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Why is cobalt's atomic mass listed on periodic tables as less than 59 amu when its main isotope (virtually 100 %) is cobalt 59 with a trace of cobalt 60? After reading a bit I'm wondering if it has to do with loss of mass through decay. But that seems like it would either change the mass number or only lose an insignificant mass of electrons.

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    $\begingroup$ Protons and neutrons bound in nuclei weigh a bit less due to binding energy. $\endgroup$ Feb 25 at 22:07
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    $\begingroup$ The mass of Co-59 is 58.933 amu because of that binding energy. $\endgroup$
    – Jon Custer
    Feb 25 at 22:08

1 Answer 1

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The mass of an atom is actually a little bit smaller than the sum of the masses of its constituents (protons, neutrons, electrons). The missing difference is due to the negative binding energy of the nucleus, which according to Einstein's $E=mc^2$ results in the so-called mass defect. The nuclear binding energy is typically berween $-7.5$ and $-8.8$ MeV per nucleon, thus resulting in a mass defect between $-0.0080$ and $-0.0094$ amu per nucleon.

For the cobalt-59 atom we have the following mass contributions:

$$\begin{array}{|c|c|c|} \hline 27 \text{ protons} & 27\cdot 1.0073\text{ amu} & 27.197\text{ amu} \\ \hline 32 \text{ neutrons} & 32\cdot 1.0087\text{ amu} & 32.278\text{ amu} \\ \hline 27 \text{ electrons} & 27\cdot 0.0005\text{ amu} & \ 0.015\text{ amu} \\ \hline \text{nuclear binding energy} & & \color{red}{-0.557\text{ amu}} \\ \hline \text{total} & & 58.933\text{ amu} \\ \hline \end{array}$$

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  • $\begingroup$ And this has to be in order for nuclear fusion to be exothermic. $\endgroup$
    – EvilSnack
    Feb 26 at 17:20
  • $\begingroup$ .... and the AMU is slightly more than one proton mass due to the historical definition from carbon, meaning it includes carbon's mass defect? Somehow I never put this together until I saw your chart... :-( $\endgroup$ Feb 26 at 17:29
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    $\begingroup$ @GlennWillen You probably mean "the AMU is slightly less than one proton mass". But yes, the AMU definition from carbon includes carbon's mass defect. $\endgroup$ Feb 26 at 23:02
  • $\begingroup$ Oops, thank you, math is hard. $\endgroup$ Feb 26 at 23:05

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