Iron, Nuclear Stability and Nuclear Energy

[Silly Questions]

TL;DR Summary

Is Fe-56 the most stable element?

Iron (Fe-56) is in terms of nuclear energy spent, which seems equivalent to saying its nuclides are the most tightly-bound. Does this also make Fe-56 the most stable nucleus, and is nuclear potential energy to stability a general correlation? Do more-stable nuclei generally have less nuclear potential energy?

What I've read so far doesn't directly address the question. "Even-even nuclide pairs" have something to do with how tightly-bound Fe-56 is, so it looks like a "yes" but I'm not sure. More elusive still has been the broader question of whether nuclear potential energy (whatever the right term is for that, with Fe-56 at the very bottom) is correlated with atomic stability and if so how closely.

Once again it's the burning question no one else is asking. ("The most stable elements are the noble gases!" Thanks for trying, Internet.) If anyone knows the actual answers it's you guys ...

Bonus question: does every nucleus have a half-life? I'm surprised to find the answer seems to be "yes" -- too surprised to trust without confirmation. If so are there any nuclei close to the line between "stable" and "unstable", or is the distinction unambiguously obvious? Lastly, if even Fe-56 can spontaneously decay given enough billions of years, and if altering an Fe-56 nucleus always costs energy, where would that energy come from?

 

[vanhees71]

https://en.wikipedia.org/wiki/Nickel-62
https://en.wikipedia.org/wiki/Stable_nuclide

 

[Silly Questions]

Yeah I read those. It seemed to suggest Nickel-62 wasn't quite as stable as Fe-56. Did I read it wrong?

I read this one, too:
https://en.wikipedia.org/wiki/Iron-56

 

[vanhees71]

Well, in a sense Nickel 62 is "more stable" than Iron-56, because it has a higher binding energy per nucleon. Also see this very informative AJP paper on the subject:

https://doi.org/10.1119/1.17828

 

[Silly Questions]

"Block Reason: This IP was identified as infiltrated and is being used by sci-hub as a proxy."

My reputation precedes me!

To be clear barring some cross-site scripting skullduggery slipping past the malware filter I've never visited that website in my life. I'd never even heard of it until I tried to follow your link.

So ... got a Plan B? [Let's call "Get a VPN" Plan C ...]

Setting aside the Ni-62 Fe-56 grudge match for the moment, any ideas on the question of correlation between nuclear energy potential and atomic stability?

 

[vanhees71]

I don't understand. The DOI-link links correctly to the official page of the AJP article,

https://aapt.scitation.org/doi/10.1119/1.17828

 

[Silly Questions]

Nope, still blocked. It says I'm an abuser from sci-hub, whatever that is.

The Bonus Question might be an easy answer, though. Tell me if this is right:
"Stable nuclides are only subject to proton decay, and proton decay has never been observed. Until proton decay can be proven the question of stable nuclide decay is moot." Good answer?

 

[PAllen]

I don't understand. The DOI-link links correctly to the official page of the AJP article,

https://aapt.scitation.org/doi/10.1119/1.17828

I would need to pay $35 to see that. Can't find a free version.

 

[Orodruin]

There really is nothing more stable than stable and there are many many nuclei that are stable. It means that, left on its own, it will not decay.

That said, the iron and nickel isotopes mentioned are very strongly bound, meaning there is also no process in which they can fusion to heavier elements.

Nope, still blocked. It says I'm an abuser from sci-hub, whatever that is.

The Bonus Question might be an easy answer, though. Tell me if this is right:
"Stable nuclides are only subject to proton decay, and proton decay has never been observed. Until proton decay can be proven the question of stable nuclide decay is moot." Good answer?

Yes, if protons decay (which there is no experimental evidence for but it is part of many beyond the standard model physics models) then no nucleus is truly stable. The half-life would be very very very long though.

Summary:: Is Fe-56 the most stable element?

"The most stable elements are the noble gases!"

The noble gases are most chemically stable, ie, inert with respect to chemical reactions. This has little to do with nuclear stability.

 

[berkeman]

Nope, still blocked. It says I'm an abuser from sci-hub, whatever that is.

Hmm, sounds like maybe you downloaded some pirated papers in the past, but I'm sure that's all behind you now...

https://en.wikipedia.org/wiki/Sci-Hub

 

[Silly Questions]

Why would I pirate papers when I can pester you guys with questions instead? 8D

Hey ... maybe I'm pirating you guys and selling the info to the highest bidder! The awkward Dunning-Krueger quality of my questions is but a clever ruse ...

