## The half-life gap

If you sort all the nuclides (isotopes of elements) in order of increasing half life, there are a fairly steady supply of them (on a logarithmic scale) up to a half-life of about 10 million years. There are also about 250 that have a half-life so long that it has never been measured. (And for about half of those, it could be infinite.)

The focus of this post is the group of 40 or so nuclides between those extremes: those whose half-life has been measured to be very long. The upper part of this range, above maybe 1014 years, is likely to gain new members as our ability to measure half lives improves. Our knowledge of the lower part, though, might be complete.

I call your attention to the fact that gadolinium-152’s half life of 1.08×1014 years is about 166 times longer platinum-190’s half life of 6.5×1011. Yet there are zero known nuclides whose half life lies in the sizable gap between them.

I don’t have an explanation for this “half life gap” around 1013 years. I’ve never seen it mentioned.

Here’s a chart to help see it. For a given half life, it shows the number of known nuclides whose half life is within a factor of 4 of that length of time. The shaded range is the actual gap.

(Well, I thought that might be a good way to visualize it. After seeing it, I’m not sure how well it worked. It’s supposed to be something like a heat map.)

Could there be any as-yet unknown nuclides in the gap? I think it’s possible. My impression is that it’s unlikely, but I might have the wrong impression. I’m guessing that nuclides whose half lives are reported to be “greater than [something]”, as opposed to just “probably not infinite”, are the ones that could be in the gap. There are three nuclides for which the minimum established lower bound on their half life makes it possible for them to be in the gap:

• osmium-192: > 9.8×1012 years
• osmium-184: > 5.6×1013 years
• molybdenum-98: > 1.0×1014 years

It is also possible that the data I’m using is erroneous, or that our best knowledge about half lives contains errors. Most of the data I’m using is quite old, though it seems to be pretty much the same as what Wikipedia offers.

I don’t think it’s realistic that some undiscovered nuclide (e.g. in the hypothesized “island of stability”) has a half life this long, though maybe that can’t be completely ruled out.

Maybe this gap isn’t so remarkable. Consider that, if it weren’t for vanadium-50 (1.50×1017 years), there would be an even bigger gap from 7.70×1015 to 1.80×1018 years, a factor of 233. I’m only guessing that this almost-gap around 1017 is more likely to be filled in as new measurements are made.

The gap around 1013 years seems to be at about the right place to make a convenient division between nuclides that are clearly radioactive, and those that can more-or-less be treated as stable. I say we call nuclides on the stable side of the gap “pretty much stable”. There are precisely 276 “pretty much stable” nuclides. Again, it might be conceivable that some undiscovered nuclides could someday push the count up to 277 or more, but that seems unlikely. 276 is probably the true and final answer.