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Understandably, the relative atomic masses of isotopes are often not close to whole numbers as they're adjusted for isotope abudandancy eg. $A_r(Cl)\approx35.45$. However, wouldn't one expect the relative atomic masses of individual isotopes to be rather close to whole numbers, given that they're merely the sum of the relative atomic masses of the protons, neutrons, and electrons within the atom and that the masses of protons and neutrons $\approx1$?

I.E, we have $Rb-85$, which has a literature $u=84.91$. Attempting to calculate $u$ given proton, neutron and electron count: $$ A_r(p^+) = 37\times 1.0073\approx 37.2701\space Da $$ $$ A_r(n^0)=48\times 1.0087\approx 48.4176\space Da $$ $$ A_r(e^-)=37\times 5.4858\times 10^{-4}\approx 0.02030\space Da$$ $$37.2701+48.4176+0.02030=85.708$$ The answer I get is $85.708$, whereas something close to $84.91$ is expected.

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    $\begingroup$ Do you consider the total nucleus mass is less than sum of masses of protons and neutrons by the nuclein bound energy? $\endgroup$
    – Poutnik
    Dec 5, 2021 at 5:32
  • $\begingroup$ E.g. Mass of 4He is less than mass of 2p + 2n by about 0.7%, AFAIK. And as average bonding energy per differ from the one for 12C, nuclei masses in Da differ from integer values. Another minor factor is various n/p ratio. $\endgroup$
    – Poutnik
    Dec 5, 2021 at 6:41
  • $\begingroup$ Please note that the dalton (unity symbol $\mathrm{Da}$) is not a unit of the quantity relative atomic mass (quantity symbol $A_\mathrm r$). Relative atomic mass is a quantity of dimension one (a so-called dimensionless quantity). Also please note that $u=84.91$ doesn't make any sense at all. $\endgroup$
    – Loong
    Dec 5, 2021 at 9:26
  • $\begingroup$ Interesting facts: The lowest mass per nucleon has 56Fe, while the highest binding energy per nucleon has 62Ni. $\endgroup$
    – Poutnik
    Dec 5, 2021 at 9:37

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In the world of atomic masses, everything is "weighed" with reference to carbon-12. Unfortunately, this is a circular approach, in the sense that carbon-12 is arbitrarily set to 12 as an exact integer. Today, there is a very small change due to the refining of the definitions of mass/ length in terms of fundamental constants.

There is no reason as to why the mass of a single isotope be an integer. Recall, carbon-12, it is arbitrary. Yes, the count of protons and neutrons is an integer but not their masses. Two centuries ago, atomic weights were all different in the time of Berzelius because they had other standards.

To add insult to injury in the nuclear world, 1+1 is not equal to 2. It is always slightly less. This is one of the fascinating mysteries of nature. The missing mass is accounted by the binding energy of nucleons (protons+neutrons) in the nucleus.

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    $\begingroup$ One can even state that each proton and each neutron loses a small fraction of its mass when joining to make a nucleus. This mass loss is transformed into energy by Einstein's law : $\pu{E = mc^2}$ $\endgroup$
    – Maurice
    Dec 5, 2021 at 11:20

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