Does stable mean that an isotope has a very long half life, for example xenon-124 has a half life of 1.8 x 10^22 years, or does it mean that fissure is theoretically not possible, or does it mean that the isotope has a very long half life, but the exact number is unknown?


Does stable mean that an isotope has a very long half life... or does it mean that fissure is theoretically not possible, or does it mean that the isotope has a very long half life, but the exact number is unknown?

"Stable" effectively means that there is no experimental evidence that it decays. However, there are nuances within that statement.

  1. Most of the "stable" light nuclei can also be shown to be theoretically stable. Such nuclei would have to absorb energy to decay via any of the known decay modes, and so such decay cannot happen spontaneously.

  2. Many heavier nuclei are energetically stable to most known decay modes (alpha, beta, double beta, etc.) but could potentially release energy via spontaneous fission. However, they have never been observed to do so; so for all practical purposes they are considered stable.

  3. Some nuclei could potentially release energy via emission of small particles (alpha, beta, etc.), but have never actually been observed to do so. Such nuclei are often called "observationally stable".

  4. Several nuclides are radioactive, but have half-lives so long that they don't decay significantly over the age of the Earth. These are the radioactive primordial nuclides; your example of xenon-124 is one of them.

Note that nuclides can in principle be moved from categories 2 or 3 into category 4 via experimental observations. For example, bismuth was long thought to be the heaviest element with a stable isotope. However, in 2003, its lone primordial isotope (bismuth-209) was observed to decay via alpha emission, with a half-life of $\approx 10^{19}$ years.

One could defensibly claim that the nuclei in categories 2 & 3 are radioactive but their half-life is unknown; after all, the totalitarian principle says that any quantum-mechanical process that is not forbidden is compulsory. If you want to take this perspective, though, you have to assume that we have a good enough grasp on nuclear physics to know what is forbidden or not.

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    $\begingroup$ I just expected that basic things like this have a good definition in physics. After all it is a hard science. $\endgroup$ – inf3rno Jul 13 '20 at 19:29
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    $\begingroup$ "Hard science" doesn't imply "unambiguous definition of words". Even in math sometimes different authors mean slightly different things by the same word - the only thing that's important is that it's unambiguous in context! $\endgroup$ – ManfP Jul 14 '20 at 15:37
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    $\begingroup$ @inf3rno: And yet, here we are. $\endgroup$ – Michael Seifert Jul 14 '20 at 18:15
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    $\begingroup$ For category 3 there are a great many "stable" nuclides with even numbers of neutrons and protons that would need to undergo double beta decay to avoid higher energy nuclides. They all almost certainly will never be observed to decay even though it may be possible $\endgroup$ – Steve Cox Jul 14 '20 at 19:34
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    $\begingroup$ @inf3rno I'd imagine an astronomer might be interested in very different time scales than, say, a nuclear engineer. And from a purely theoretical standpoint the difference between "the radiation of one gram will quickly kill you" and "has decayed approximately twice since the universe existed" might not even be all that interesting. $\endgroup$ – ManfP Jul 15 '20 at 20:39

This half-life of $1.8\cdot 10^{22}$ years was actually measured. At first glance it seems impossible to measure such a long half-life. But let's go through the numbers to see that is indeed scarcely measurable.

The actual measurement has been done with the XENON1T detector. This experiment used 3 tons of liquid xenon, which are around $10^{28}$ xenon atoms. Natural xenon is known to contain $0.1$ % of the isotope xenon-124. So they had around $10^{25}$ xenon-124 atoms. The experiment detected a few xenon-124 atoms per day decaying to tellurium-124 by double electron capture (see "Dark-matter detector observes exotic nuclear decay"). Now you can use $\frac{dN}{dt}=-\frac{N}{t_{1/2}}\ln(2)$, and find the half-life of xenon-124 to be $t_{1/2}=1.8\cdot 10^{22}$ years.


A stable isotope does not decay naturally. Usually through experiments, one can determine a lower limit for the half-life. Theory or location on the chart of Nucleids may predict this to be an unstable isotope but the half life-life is either non-existent (stable isotope) or is too long to measure. Since it's thought to be unstable it listed with a long half-life.

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    $\begingroup$ Doesn't everything decay, given enough time? $\endgroup$ – vsz Jul 15 '20 at 9:27
  • $\begingroup$ @vsz no, there are isotopes for which we know that they can't decay without gaining energy from somewhere. It's just that not all "stable" isotopes are like that, some could decay but either don't or do it very, very rarely. $\endgroup$ – Peteris Jul 15 '20 at 17:04
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    $\begingroup$ @vsz there is no predicted decay of massless particles -- that's just photons for what we know. Otherwise everything is predicted to decay. However, Proton decay, while predicted, has never been observed. That's not because they never tried either. $\endgroup$ – Martijn Jul 16 '20 at 8:03
  • $\begingroup$ @Martijn : well, if the half-life of something is long enough, it's unlikely to observe it decaying during a human lifetime... $\endgroup$ – vsz Jul 16 '20 at 8:14
  • $\begingroup$ @vsz that depends on how many of them you have. $\endgroup$ – Martijn Jul 16 '20 at 8:46

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