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Half-life and random decay

Radioactive decay is random. In a sample of unstable nuclei you cannot tell which nucleus will decay next or when a particular nucleus will decay. Each nucleus has the same chance of decaying in any given time, and nothing you do to the other nuclei changes that.

Even so, when there are very many nuclei the overall behaviour is predictable. The half-life is the time it takes for half of the unstable nuclei in a sample to decay. It is also the time it takes for the activity (the count rate from the sample) to fall to half its starting value. For example, with a half-life of 10 minutes, a sample of 800 unstable nuclei has about 400 left after 10 minutes and about 200 left after 20 minutes. The numbers are only approximate, because the process is random.

You can model this with dice. Each die stands for a nucleus. Throw them all, remove the ones that show a six (these have decayed) and count the rest. The number left falls by roughly the same fraction each throw. Your results will vary a little between runs, which shows that decay is random, but the pattern in a large sample is clear.

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