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Oct 23, 2022 at 7:16 vote accept aayush
Oct 18, 2022 at 16:10 comment added matt_black @jimchmst This is correct. The underlying reason why the numbers we get for isotope and nucleon masses is the mass deficit caused by nuclear binding energy. The "circular definition" isn't circular: it is simple about choosing a point (specific isotope) to which other masses are referenced. The fact we need to choose a reference point is a side effect of the mass deficit issue, not the cause of non-integer masses.
Oct 18, 2022 at 15:07 comment added jimchmst Carbon -12 was chosen to keep the atomic weight of the natural abundance of oxygen as close to 16. as possible and choosing an isotope for the physical scale. This prevented previous chemical data from becoming not so good. The improvements in mass spectrometry meant all the physical masses were being redone anyway. The chemical scale was based on the mix of oxygen set to 16. There is nothing circular about defining a standard mass.
Oct 18, 2022 at 13:35 comment added ACR @Karsten, I agree but the student should also ask why the masses and protons are non-integers. These numbers are all circularly defined but they are also self-consistent.
Oct 18, 2022 at 13:17 comment added Karsten @AChem The title of the question mentions integers, but the body of the question is more about the non-additivity. Trivially, 1.0073 looks more like an integer than e.g. 1.0073 * 100 = 100.73. BTW the molar mass of 12C is 11.999 999 9958(36) g/mol according to CODATA2018.
Oct 18, 2022 at 12:47 history edited matt_black CC BY-SA 4.0
added paragraph explaining why isolated nucleons are not of integer mass.
Oct 18, 2022 at 12:44 comment added matt_black @achem That is simply an obvious result of measuring the mass relative to a particular isotope.
Oct 18, 2022 at 12:41 comment added ACR This explanation better suits why 2+2 is not equal to 4 for atomic masses, however there is no fundamental explanation as to why the mass of a single proton or a neutron is not an integer. In short, we do not know why atomic masses are non-integers. The Einstein's equations is perhaps only a small part of the story. The reason is more or less circular- C-12 has been historically set to an integer. I know it has been changed very marginally but...
Oct 18, 2022 at 12:02 history edited Karsten CC BY-SA 4.0
deleted 12 characters in body
Oct 18, 2022 at 9:57 history answered matt_black CC BY-SA 4.0