How Many Naturally-Occurring Elements are there? Corrigendum

And in non-COVID news…

… I received an e-mail from ‘Claire’ the other day pointing out that there was an error in one of my blog articles.

I try quite hard to be ‘right’ on this blog, so despite her politeness, I was distressed to hear this.

The error was in an article written on 15th February 2010 – yes, more than 10 years ago – entitled: Just How Many Naturally Occurring Elements are there?

Reading it again after all these years I was pleased with it. The gist of the article is that there is not a clear answer to the question.

It turns out that the nuclei of the atoms of some elements are so radioactively unstable that even though they do exist on Earth naturally, at any one time there are only handful of atoms of the substance in existence.

These elements seemed to be in a different category from, say, carbon (which has some stable isotopes) or uranium (which has no stable isotopes). But some of the isotopes of uranium have very long half-lives: 238U has a half-life 4.468 billion years – roughly the length of time that the Earth has existed.

So of all the 238U has which was donated to the Earth at its formation – very roughly half of it has decayed (warming the Earth in the process) and half of it is still left.

So I had no problem saying that 238U was ‘naturally-occurring’, but that it was a moot point whether Francium, of which there are just a few atoms in existence on Earth at one time, could really be said to be ‘naturally-occurring’.

So in the article I stated that I had stopped giving an exact number for the number of ‘naturally-occurring’ elements – I just say it is ‘about 100’ – and then discuss the details should anyone ask for them.

What was my error?

In the article I stated that Bismuth – atomic number 83 – is the heaviest element which has at least one stable isotopes. For elements with larger atomic numbers than Bismuth, every isotope is radioactively unstable.

What Claire told me was that in fact the one apparently stable isotope of bismuth (209Bi, the one which occurs naturally) had been found to be unstable against alpha decay, but with an exceedingly long half-life. The discovery had been announced in Nature in 2003: link

Click image for a larger version. Link to Nature here

What I want to comment on here is the length of the half-life: The authors estimated the half life of 209Bi was:

  • 1.9 (± 0.2) x 1019 years.
  • 19 billion billion years

This is an extraordinarily long time. For comparison the estimated age of the Universe – the time since the Big Bang – is estimated to be about:

  • 1.4 x 1010 years.
  • 14 billion years

Imagining that 1 kilogram of pure 209Bi was gifted to the Earth when it was formed roughly…

  • 0.4 x 1010 years.
  • 4 billion years

…ago. Then since that time less than 1 in a billion atoms (0.15 micrograms) of the 209Bi would have decayed.

We might expect a single nuclear decay in 1 kilogram of pure 209Bi every 5 minutes.

How could one measure such a decay? The authors used a transparent crystal of Bismuth Germanate (Bi4Ge3O12) which scintillates when a radioactive particle – such as an alpha particle passes through it. In this case, the crystal would ‘self-scintillate’.

But the background rate of scintillation due to other sources of radiation is much higher than the count due to the decay of the 209Bi.

To improve the discrimination against the background the authors cooled the crystal down to just 0.1 K. At this very low temperature its heat capacity becomes a tiny fraction of its heat capacity at room temperature, and the energy of even a single radioactive decay can be detected with a thermometer!

Combining light detection and heat detection (scintillating bolometry) helps to discriminate against spurious events.

And my point was…?

For all practical purposes 209Bi is stable. Anything with a half-life a billion times longer than the age of the Universe is at least stable-ish!

But Claire’s e-mail caused me to reflect that the apparently binary distinction between ‘stable’ and ‘unstable’ is not as obvious as I had assumed.

By this extraordinary measurement, the authors have reminded me that instead of saying that something is ‘stable’ we should really state that it may be stable, but that if it decays, its rate of decay is beyond our current limit of detectability.

So for example, we know that neutrons – outside a nucleus – decay with a radioactive half-life of just 10.2 minutes. But what about protons? Are they really unconditionally stable?

People have searched for the decay of the proton and established that protons may be stable, but if they do decay, their half-life is greater than 1.7 x 1034 years – or more than a million, billion, billion times the age of the Universe.

So now we know.

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4 Responses to “How Many Naturally-Occurring Elements are there? Corrigendum”

  1. Simon Says:

    Nice discussion, Michael, as always (!) – thanks!

    (I had composed a much much longer comment, making an analogy with a question I was pondering, professionally, only yesterday. But in an irritating example of fat finger syndrome I just managed to delete the whole thing. Ah well. I’ll regard what I had written as the disposable prototype. The released version will be all the better, if only I can remember enough to create one. Later …)
    All the best!
    Simon

    • protonsforbreakfast Says:

      Ahh! The wisdom that hath evaporated… I am sure it will occur to you again! I would love to read about the measurement which I am sure is where your professional commentary would have been insightful. Best wishes: M

  2. PeterG Says:

    I’m taken with the phrase “naturally occurring” which, in these discussions, usually excludes atoms produced in particle accelerators.
    Humans are a part of nature, and everything we do is natural and in conformity with the Laws of Nature. Unnatural processes scarcely ever happen, a fact of nature codified in The Second Law of Thermodynamics.

    • protonsforbreakfast Says:

      Indeed. Colloquially we do not consider ‘manufactured objects’ to be natural. But of course objects manufactured using techniques outside the Laws of Nature are pretty rare. Best wishes: M

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