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Writing a piece for laymen which happens to mention nucleosynthesis, I realise that I do not know the answer to the following question:

Are there stable isotopes which do not occur in nature?

One could make an equally striking point either way:

  1. Yes, there are isotopes which would be stable if any atoms of them existed, and we can make them in the laboratory, but conditions in nature have never led to them being created.

  2. No, the unholy mess of a supernova explosion is such that anything that could possibly exist ends up getting made, even if only in small quantities.

I mentioned ${^{180}}\mathrm{Ta}^\mathrm{m}$ in the heading because it is frequently described as "the rarest stable isotope". Even if this is true, "the rarest stable isotope" is ambiguous, because it could mean "the stable isotope with the smallest abundance $>0$" (thus: the rarest of those that exist) or "the stable isotope with the smallest abundance $\ge 0$".

Specific example

Note that deuterium is hard to make in the Big Bang because it is easily photodissociated and so cannot exist at high temperatures. In this case, the kinetic energy required to make D is low enough that there is a range of temperatures at which D can be created but not destroyed. But consider another (imaginary) stable isotope - call it X - which requires more kinetic energy for its creation and is also more unstable to photodissociation. X would not be creatable in a hot gas, because a gas hot enough to make it would break it; but would be creatable in a cold environment: for instance with particles accelerated at a target and no hot radiation around to destroy it afterwards.

This is not to assert that such an isotope exists - merely to clarify the question.

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According to https://en.wikipedia.org/wiki/Synthetic_element , all stable isotopes created artificially can also be found in nature (I don't have a more reliable source).

EDIT(06/07/2016): see also the table of natural abundance of stable nuclides at https://www.ncsu.edu/chemistry/msf/pdf/IsotopicMass_NaturalAbundance.pdf (if an element does not have stable nuclides, they give data for the longest-living isotope). As far as I know, all elements without data on natural abundance there are unstable.

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  • $\begingroup$ I can't see where that Wikipedia articles states all stable isotopes created artificially can also be found in nature $\endgroup$ – John Rennie Jun 7 '16 at 8:43
  • $\begingroup$ @JohnRennie: "So far, 24 synthetic elements have been created (those with atomic numbers 95–118). All are unstable, decaying with half-lives ranging from 15.6 million years to a few hundred microseconds. Seven other elements were first created artificially and thus considered synthetic, but later discovered to exist naturally (in trace quantities) as well" - they say that the 24 elements are all unstable, whereas the other 7 occur in nature. I believe this confirms my answer (subject to our belief in Wikipedia:-) ) $\endgroup$ – akhmeteli Jun 7 '16 at 8:50
  • $\begingroup$ I have to agree with John Rennie. That Wikipedia article talks about elements, not isotopes, so it doesn't really touch the question. $\endgroup$ – Martin Kochanski Jun 7 '16 at 9:43
  • $\begingroup$ @MartinKochanski: Technically, yes, this quote does not fully eliminate stable isotopes not occurring in nature (although it does touch the question, at least in the part related to the 24 synthetic elements not occurring in nature: if an element is unstable, that means all its isotopes are unstable). However, the table I quoted in the EDIT confirms the conclusion: I additionally checked that "all elements without data on natural abundance there are unstable". $\endgroup$ – akhmeteli Jun 7 '16 at 9:54
  • $\begingroup$ Yes, the EDIT table does address the question and seems authoritative enough to quote. Thank you! $\endgroup$ – Martin Kochanski Jun 7 '16 at 10:57

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