There's actually a nugget (err, doubloon) of truth to the piracy claim. Ever since I told my friends that "Zero Point Energy" as an energy source was the dumbest idea ever -- using a tube of toothpaste as a prop no less! -- I became, "The physics guy." If based on the quality of my questions that scares the Maxwell's Demon out of you imagine how much that idea scares me ... but yeah, if I learn right answers here there's a good chance they'll get passed on. "Piracy" that may well be, but consider the alternative ...

"But why don't your friends just read the Wikipedia articles on nuclear physics?" The world of people is so vastly different than what anyone might imagine it to be. Some have need of a good pirate who can stash the booty of an accurate physics answer into an empty tube of toothpaste.

 

[snorkack]

If so are there any nuclei close to the line between "stable" and "unstable", or is the distinction unambiguously obvious?

A lot, starting with the notorious Mattauch violators Te-123 and Ta-180.

 

[Astronuc]

Ni-62 Fe-56

Adding to what information others have provided -
see http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin2.html

The binding energy per nucleon of ⁶²Ni is 8.7946 MeV, while that of ⁵⁶Fe is 8.79036 MeV, with ⁵⁸Fe in between at 8.79223 MeV.

Summary:: Is Fe-56 the most stable element?

if altering an Fe-56 nucleus always costs energy, where would that energy come from?

It depends on what one means by altering. Any of the aforementioned isotopes may absorb a neutron, which would increase the atomic mass by ~1 amu. Free neutrons can be produced by fission in nuclear reactors, in accelerators and with certain fusion reactions. Gamma radiation of ~8.8 MeV could cause a photonuclear reaction in which a neutron would be ejected, however, such a gamma ray would more likely cause pair (positron-electron) formation or be deflected by Compton scattering. Accelerated particles (electrons, protons, deuterons, alpha particles, . . . ) could also be used to modify nuclei by nuclear interactions.

 

[Silly Questions]

From the link:
"Though the championship of nuclear binding energy is often attributed to 56Fe, it actually comes in a close third."

Nobody has all the answers like you guys have the answers. It's amazing so many of you are gathered in one place.

When I asked, "Where would the energy come from?" I meant in the exclusive case of spontaneous decay, but the [forum-confirmed!] answer to whether spontaneous decay of stable nuclides can even occur at all is that proton decay has never been observed thus the question is, for now, moot. If you wanted to speculate where the energy for spontaneous proton decay might come from hypothetically I totally wouldn't say "no" to hearing your explanation. I'm sure it would be elucidating even as a hypothetical.

The last question, of whether there is a correlation between stability and nuclear energy, is mostly answered by the proton decay problem. If anyone wanted to chime in concerning a correlation among unstable nuclides I'd love to hear it, otherwise I am thrilled to have had my questions answered so thoroughly -- and once again misconceptions cleared up, especially Fe-56 vs Ni-62. Just because stellar furnaces bottom out at Fe-56 doesn't mean Fe-56 is at the very bottom. That's really good to know!

Oh no. Another question. If Fe-56 is so prevalent not because it's at the very botom but simply because it's below the line enough to end the universe's most common fuel cycle are there any other elements in important nuclear fuel cycles (am I using that term correctly?) which end the same way? And is there a more correct term for "below the line" or "very bottom"? (Chemistry has "endothermic", but I don't want to misuse it.) Also, as I read the explanation but didn't fully understand it, why exactly is there not more Ni-62?

I almost escaped from this thread with all questions answered. Almost ...

 

[Astronuc]

When I asked, "Where would the energy come from?" I meant in the exclusive case of spontaneous decay, but the [forum-confirmed!] answer to whether spontaneous decay of stable nuclides can even occur at all is that proton decay has never been observed thus the question is, for now, moot.

We do observe decay by positron emission for some neutron deficient radionuclides, in which a proton transforms into a neutron, positron and neutrino.
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/beta.html#c4 shows transformation of ⁶⁴Cu to ⁶⁴Ni via positron emission.

