the chain. After a number of further decays, stable lead (weight 206) is produced and the chain terminates.
The other chains are similar to the U²³⁸ chain, though not quite as long. One chain starts with the rare isotope of uranium, U²³⁵; another starts with the isotope of thorium that weighs 232. Both of these terminate in stable isotopes of lead. In all cases the first decay of the chain has a very long half-life. The half-life of U²³⁸ is 4.5 billion years; of U²³⁵, 710 million years; and of thorium, 14 billion years.
The fourth radioactive chain has been made in the laboratory but is not found in nature because its first isotope, neptunium with weight 237, has too short a half-life. It decays in two million years and all the other members of the chain live for even shorter periods. Thus the neptunium chain decayed long ago, whereas the three other chains have survived from the time when the elements were made.
It is interesting to notice that the lesser abundance of U²³⁵, as compared with U²³⁸, is connected with its shorter half-life. Assuming that comparable amounts of both isotopes were present at the beginning of the universe (and there is good reason to believe that this was the case), one would expect to find significantly less U²³⁵ than U²³⁸ after a period of a few hundred million years. After 710 million years (the half-life for U²³⁵) only one half of the original number of U²³⁵ nuclei would still exist. But 90 per cent of the original U²³⁸ nuclei (half-life 4.5 billion years) would remain. From the presently observed ratio of U²³⁵ to U²³⁸ nuclei (1 to 139), it may be calculated, using the law of radioactive decay, that 6 billion years ago natural uranium consisted of equal parts of U²³⁵ and U²³⁸. The age of the universe is hotly debated. With each passing year the universe seems to be a billion years older. Right now six billion years does not seem widely off the mark.
Natural radioactivity occurs mainly among the heavy elements, but there are a few light elements that are naturally radioactive. Of these, potassium⁴⁰ is an especially interesting one because it can decay either by electron emission or by electron capture. The processes are:
potassium⁴⁰ → calcium⁴⁰ + electron + neutrino,
(1.1 billion years)
and
potassium⁴⁰ + electron → argon⁴⁰ + neutrino.
(11 billion years)