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I've seen in many stories where someone has powerful telekinesis or something similar as a power and threaten to split an atom and create some massive nuclear explosion.

From my understanding, this kind of nuclear explosion only happens because when one atom splits, it releases more than one neutron which then go on to split more atoms, which go on to do the same thing, creating a massive domino effect of increasing proportions. But this only works if the atoms you split are specific ones which will release the correct amount of neutrons to cause a chain reaction.

So, I'm wondering, if someone who had the ability to do so with some kind of super power decided to split a random oxygen atom or something similar in an open space, would there actually be any kind of noticeable effect?

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Ignoring the "super power" idea, the question boils down more or less to the question what happens if an atom of a radioactive isotope decays in an environment of mostly non-radioactive atoms. But that is just the normal situation: Small concentrations of different weakly radioactive substances can be found everywhere, and at every moment some of those atoms decay, causing a very weak radioactivity. This has no really relevant effect as long as the concentration stays low. One single atom more definitely would not be enough to make any relevant change.

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