The difference between 1g and
1.0079g comes marginally from deuterium, which adds 0.0001g
http://www.webelements.com/hydrogen/isotopes.htmland mainly from the
nuclei binding energy in heavier atoms.
That is, the mole is defined from
12C where nucleons hold together firmly hence weigh less than individually. The 6 neutrons each slightly heavier than a proton+electron would work the opposite way and the electrostatic repulsion as well but the strong force is more important. Carbon's deep electrons being attracted by more protons make only 1µg/mol difference.
The
12C reference gives masses closer to integers for (mono-isotopic) nuclides near C, N, O but farther for hydrogen and iron. Carbon is also nearly mono-isotopic, so it's one possible convenient compromise.
16O would be one other, and Silicon may become one day the new kilogram standard.
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I've read occasionally "protium" for hydrogen free of deuterium.
And, my apologies for the digression: sea water contains no tritium for nuclear fusion reactors.