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== Do we have a table of nuclear masses? == |
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I mean a table of masses of bare nuclei, not of atoms. |
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I see you changing the split point 5 × 10<sup>8</sup> years to 10<sup>8</sup> years. But now, "Primordial radioactive nuclides (half-life > 10<sup>8</sup> years)" looks inconsistent: A radionuclide having suffered 9 half-lives would be primordial, but certainly not one that has suffered 45... [[Special:Contributions/103.166.228.86|103.166.228.86]] ([[User talk:103.166.228.86|talk]]) 18:40, 15 September 2024 (UTC) |
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:Well, current sensitivity is actually not that far off finding [[plutonium-244|<sup>244</sup>Pu]] (see the article): we're about an order of magnitude away. I won't be surprised if it really gets confirmed as primordial at some point (though maybe we need to wait another decade or two). Of course <sup>146</sup>Sm and <sup>244</sup>Pu will still not be useful primordials, but it'd be fun to have them back (for a while we had <sup>244</sup>Pu as primordial based on the 1971 result, that in retrospect cannot be right). :) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 04:29, 16 September 2024 (UTC) |
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::I would indeed be happy to see <sup>146</sup>Sm be confirmed as primordial, for the sake of completeness - the hole of even-even nuclides between <sup>144</sup>Sm and <sup>148</sup>Sm is just unbearable... [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 00:02, 18 September 2024 (UTC) |
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::::The magic numbers only care about their own comfort and don't care about the lives of others :( [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 11:20, 19 September 2024 (UTC) |
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::::The combo of ''Z'' = 82 and ''N'' = 126 is also harsh, killing Po~Ac with no mercy... :( [[User:Nucleus hydro elemon|Nucleus hydro elemon]] ([[User talk:Nucleus hydro elemon|talk]]) 15:12, 19 September 2024 (UTC) |
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:::::But at least Ra gets enough beta-stable isotopes that it gets out of the killing zone of ''N'' = 126, with <sup>226</sup>Ra (''Z'' = 88, ''N'' = 138) able to have a respectable 1600-year half-life. :) |
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:::::Unfortunately, as if making new superheavies wasn't hard enough already, the 5g row will probably head straight into the firing squad of ''N'' = 184 when it comes to doing Cf+Ni for 126. :( [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 15:17, 19 September 2024 (UTC) |
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::::::You guess what? My biggest wish is to live in my next life in a universe where the energy of the alpha nuclide is at least 5 MeV higher than in our universe :( [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 15:29, 19 September 2024 (UTC) |
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::::::Yeah but the cruelest enemy of superheavy elements is SF, not alpha decay... [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 15:32, 19 September 2024 (UTC) |
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:::::::If nothing else, such a universe would probably not make the mistake of predicting astatine to be a black solid. That always got on my nerves from the time I realised what was wrong with it. Groups 13 to 16 eventually turn metallic, so why shouldn't groups 17 and 18!? (I'm still betting on oganesson turning out to be a full-fledged metal at STP, not just a semiconductor. But who really knows?) It would also be nice to know more about radon chemistry: the absence of chlorides is still a mystery, but the ionic-looking difluoride is really cool. And it would be nice to know if the destabilisation of 6p<sub>3/2</sub> is enough to make francium have oxidation states above +1. Ah well. Such forbidden mysteries. :( |
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:::::::That's true, but the shell closure strongly hinders SF, and is the only reason they're protected enough to be seen in the first place. When that protection gets lost, there's nothing holding back the terrible onslaught of fission. :( |
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:::::::P.S. the superheavy I would most like to see "stabilised" is copernicium. :D [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 15:50, 19 September 2024 (UTC) |
