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First of all, I know this (or, similar) question has been discussed previously here. But the discussion there couldn't help me completely getting rid of my confusion, hence this attempt.

In any radioactive sample of a particular element all the atoms involved in that accumulation of sample are obviously seem to be indistinguishable in every aspect. Then why all the atoms don't start decaying at the same time?

In practice we obviously know that they don't disintegrate simultaneously and hence my question arises that what is that x-factor that differentiates between the atom which decays first than the others?

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    $\begingroup$ For all we know, there is no x-factor. The atoms are identical, and then one of them just up and decays, while the other continues to wait for another hour, or maybe a year. It is just blind chance, as random as it gets. $\endgroup$
    – Ivan Neretin
    Commented Nov 17, 2017 at 13:56
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    $\begingroup$ The universe is probabilistic. $\endgroup$
    – Zhe
    Commented Nov 17, 2017 at 14:14
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    $\begingroup$ While probability is entirely sufficient to explain this, also consider that not all the atoms in your sample necessarily were formed at the same time - they may be the result of several supernovae etc. $\endgroup$
    – TAR86
    Commented Nov 17, 2017 at 14:32
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    $\begingroup$ @TAR86 Atoms don't have memory of their age, that's the point. Atoms are dumb. $\endgroup$
    – Ivan Neretin
    Commented Nov 17, 2017 at 14:46
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    $\begingroup$ @IvanNeretin - no, it is just the nucleus that is dumb (must be something to do with the strong force?) - electrons can solve Schrodingeer's equation in their sleep... $\endgroup$
    – Jon Custer
    Commented Nov 17, 2017 at 14:48

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