Radioactive decay is a first-order reaction in which the atoms of a substance may spontaneously break apart, thereby turning into atoms of a different substance.
The probability of an individual atom decaying is an intrinsic property of the given chemical element.
Having decayed, that atom is now transformed into an atom of a different type, and so is not subject to any further occurrences of that particular decay process.
However, the new atom may have its own particular (different) mode of decay itself.
An isotope of a chemical element which is subject to radioactive decay is known as a radioactive isotope.
A chemical element whose isotopes are all subject to radioactive decay is known as a radioactive element.
The half-life of a radioactive isotope is the time it takes for exactly half of an arbitrary quantity of that isotope to undergo radioactive decay.
Thus it is the time it takes for exactly half of an arbitrary quantity of that isotope to remain.
An isotope of a chemical element which is not subject to radioactive decay is described as stable.
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions