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Scientists are certain that there are no undiscovered elements missing from the periodic table from hydrogen to lawrencium. How? and why?

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You may find it of interest that there are atoms which don't belong in the periodic table. They're called Exotic atoms, and one rather crazy type is an -onium. There may be some unsynthesized or even undiscovered(this corresponds to an undiscovered particle) ones here... – ManishEarth Oct 28 '12 at 10:33
@Manishearth: Interesting stuff! I think from a chemist's standpoint, exotic atoms would be viewed like isotopes and ions; i.e. proton count would still define "element". – trb456 Oct 28 '12 at 11:28
trb456: Exotic elements often don't have protons (For example, there is one that is 2 electrons and 2 positrons orbiting one another). Or an 'isotope 0' of hydrogen that is an electron and a muon. – Canageek Nov 1 '12 at 3:19
@Canageek: Again interesting! But can we really consider these "elements" then, or just unusual structures of subatomic particles? For example, a chemist would want to consider chemical bonds. Can we get bonds with these structures? Presumably if they could share electrons (or positrons), then perhaps you would have to come up with a way to make them fit the current system (i.e. your H0 isotope). – trb456 Nov 1 '12 at 21:31
@trb456 You can get H-X with the mueon one. However, the scientist presenting it considered it to be an isotope of hydrogen, just the '0 mass' element. Its reactivity for the microsecond it exists is apparently quite similar. I wish I could remember the name of the scientist doing that work; he is at TRIUMF in BC. – Canageek Nov 2 '12 at 1:23

You are talking about the first 103 elements. An element is by definition identified with the number of protons in its nucleus, the so-called atomic number. Any atom with 6 protons is carbon, it cannot be anything else. So there cannot be any missing elements out to 103, as all of these elements have been confirm discovered by accepted scientific methods.

For example, here is a link to a CHEM Study film showing how transuranium elements (i.e. atomic number > 92 and man-made) can be separated from one another and verified as distinct.

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