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You have just read reasonable answers of knowledgeable people, so now you know that "radioactive decay...- it's completely stateless (@Luaan)", "There are no patterns" (@LuboŇ° Motl), and "Atoms are dumb" (@David Hammen). However, there is a bit more to it. Atoms may be dumb, but they happen to know quantum mechanics much better than we, mere mortals, do. So ...


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Is there some sort of pattern to which atoms decay at which time, or is it some miraculous property of quantum mechanics that somehow each atom knows when to decay? Atoms are dumb. They don't know anything. Radioactive decay is a memoryless process, a process that doesn't depend on history. Consider three atoms of radon 222. One was created a month ago ...


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There are no patterns. When a particle decays, the moment when it does so is absolutely random, chosen from the distribution $$ P_{\rm decay}(t\lt T\lt t+dt) = \frac{dt}{t_0}\cdot \exp(-t/t_0) $$ For $t=t_0$, the beginning of time when we knew that the particle still existed, the exponential is equal to one and we see that the "probability of the decay per ...



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