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::::::::Gd would have 9 naturally occuring isotopes, At would behave like Ta to occur mainly as <sup>215</sup>At and a small portion of [https://en.wikipedia.org/wiki/Talk:Even_and_odd_atomic_nuclei#Odd-odd_nuclides_that_are_very_stable_to_beta_decay_and/or_IT <sup>214m</sup>At], and there will perhaps be no more beta-decay mystery for <sup>222</sup>Rn and <sup>247</sup>Cm. What a fantastic world... [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 18:19, 19 September 2024 (UTC) |
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:::::::::Come to think of it, a world where Rn is stable immediately suggests an earlier discovery of noble gas chemistry. That would be fun. I wonder what the last natural element would be in this case. If the actinoid series can be completed (or nearly so), then perhaps a separate f-series could be recognised earlier: then Nd (maximum +4) vs U (maximum +6) somewhat brings to mind Fe (maximum +6 in bulk) vs Ru (maximum +8), and Cm–No will make a more extreme partner to Gd–Yb. The big drop in oxidation states near the end of the 5f series makes one think of the 4d series; I've thought for a while that if we had long-lived quasi-stable elements to the 6d series, then we wouldn't be having the La vs Lu argument, as it would be obvious that Lr is much more like a transition metal than Ac is. (Lu is also more like a transition metal than La, but not quite as obviously.) Ah well, I can dream about the chemical consequences while you dream of the nuclear-physics ones. ;) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 10:38, 20 September 2024 (UTC) |
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::::::::::I dream about their geochemical properties then. :) I only guess up to Rg because Cn will be too weird, see below. |
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::::::::::Tc probably lives together with Re, so do Rn with noble gases, Fr with Rb/Cs, Ra with Sr/Ba, and Pm, Ac, Am–Fm, Lr with rare-earth elements. Rf–Rg might be similar to their lighter congeners Hf–Au if the relativistic effects aren't too crazy. |
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::::::::::I'm not sure do Pa, Np, Pu comes together with U or have its own ore. Md and No have stable +2 cations, not sure will this let them become closer to Ba than rare-earth elements. I don't know do Po behaves more similar to Bi or Te. Both At<sup>−</sup> and At<sup>+</sup> are stable, I'm not sure which one will dominate the geochemistry of At. |
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::::::::::Cn probably have some noble gas character, and its predicted melting point and boiling point might cause a rain of Cn happen in that world. I don't want to live in a world with copernicium rain, it is just too dangerous. [[User:Nucleus hydro elemon|Nucleus hydro elemon]] ([[User talk:Nucleus hydro elemon|talk]]) 11:28, 20 September 2024 (UTC) |
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:::::::::::There would be no need to worry about copernicium rain - remind that this is a world full of <sup>8</sup>Be :) [[Special:Contributions/129.104.65.10|129.104.65.10]] ([[User talk:129.104.65.10|talk]]) 12:07, 20 September 2024 (UTC) |
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::::::::::::I kind of suspect that in this world Be is like Al: useless to biology because it's insoluble at physiological pH, but tolerated because it's so common. Copernicium would be weird indeed. Still, I think it'd be quite rare like krypton and xenon already are in the real world. :) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 14:46, 20 September 2024 (UTC) |
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:::::::::::::Before discussing implications for biology, we also have to consider how hypothetical beryllium burning would affect stellar evolution. A while back I had read a few interesting papers on the subject and written a bit about it ([[Beryllium-8#Hypothetical universes with stable 8Be]]). <sup>[[User:ComplexRational|'''<span style="color:#0039a6">Complex</span>''']]</sup>/<sub>[[User talk:ComplexRational|'''<span style="color:#000000">Rational</span>''']]</sub> 16:18, 20 September 2024 (UTC) |
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::::::::::::::If <sup>8</sup>Be is stable because <sup>4</sup>He is destabilized, then <sup>5</sup>He and <sup>5</sup>Li might be bound too. This will drastically change the Big Bang nucleosynthesis at that universe. [[User:Nucleus hydro elemon|Nucleus hydro elemon]] ([[User talk:Nucleus hydro elemon|talk]]) 04:36, 21 September 2024 (UTC) |
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:::::::::::::::Well, in that case all the elements might've been made in that universe's Big Bang, just as [[Alpher–Bethe–Gamow paper|αβγ]] originally expected. :) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 04:40, 21 September 2024 (UTC) |
