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I was looking at the isotopes of technetium page on Wikipedia recently, and it seems that the metastable ${^{95m}Tc}$ has a substantially longer half-life (61d) than its most stable state of ${^{95}Tc}$ (20h). Several alternative sources gave the same numbers.

That seems quite peculiar to me. Is it just a general thing that I shouldn't count on the most stable state of an isotope having the longest half-life, or is there some quirkiness there (alternatively, an inaccuracy that got replicated in a bunch of places)?

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migrated from chemistry.stackexchange.com Apr 28 '13 at 5:49

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Hopefully a moderator can shift this to phys.SE. Just surfing around tables of isotopes does however reveal that isomers that are longer-lived than their ground states are not uncommon (102mTc, 116mCs, etc.). Anyhow, this looks like another application of the difference between thermodynamic and kinetic stability. Intuitively, the decay pathways that lead to rapid decay of a ground-state isotope are less probable (maybe totally impossible) in an isomer. The isomer, whilst less thermodynamically stable, is stuck in a potential energy rut that it can only escape through slow processes. –  Richard Terrett Apr 26 '13 at 3:07
    
A very interesting case is $^{180m}Ta$, where the metastable isomer has a half-life much longer than the current age of the Universe, and is in fact the only naturally occurring excited nucleus. More information is available at this wiki article. –  Nicolau Saker Neto Apr 26 '13 at 3:45
    
@RichardTerrett: I can, but isn't this on topic on Chem as well? I thought we allow questions about nuclei.. –  Manishearth Apr 26 '13 at 7:06
    
This question is probably on topic on Chemistry and Physics. Nuclear transformations, radioactivity, fusion, and fission are covered in most general chemistry books. Let's leave this one for awhile and migrate it only if it does not seem to be getting the appropriate attention. –  Ben Norris Apr 26 '13 at 11:31
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@ManishEarth, BenNorris - I respectfully submit that nuclear isomerism is far more nuclear physics than chemistry, taking place on energy and length scales orders of magnitude removed from chemical processes and not involving electronic structure. I've only ever seen it discussed in chemistry in the context of understanding Mössbauer spectroscopy. Whilst I apologise for being a bit presumptuous, I do think this question would attract a greater breadth and depth of answers on the physics site. –  Richard Terrett Apr 27 '13 at 5:44
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Your confusion comes from the oft-made, but not strictly true, assumption that global potential energy minima must be deep local minima. Stability is a function of the local depth of a potential energy well in a potential curve, and excited states in atoms/molecules have different potential curves, above those of their ground states. It is however possible for the potential energy curves in the excited state to have deeper wells than in the ground state, like so. The additional detail with excited states is that they can decay by de-excitation as well as decomposition. If the excited state is to be long-lived, then not only must its potential well be deep, but once the atom/molecule is excited, de-excitation must be somehow suppressed. It could be a process forbidden by some selection rule, for example a spin-forbidden transition.

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