# Why is iron the peak of the binding energy curve?

If Nickel-62 and Iron-58 have more binding energy per nucleon than Iron-56 does, then why is iron-56 shown as the peak of the binding energy curve? Also, does adding neutrons always make the atom more stable because it will increase the strong nuclear force but not add any more electrorepulsive force?

From Wikipedia:

Iron-56 (56Fe) is the most efficiently bound nucleus meaning that it has the least average mass per nucleon. However, nickel-62 is the most tightly bound nucleus in terms of energy of binding per nucleon. (Nickel-62's higher energy of binding does not translate to a larger mean mass loss than Fe-56, because Ni-62 has a slightly higher ratio of neutrons/protons than does iron-56, and the presence of the heavier neutrons increases nickel-62's average mass per nucleon).

In any case, iron-56 is not necessarily usually shown (anymore) as the highest binding energy per nucleon, mostly because it's not usually possible to show the tiny difference in binding energy between iron-56 and nickel-62. The difference is so tiny that accounting for the fact that the neutron is 0.1% heavier than the proton, instead of treating all nucleons equally, changes which is bound more tightly. Because of this tiny difference, it's unlikely that you'll see one depicted as higher than the other on any plot that actually shows both of them, like this one (source: https://www.asc.ohio-state.edu/kagan.1/phy367/Lectures/P367_lec_14.html):

Can you tell which of the two has higher binding energy? I certainly can't.

In addition, adding neutrons does not always make the nucleus more stable. In the nuclear shell model, protons and neutrons, being distinguishable from each other, occupy distinct sets of energy levels in the nucleus. (As a side note, the neutron energy levels are shifted lower than the proton energy levels because there is no Coulomb repulsion among neutrons. This is why the heavier stable nuclei tend to have more neutrons than protons - you can fill more of the neutron energy levels for the same valence nucleon energy.) Since they're both fermions, you have to add new neutrons to higher and higher energy levels. Adding too many neutrons, enough to put the highest filled neutron energy level significantly above the highest proton energy level, will cause the highest-energy neutrons to spontaneously convert to protons via beta decay so that they can occupy a lower (proton) energy level.

• It is pretty clear that Ni62 is displayed higher than Fe56 if that's what you ask by "Can you tell which of the two has higher binding energy?". And the 3rd higher would be the one on the left of As 75, but which has no symbol, followed by the one on the left of Ni62. – thermomagnetic condensed boson Feb 13 at 8:46
• @thermomagneticcondensedboson: that is ... not at all clear to me. :) – abeboparebop Feb 13 at 9:29
• FWIW, the silicon burning ladder, which lasts about 5 days, proceeds by alpha addition. It ends in Fe-52, Ni-56 & Zn-60, with half-lives of 8 hr, 6 d & 2.4 m, respectively; the production of Zn is endothermic, and the extreme temperature required causes it to photodisintegrate. The Ni decays to Fe-56. Also see astronomy.stackexchange.com/a/21288/16685 – PM 2Ring Feb 13 at 11:49
• The size of the dots is so significant, and H such a distorter of the scale of the axis that it's hard to see any changes at all.... but that doesn't stop this being right – UKMonkey Feb 13 at 16:30
• @thermomagneticcondensedboson yes, especially if you take another window on your PC and drag its bottom edge over the chart. Then you can clearly see that the Ni dot is one pixel higher. Though I'm not sure what the error bar for one pixel is on this chart, especially because they are antialiased. – DaveInCaz Feb 13 at 17:04
1. The "folk wisdom" that iron-56 has the highest binding energy per nucleon is in fact incorrect; both iron-58 and nickel-62 have a higher binding energy per nucleon, with nickel-62 being the highest. I can't do much better than citing an article on the subject:

M. P. Fewell, "The atomic nuclide with the highest mean binding energy". Am. J. Phys. 63, 653–658 (1995).

The author of that work traces this misconception back to texts on stellar nucleosynthesis in the '50s and '60s. Stellar nucleosynthesis does favor the production of iron over nickel, and the author postulates that this fact may have been conflated with the peak of the binding energy curve.

2. We can roughly model nuclei as having a set of "proton energy levels" and "neutron energy levels". Since both protons and neutrons are spin-$$\frac12$$ fermions, this means that one can have at most two neutrons per energy level in the nucleus. Adding more neutrons to the nucleus will thus result in the neutrons being piled into higher-energy states.

However, neutrons can undergo beta-decay into protons: $$n \to p^+ + e^- + \bar{\nu}$$. Suppose a neutron is in a relatively high energy level in the nucleus, and there is a vacant proton energy level below it. It can be energetically favorable for this neutron to turn into a proton and drop into this lower energy level. Thus, nuclei with too many neutrons will tend to undergo beta decay. (The same argument shows why nuclei with too many protons will tend to undergo inverse beta decay.)

• Inverse beta decay isn't so common, compared to normal beta decay. And when it does happen, it's often in the form of electron capture, rather than positron emission. Nuclei with a large proton excess tend to spit out protons, borderline heavy nuclei can reduce their need for neutrons by emitting alphas. – PM 2Ring Feb 12 at 23:06
• So if nickel is more stable/tightly bound than iron, why do stars favor iron production over nickel? – Student Feb 13 at 1:38
• Because fusion is easier in multiples of 4 (helium cores), which Iron-56 is and Nickel-62 is not. Full reasoning is beyond a comment-length. – Jacco van Dorp Feb 13 at 9:01
• @Student - Iron-56 is easier to form by fusion than Nickel-62, since it does not require as many neutrons to stabilise. In the stellar environment there is also a lot of Nickel-56 produced that decays quickly (a few days) via Cobolt-56 to Iron-56. – Anders Sandberg Feb 13 at 9:34
• So what has the highest binding energy per nucleon? Can you add that? – Peter Mortensen Feb 14 at 1:01