Otherwise, unstable nuclides ⁵³Fe and ⁵⁵Fe, or ⁵⁷Ni and ⁵⁹Ni decay by electron capture, usually a K-electron in the innermost orbital capture by a proton, producing a bound neutron and a neutrino (p + e- => n + ν).
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/radact2.html#c3

If Fe-56 is so prevalent not because it's at the very bottom but simply because it's below the line enough to end the universe's most common fuel cycle are there any other elements in important nuclear fuel cycles (am I using that term correctly?) which end the same way? And is there a more correct term for "below the line" or "very bottom"? (Chemistry has "endothermic", but I don't want to misuse it.) Also, as I read the explanation but didn't fully understand it, why exactly is there not more Ni-62?

Some discussion of element abundance here
https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elements

To get Ni isotopes, one needs to form Fe first, and then Fe nuclei absorb neutrons to become heavier elements. The lighter nuclei are formed by fusion reactions, and potentially spallation reactions, and given presence of high energy gammas, one may observe photo-neutron reactions. Note that all the elements above Fe tend to be less stable, except for ⁶²Ni. Most radionuclides will have decayed to stable nuclides over the lifetime of the Universe, Sun/Earth, while some like ²³²Th, ²³⁵U and ²³⁸U are still around, since they were formed locally in some event involving the sun and earth.

http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/neutexc.html
http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html#c2

 

[Silly Questions]

Fascinating.

Is it accurate to summarize by saying Ni-62 is rare because the chain of stellar reactions which cause element formation passes through Fe-56 first, and because Fe-56 poisons nuclear reactivity ANY elements formed "downstream" of Fe-56, including Ni-62, are going to end up much rarer than Fe-56, as once the cycle is poisoned Fe-56 becomes the end of the cycle? Is it safe to say that Ni-62 itself contributes to its own formation's demise, as it helps poison the post-iron part of the cycle that turns Fe-56 into Ni-62?

In your reply to this, "the ... answer to whether spontaneous decay of stable nuclides can even occur at all is that proton decay has never been observed," where you spoke about when decay does occur, just to clarify you were offering extra information, not declaring this statement in error? You did specify "neutron-deficient nuclides", which I understand to be a subset of "unstable nuclides", but I wanted to double-check just to be sure. Stable nuclides = no observed proton decay?

 

[Astronuc]

Is it accurate to summarize by saying Ni-62 is rare because the chain of stellar reactions which cause element formation passes through Fe-56 first, and because Fe-56 poisons nuclear reactivity ANY elements formed "downstream" of Fe-56, including Ni-62, are going to end up much rarer than Fe-56, as once the cycle is poisoned Fe-56 becomes the end of the cycle? Is it safe to say that Ni-62 itself contributes to its own formation's demise, as it helps poison the post-iron part of the cycle that turns Fe-56 into Ni-62?

It's not accurate to say "Fe-56 poisons nuclear reactivity". As we understand stellar nucleosynthesis, fusion occurs with light elements. Fe is produced under special conditions, as are the heavier elements, and to get to heavier elements, one has to pass through a stage where Fe and Ni are produced.

One should research 'stellar nucleosynthesis' and r- and s-processes, as we understand them.

https://ned.ipac.caltech.edu/level5/Sept16/Rauscher/Rauscher4.html
https://ned.ipac.caltech.edu/level5/Sept16/Rauscher/Rauscher6.html

https://en.wikipedia.org/wiki/Supernova_nucleosynthesis - see Silicon burning and the alpha particle interactions with various elements.

See also papers like - THE WEAK s-PROCESS IN MASSIVE STARS AND ITS DEPENDENCE ON THE NEUTRON CAPTURE CROSS SECTIONS
https://iopscience.iop.org/article/10.1088/0004-637X/710/2/1557

Gas Dynamics of the Nickel-56 Decay Heating in Pair-instability Supernovae
https://iopscience.iop.org/article/10.3847/1538-4357/ab9819

"the ... answer to whether spontaneous decay of stable nuclides can even occur at all is that proton decay has never been observed,"

By definition 'stable nuclei' do not decay, not spontaneously or otherwise. Similar protons do not seem to spontaneously decay. See Orodruin's comment:

Yes, if protons decay (which there is no experimental evidence for but it is part of many beyond the standard model physics models) then no nucleus is truly stable. The half-life would be very very very long though.