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By energy conservation we have nuclear mass + Z*electron mass - atomic mass = sum of ionization energies. For <sup>4</sup>He, the left side is |
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== About <sup>222</sup>Rn/<sup>222</sup>Fr == |
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<math>(4.001506179129 + 2\times 0.0005485799090441 - 4.002603254130)\times 931494103.72=79.00662\,\mathrm{eV}</math>, |
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Hi! I have just noticed the mass excess of <sup>222</sup>Rn given in NUBASE is 16372.0 ± 1.9 keV, while the mass excess of <sup>222</sup>Fr is 16378 ± 7 keV, corresponding to an atomic mass of 222.0175825(75) for <sup>222</sup>Fr. While the data are not decisive, <sup>222</sup>Rn has lower energy if we ignore the error margin. So what do you think of the status of <sup>222</sup>Rn? This will affect how we formulate in [[Isotopes of radon]] and [[Double beta decay]]. [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 11:23, 19 September 2024 (UTC) |
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:I think we should leave it open still, since Belli et al. [https://arxiv.org/abs/1407.5844 explicitly predicted the single beta] of this isotope and tried to find it. I'm naturally quite curious which way round it'll go. :) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 13:30, 19 September 2024 (UTC) |
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which is consistent with the sum 79.00514 eV of data given [[Ionization energies of the elements (data page)|here]]. |
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== The existence of Vitali sets == |
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In general, if we need to find nuclear mass, we must also know the data of ionization energies, which are in general incomplete and (more seriously) are suspected to vary for different isotopes of an element. (The calculation above works because the proportion of <sup>3</sup>He in natural helium is much, much too tiny). Any idea? [[Special:Contributions/169.155.234.214|169.155.234.214]] ([[User talk:169.155.234.214|talk]]) 09:09, 26 December 2024 (UTC) |
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Reply to "Doesn't the existence of Vitali sets (a result of AC) already challenge intuition?": No, not at all in my opinion :) Anyway, why should <math>\mathbb{R}</math> be so great that every subset is measurable? The existence of non-measurable sets rather than the non-existence is what looks more natural for me. |
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== Ad: Barnstar == |
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By the way, I love the reference you gave, thanks a lot :) [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 21:33, 21 September 2024 (UTC) |
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Thank you! [[User:Szelma W|Szelma W]] ([[User talk:Szelma W|talk]]) 11:26, 3 January 2025 (UTC) |
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:I am neither a fan of CH nor a fan of ¬CH. I could have insisted that <math>2^{\aleph_0} = \aleph_{85}</math> because 85 is my favorite neutron number, but I really do have no opinion: both consequences of CH and of ¬CH are equally valid for me, and it is worthy to state them both. :) [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 21:39, 21 September 2024 (UTC) |
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::My personal take is basically: both consequences of CH and ¬CH are indeed equally valid. But the same holds for consequences of AC and ¬AC, despite the fact that mathematicians seem a lot happier to assume AC than otherwise. To that extent, I think it makes sense to ask which one conforms more with my intuitions about sets. So when I say "I'm a fan of CH", I suppose what I really mean is that my fuzzy ideas about how sets should behave are more consistent with the consequences of CH than with those of ¬CH. If we speak this way, about properly axiomatising intuitions, I think it makes sense to say that "CH is true of my sets" and simultaneously "¬CH is true of somebody else's". |
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::With that said, Hamkins' presentation strongly persuades me that CH (actually, GCH) should be true of more people's sets. This is because I think hyperreals are in some sense the "natural" way to do analysis, and that epsilon-delta formulations are to some extent dancing around the intuition. It makes me think of, say, Cardano having to solve many types of cubics because he didn't like negatives. As such I think there's a strong argument that GCH "should" have the status AC currently enjoys among non-set-theorists (well, actually ZF+GCH implies AC, but you know what I mean). |
