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How does half life relate to isotope stability?
The half-life of an isotope is the period of time it takes for 1/2 of its atoms to undergo nuclear decay. A very long half-life means that it takes a long time for something to decay, and a short one means that it decays relatively quickly.
This suggests that with long half-lives are more stable than those with short ones, because they don't decompose as quickly (i.e. they're happier the way they are). Similarly, elements with short half-lives are less stable, because they fall apart quickly.