Also, consider the local, terrestrial (Earth) Earth abundance of stable Fe and Ni isotopes

Terrestrial (Earth)
Isotope Abundance
Fe-54 0.05845
Fe-56 0.91754
Fe-57 0.02119
Fe-58 0.00282

Ni-58 0.68077
Ni-60 0.26223
Ni-61 0.011399
Ni-62 0.036346
Ni-64 0.009255

Those isotopic vectors do not necessarily represent a universal trend. Nevertheless, Fe-56 is the most abundant Fe-isotope even though Fe-58 is slightly more stable (and least abundant), and Ni-58 is the most abundant Ni-isotope, even though Ni-62 is the most stable of the Ni-isotopes.

https://www.eso.org/public/news/eso0129/

In the Hyperphysics article, a comment attributed to Fewell is given, "Fewell discusses this point, and indicates that the reason lies with the greater photodisintegration rate for ⁶²Ni in stellar interiors." Fewell, M. P., "The Atomic Nuclide with the Highest Mean Binding Energy", Am. J. Phys. 63, July 1995. This is the same paper cited by vanhees71 above.

 

[Silly Questions]

Interesting!

If "poison" is wrong -- and I see why, Fe-56 doesn't "poison" the fusion of other elements simply by not itself fusing -- what word(s) can I use to describe the slowing down of nuclear reactions concurrent with the buildup of Fe-56? Could I say that Fe-56 is the "spent fuel" of stellar fusion?

 

[Orodruin]

Could I say that Fe-56 is the "spent fuel" of stellar fusion?

Basically.

 

[Astronuc]

If "poison" is wrong -- and I see why, Fe-56 doesn't "poison" the fusion of other elements simply by not itself fusing -- what word(s) can I use to describe the slowing down of nuclear reactions concurrent with the buildup of Fe-56?

Perhaps my comment is too strong. In a sense, as "spent fuel", any fusion product with high binding energy does not contribute sufficient energy to maintain a given star, and so, in essences fusion products behave has poisons, just as fission products become poisons in a fission reactor. In other words, any element that doesn't fuse or produces insufficient energy acts as a poison, so even He is a poison (ash or spent fuel) to the pp and CNO cycles, but eventually it becomes fuel.

It's not only Fe-56, but all the metals like Fe and Ni, which would include all the elements above helium to some extent. Note that there are stable isotopes from Ni up to Pb. How they end up forming depends on the mass of the star and its composition to some extent (the initial conditions of the gas cloud that formed the star), whether or not the star is a member of a binary system and the nature of the partner.

 

[vanhees71]

All the elements heavier than Fe are produced in supernova and kilonova explosions. AFAIK, with fusion you don't get beyond Fe-56.

 

[Astronuc]

I'm behind the times on the details of various processes in stellar evolution, but this thread has piqued my interest.

Ni can be formed via an alpha (or helium fusion) process - ⁵²Fe + α => ⁵⁶Ni + γ, and ⁵⁶Fe + α => ⁶⁰Ni + γ, and ostensibly some neutron source to drive neutron capture. A neutron source would be (α,n) fusion reactions, or photo-neutron (γ,n) reactions.

Ref: https://en.wikipedia.org/wiki/Stellar_nucleosynthesis#Helium_fusion
which leads to https://en.wikipedia.org/wiki/Alpha_process (needs additional citations/verification)


Then there is the slow neutron-capture process, or s-process, is a series of reactions in nuclear astrophysics that occur in stars, particularly asymptotic giant branch stars. The s-process is responsible for the creation (nucleosynthesis) of approximately half the atomic nuclei heavier than iron.
https://en.wikipedia.org/wiki/S-process

I dislike relying on Wikipedia (especially articles that need additional verification) and would much prefer textbooks or original peer-reviewed papers. I think we are still learning about the various possibilities for nucleosynthesis, but clearly there are constraints/limits on the formation of elements.

 

[vanhees71]

A review article about kilonovae and the corresponding nuclear research concerning element synthesis is this (open access):

https://doi.org/10.1007/s41114-019-0024-0

and here are some concerning supernovae

https://arxiv.org/abs/astro-ph/0612072v1
https://arxiv.org/abs/1704.00415
https://arxiv.org/abs/1805.04637

 

[Astronuc]

A review article about kilonovae and the corresponding nuclear research concerning element synthesis is this (open access):

https://doi.org/10.1007/s41114-019-0024-0

I was thinking about neutron star interactions with other stars, and NS-NS interactions. Also, gamma ray bursts would ostensibly produce gammas of sufficient energy to produce photo-neutron reactions in otherwise stable elements.

 

[Silly Questions]

I stand enlightened far beyond the original question, which is just how I like it. Thanks to all of you for sharing your knowledge. (I'll keep lurking on the thread in case you guys keep talking, heh heh.)