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::Non-measurability was indeed a bit of a mind-blowing fact when I first encountered it in mathematical popularisations at about eight. :) I would find it intuitive now, but perhaps it has to do with von Neumann's dictum about getting used to things in mathematics. But I think [https://mathoverflow.net/a/331962 Rodrigo Freire's answer to a MathOverflow question about V=L] gets philosophically at the issue here. Though actually his argument persuades me towards V=L, because I would indeed take AC's attitude towards measurability as a "precedent" of sorts, which is why I reject [[Freiling's axiom of symmetry|Freiling's argument for ¬CH]]. BTW, Nik Weaver's answer on that page gets at something interesting: it seems quite plausible that we are in the current situation because non-set-theorists would have quite different intuitions about sets from set-theorists. The former would likely be a lot happier with V=L than the latter. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 03:55, 22 September 2024 (UTC) |
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::P.S. Regarding another case of set-theorists and non-set-theorists having quite different intuitions, see [https://arxiv.org/pdf/1203.4026 this other paper by Joel David Hamkins] (2012), where he gives a specific example of an axiom (<math>\kappa < \lambda \implies 2^\kappa < 2^\lambda</math>) that seems extremely natural to non-set-theorists and yet is generally rejected by set theorists. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 08:13, 22 September 2024 (UTC) |
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:::Most of the real analysis relies on [[Axiom of dependent choice|DC]], and it is written in the Wikipedia page "It is possible to generalize the axiom to produce transfinite sequences. If these are allowed to be arbitrarily long, then it becomes equivalent to the full axiom of choice", so I have no doubt on AC. That said, my attitude is that whenever ZF/AC<sub>ω</sub>/DC is enough to prove a proposition, don't overuse the power of AC :) |
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:::Thanks for the link provided, and by the way, I just remembered [https://en.wikipedia.org/wiki/Meagre_set#Erdos%E2%80%93Sierpinski_duality this interesting implication] of CH. [[Special:Contributions/129.104.241.231|129.104.241.231]] ([[User talk:129.104.241.231|talk]]) 14:22, 22 September 2024 (UTC) |
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::::Well, if you like interesting remarks on what's actually necessary to prove what, you might enjoy [https://mathoverflow.net/questions/21367/proof-that-pi-is-transcendental-that-doesnt-use-the-infinitude-of-primes this MathOverflow question], regarding whether or not the infinitude of prime numbers is necessary to prove <math>\pi</math> transcendental. :) |
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::::My philosophy is basically that the infinite should be like the finite, on the grounds that ordinals seem to be the most obvious way to introduce "infinity" to children. |
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::::I think "don't overuse the power of [just about anything really]" is sound advice. On the other hand, sometimes the proof that uses more firepower is the more intuitive one. So, maybe I'd say: do all the crazy stuff you want if it helps you get to the correct result. Then, after admiring your fireworks, step back and ask yourself how much of it was really needed. :) [[User:Double sharp|Double sharp]] ([[User talk:Double sharp#top|talk]]) 16:06, 22 September 2024 (UTC) |
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Revision as of 11:26, 3 January 2025
 | This user is busy in real life and may not respond swiftly to queries. |
Do we have a table of nuclear masses?
I mean a table of masses of bare nuclei, not of atoms.
By energy conservation we have nuclear mass + Z*electron mass - atomic mass = sum of ionization energies. For 4He, the left side is
,
which is consistent with the sum 79.00514 eV of data given here.
In general, if we need to find nuclear mass, we must also know the data of ionization energies, which are in general incomplete and (more seriously) are suspected to vary for different isotopes of an element. (The calculation above works because the proportion of 3He in natural helium is much, much too tiny). Any idea? 169.155.234.214 (talk) 09:09, 26 December 2024 (UTC)
- Currently away on holiday, so a search will have to wait. But indeed no idea off the top of my head. Double sharp (talk) 05:51, 27 December 2024 (UTC)
- OK thanks :) 169.155.234.55 (talk) 11:18, 27 December 2024 (UTC)
Ad: Barnstar
Thank you! Szelma W (talk) 11:26, 3 January 2025 (UTC)