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I think I generally understand what half-life means. What I wonder is, in a large collection of atoms of a radioactive element, are some atoms more likely to decay than others due to internal state or is it completely random? If the former, can an atom be examined to determine if it is more likely to decay than some other atom?

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No, it is NOT possible because the radioactivity is completely random, unpredictable in time, and certain.

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  • $\begingroup$ Did you mean to write “certain”? $\endgroup$
    – G. Smith
    Feb 6, 2020 at 6:28
  • $\begingroup$ yes, I mean INEVITABLE. A radioactive nucleus must decay sooner or later, but we cannot say nucleus $A$ will decay at a time $t$ (not deterministic)... sorry if it is not the right word, English is not my mother tongue. $\endgroup$
    – kbk
    Feb 6, 2020 at 6:34
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It’s totally random.

We can only statistically say that in time $t_{1/2}$ the initial amount of radioactive substance becomes half.

The reason behind this is that for decay to happen (let’s say alpha decay), the nucleus has to emit an alpha particle. This, classically speaking, shouldn’t happen and the alpha particle shouldn’t come out of the nucleus. Nevertheless, this emission of alpha particle happens anyway. This problem can be solved if we consider the wave nature (matter wave) of the alpha particle. There is some probability that this alpha particle can pass through this potential barrier of the nucleus, that is, the alpha particle can quantum tunnel and come out of the nucleus. This quantum tunnelling effect is probabilistic.

As the event is probabilistic, we cannot say which atom will decay rather we can only we can only statistically say that in time $t_{1/2}$ the initial amount of radioactive substance becomes half.

Reality is inherently probabilistic.

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