In reading this article about the origins of elements, I found the following diagram:

enter image description here

What strikes me about this image is the very consistent zig-zagging of the line that appears to indicate that elements/isotopes with an even number are more abundant.

Am I correct? What's going on here?

  • 1
    $\begingroup$ Similar: physics.stackexchange.com/q/158251 $\endgroup$
    – BowlOfRed
    Jun 20, 2017 at 14:46
  • 1
    $\begingroup$ Hydrogen has an atomic number of 1, so it runs counter to the (general) claim ;) $\endgroup$
    – Kyle Kanos
    Jun 20, 2017 at 14:58
  • $\begingroup$ Beryllium is neglected by the universe as well ;( $\endgroup$ Jun 20, 2017 at 17:00
  • $\begingroup$ Except, the pattern seems to reverse itself between Mo and Tc, and then again between Nd and Pm. $\endgroup$ Jun 20, 2017 at 17:34
  • $\begingroup$ Image search bought me to here: Oddo-Harkins rule which seems like a fairly complete explanation of what I saw. $\endgroup$
    – spender
    Jun 20, 2017 at 17:37

2 Answers 2


I will add to the answer from @BowlofRed https://physics.stackexchange.com/a/158270/36194 that the nuclear pairing interaction lowers the energy in nuclei where the number of like nucleons is even: thus for instance there are more isotopes with even rather than odd number of neutrons. This also favors the formation of even-proton-numbered nuclei over the neighbouring odd ones.


The binding energy of a nucleus depends on the pairing status of the protons and neutrons. In particular, in the semi-empirical mass formula, there is a pairing term which captures the mutual interaction associated with the energetic favourability of pairing nucleons with opposite spin. That means nuclei with even numbers of protons and neutrons have higher binding energies than those with odd/even and especially odd/odd nuclei.

What this means in practice is that there is an energy penalty and therefore a reduced probability of producing elements with odd numbers of protons during equilibrium nucleosynthesis reactions inside stars.

For example a heavy nucleus with an odd number of protons might be more likely to undergo beta decay if it is neutron-rich or more likely to undergo neutron capture if it is neutron poor, than an adjacent nucleus with an even number ofprotons.


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