The number at the top is how many half-lives have elapsed.Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.) is the time required for a quantity to reduce to half its initial value.
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This decay is an example of an exponential decay, shown in the figure below.
Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle.
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.