Radioactive decay
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This article is only a brief description of the subject, and is not intended to give a full explanation.
Check out the "see also" or "references" sections, or Wikipedia's article for more detail.
Radioactive decay is the process whereby an atom "fissions", or breaks into two or more parts spontaneously. All atoms are subject to radioactive decay, although the timing of the decay is characterised by an overall randomness within the total number of atoms of the same atomic weight and atomic number (isotopes). The time when an individual atom decays is random, but over a large sample of atoms the proportion which will decay over a given time interval is predictable. The "half life" of an isotope is the amount of time it takes for one half of the remaining atoms to decay.
The rate at which atoms decay is used for dating objects with varying levels of accuracy. This is called Radiometric dating, carbon dating is the most common, and well known, example. There are many different methods used, depending on the half lives of the isotopes concerned. They rely on the presence of the products of decay in either chemical or crystaline situations where they would not otherwise occur.
The subject is exceedingly complex and is best explained in specialist publications[1].
Since radioactive decay releases energy, it can be harnessed to blow things up or make electricity, usually involving a complex pile of tubes, wires, and concrete. These applications are known as "controlled fission," and usually use highly concentrated unstable isotopes as fuel.
Note: decay is not confined to atoms - subatomic particles decay also with half lives. The fact that particles from cosmic rays lasted long enough to reach the surface of the Earth after creation in the upper atmosphere was shown to be due to relativistic time dilation at the very high speeds of the particles (muons).
Note: Randomness does not imply chaos.

