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We currently know that there are atoms with atomic number up to 118 are possible.

Is it possible that atoms with 120 protons are possible, but that atoms with 119 protons aren't possible? Or are there theoretical arguments or maybe heuristic arguments why this can't happen?

I suspect the answer to be yes, because technetium and promethium have no stable forms while the elements surrounding it in the periodic table do have stable forms. A similiar thing might happen here. The more general question: Does there exist $k > l > 118$ such that atoms with $k$ protons are possible, but that atoms with $l$ protons aren't possible?

It is not a duplicate of The last element's atomic number. I wonder whether there could be 'gaps' in the periodic table, not what the last element's atomic number is.

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    $\begingroup$ Please define 'possible' - do you mean a short lifetime, or completely unbound? $\endgroup$ – Jon Custer Oct 11 '15 at 18:23
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    $\begingroup$ @JonCuster What I meant: An element is possible if there is at least one isotope with a half live greater than the Planck time. I'm not sure if it really works, and whether there are isotopes with half live smaller than the Planck time, but I think it will do for this question. $\endgroup$ – wythagoras Oct 11 '15 at 18:32
  • $\begingroup$ Your 'definition' doesn't make much sense, becuse for sth to decay in time shorter than Planck time, it would need to be about Planck radius small, and even single proton in comparison huge. $\endgroup$ – Mithoron Oct 15 '15 at 17:35
  • $\begingroup$ This is of course more of a nuclear physics question rather than a chemistry question. I'd expect just about any atomic number is possible, but that all elements above lead z=82 are radioactive. So for z>82 then it is a question of how long is the half-life. $\endgroup$ – MaxW Dec 15 '15 at 0:58
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    $\begingroup$ Look at "Island of stability" that might help too $\endgroup$ – David Wyn Williams May 23 '18 at 13:46
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According to the Wikipedia page element 119 synthesis has been attempted indicating physicists think it is possible. There is some speculation as to whether our current technology could even detect such short lived elements such as elements 119 or 120. There is also speculation that the technology today may not be able to produce element 120. It may be possible for such gaps (who knows maybe element 562 is stable and element 561 cannot form?) but at the current time no gaps are known with certainty.

One of the bigger problems for higher atomic number atoms is that as the nucleus becomes more charged the electrons orbiting the nucleus must go faster and faster to stay in orbit. However nothing can exceed the speed of light and thus if an atom were to have electrons near the speed of light (say 99.99999% of c) at rest. The mere revolving of the earth around the sun would require the electron to move faster than light which presents and interesting case/thought experiment. Because of this it is reasonable to deduce that there is a penultimate element atomic number where anything larger would required electrons to exceed the speed of light though I cannot say what the magic number would be.

I will say though your question has a quite lot of merit as the Oddo-Harkins rule holds that the abundance of elements with odd atomic numbers in the universe is far less than that of elements with even atomic numbers except for hydrogen of course. Further radioactive nuclei with even atomic numbers tend to be more stable and have a longer half life than those with odd atomic numbers.

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    $\begingroup$ There is no magic limit related to speed of light. (If it would be, it would occur around the number 137). Relativity does not work that way. As electrons move faster, they grow heavier, so it's still totally possible to have a stable orbit for any atomic number. Also, in fact they don't literally "move" at all, and there are no orbits - just the clouds of probability density. $\endgroup$ – Ivan Neretin Dec 15 '15 at 14:26
  • $\begingroup$ Hey Ivan, I don't follow this train of thought: "As electrons move faster, they grow heavier, so it's totally possible to have a stable orbit for any atomic number." Could you elaborate more? $\endgroup$ – KanyeBest Dec 15 '15 at 15:01
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    $\begingroup$ Imagine that electrons follow Bohr's orbits (which they do not, but let's forget about that for a moment). Then we have to balance the centripetal force $mv^2\over r$ against the electrostatic force $kZe^2\over r$. As Z exceeds ~137, the necessary $v$ exceeds the speed of light, so we might be tempted to think this is the end. But no, this is derived in the assumption that $m$ does not depend on $v$, which is not quite so (as per special relativity). $\endgroup$ – Ivan Neretin Dec 15 '15 at 15:17
  • $\begingroup$ @A.K. what about the Viola-Seaborg relationship, that odd numbers of protons and odd number of neutrons provide longer half lives for alpha decay. If alpha decay is the limiting factor, 119 should be favored over 120 as far as stability. arxiv.org/ftp/arxiv/papers/1504/1504.00872.pdf $\endgroup$ – DavePhD Dec 15 '15 at 15:50
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    $\begingroup$ Thank you for your nice answer. There is however one thing about relativity, which is that you may not add speeds. So if something moves with the speed 0.9999999c, and then the Earth rotating with 0.00001c, the total will be something like 0.999999901c. $\endgroup$ – wythagoras Dec 15 '15 at 16:21

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