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I have seen online that the amu is equal to approximately $1.661 \times 10^{-27}\,\text{kg}$ and is $\frac{1}{12}$ the mass of carbon-12. However, I have also seen it described as the average nucleon mass and equal to approximately $1.673 \times 10^{-27}\,\text{kg}$. Are both definitions widely used?

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    $\begingroup$ 1.661 is approximately 1.673, or vice versa. $\endgroup$
    – my2cts
    Aug 5, 2021 at 14:17
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    $\begingroup$ @my2cts, more precisely: 1.661 is approximately 99.3% of 1.673. That's a ratio that can be ignored for some purposes, but may be significant in other situations. $\endgroup$ Aug 5, 2021 at 14:26
  • $\begingroup$ Does that explain how it happened? $\endgroup$
    – Al Brown
    Aug 7, 2021 at 9:27

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The first definition is correct – the atomic mass unit (or Dalton) is defined to be $1/12$ the mass of carbon-12. The IUPAC definition elaborates on this:

Non-SI unit of mass (equal to the atomic mass constant), defined as one twelfth of the mass of a carbon-12 atom in its ground state and used to express masses of atomic particles, $u\approx1.660\;5402(10)\times10^{−27}\,\text{kg}$.

This definition was also not affected by the 2019 redefinition of SI base units.

It is in fact true that the average nucleon mass is about $1.673 \times 10^{-27}\,\text{kg}$, though this is not used as a definition for the atomic mass unit – it might be helpful to provide the sources that claim so. Another possibility might be that the second (wrong) "definition" for the atomic mass unit was actually referring to the mass of hydrogen-1 which is $1.008\,\text u\approx1.673\times10^{-27}\,\text{kg}$.

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    $\begingroup$ It's also true that the amu is approximately the average mass of a nucleon, to better than 1% accuracy. That might be good enough in some circumstances, and I could envision some introductory textbooks glossing over this distinction for the sake of being more easily understood. $\endgroup$ Aug 5, 2021 at 14:03
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Technically, the former definition is correct. Such an exact value only became an issue when technology allowed us to care about any actual differences in the mass of nucleons. Until then, the best estimate at the time had been 1.673 and had become the standard convention by use.

But when it came time to standardize, the IUPAC needed something rigorous, not the colloquial best-estimate, and needed something they felt would be most representative - because the masses differ by proton/neutron and slightly by atom. Carbon-12 fits both. It is 12 nucleons with half protons and half neutrons (a fairly representative ratio) and was measurable.

The first one is right. The second is old. But papers from the past are sometimes sighted a lot, plus books.. anything published.

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