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I understand that this deviation from the general trend of increasing atomic number and atomic mass is because cobalt's isotopes tend to have more neutrons than nickel's. Why is that the case? How would one go about predicting similar cases like this?

I've read a bit about the shell model. I understand that 28 is a "magic number" of nucleons, i.e. a filled shell. In that case, wouldn't it be the most stable for both atoms to mainly be found with 28 neutrons; and so, cobalt-55 and nickel-56 would be the most stable isotopes of each element. Why is that not the case? Am I missing or misunderstanding something?

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Protons in each nucleus repel each other electrostatically.

As atomic number increases, there is more repulsion and an increasing advantage of spreading out the protons with neutrons.

Calcium-40 is the last (greatest atomic number) observationally-stable isotope with an equal or greater number of protons than neutrons.

Cobalt-55 and Nickel-56 are both unstable to beta decay, because it is favorable to emit a positron converting a proton into a neutron.

The natural abundance of isotopes are not necessarily in proportion to the stability, but instead stellar and cosmic processes. As explained in the 1963 article Computer Guides Professor Hoyle to New Hypotheses:

Working with Professor W. A. Fowler of the California Institute of Technology, he had begun with an analysis of the distribution of isotopes of the common metals, and found that nickel presented an unusual case; in the natural metal on Earth, nickel-58 is some three times more abundant than nickel-60, which is contrary to what one would expect from considerations of nuclear stability. He found the solution to this puzzle in the effect of neutrino emission from highly evolved stars, leading to extremely short life times, in the range of 20 minutes to 10 hours, and also in the phenomenon of electron-positron pair production. Nickel-58 could be made in an explosion in a large star which occurred so rapidly that the process of synthesis was cut short.

So, while the details of that article may be out of date, the reason cobalt has a higher natural abundance atomic mass than nickel is a combination of nuclear stability and stellar processes.

See On the e-process - Its components and their neutron excesses for further discussion of natural abundance ratios of Co and Ni isotopes.

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