# Why are the relative masses of isotopes not close to whole numbers?

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.

• Do you consider the total nucleus mass is less than sum of masses of protons and neutrons by the nuclein bound energy? Dec 5, 2021 at 5:32
• 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. Dec 5, 2021 at 6:41
• 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. Dec 5, 2021 at 9:26
• Interesting facts: The lowest mass per nucleon has 56Fe, while the highest binding energy per nucleon has 62Ni. Dec 5, 2021 at 9:37

• 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 : $\pu{E = mc^2}$ Dec 5, 2021 at 11:20