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In "The Greatest Show On Earth", author Richard Dawkins spends a chapter discussing radiometric dating. I find myself confused by the following lines, though I'm sure the reason is elementary. (excellent pun and emphasis both mine)

Among all the elements that occur on Earth are 150 stable isotopes and 158 unstable ones, making 308 in all. Of the 158 unstable ones, 121 are either extinct or exist only because they are constantly renewed, like carbon-14.

What is meant by "occur on Earth" and "extinct" here? I take "extinct" to mean "decayed to the point that it cannot be detected". If I am using that word correctly, then in what sense does an extinct element "occur on Earth"?

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    $\begingroup$ You have the right notion. The matter that makes the earth came from some supernova(s) in the distant past. The matter ejected collected to form the sun and planets of our solar system. At the time of the supernova all sorts of isotopes were created. But if those isotopes had a half life much shooter than the time in the past to the supernova, then all of that isotope would have decayed. For example carbon-14 has a half life of 5,730 years. Thus all of the carbon-14 created in the supernova event would have decayed long ago. C-14 is now formed in upper atmosphere which is why it exists now. $\endgroup$ – MaxW Jan 4 '16 at 6:43
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    $\begingroup$ Hmm, Dawkins' statement doesn't quite match the information in a previous answer of mine, so that may make it more complicated to figure out exactly what he meant. $\endgroup$ – Nicolau Saker Neto Jan 4 '16 at 7:26
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Defintions

Occur on Earth differentiates between all isotopes in the universe and isotopes which exist or have existed on Earth. The passage identifies that there are a total of 308 isotopes occurring on Earth, but it is worth noting that there are more than 308 total isotopes in the universe. This discrepancy is because some isotopes have extremely short half-lives, making their total "lifetimes" extremely short. As an example, an isotope generated in a supernova which has a half-life of 1 second will have totally degraded in at most 32 seconds (32 half-lives degrades the sample completely no matter the original amount). That is not nearly enough time for the isotope to travel from the exploded star to Earth, so that isotope does not occur on Earth (and it never can). This hypothetical supernova isotope would exist but it would not be part of the 308 Earth occurring isotopes.

Extinct means that the isotope is no longer naturally occurring within a given environment. Isotopes have differing half-lives, and a currently extinct isotope would have degraded so completely as to no longer be present at all. The isotopes would have originally been seeded into the environment by processes like supernovas, which produce ejecta containing the elements produced by nuclear fission and nuclear fusion. When that ejecta reaches the Earth the isotopes within it begin to occur on Earth, but eventually those isotopes will disappear due to half-life degradation. There are processes which can replace degraded isotopes in a self-regenerating manner and thus those isotopes never go extinct due to self-regeneration. An example of this type of self-regenerating isotope is Carbon-14; in fact, Carbon-14 will likely never become extinct. Self-regeneration is not the only process to replenish isotopes; the aforementioned supernovas are another. Unlike self-regeneration, which is a continuous process in which degraded isotopes continuously get replaced, supernovas deposit isotopes intermittently and comparatively infrequently. In fact, if a supernova deposit is delayed for an extended amount of time, isotopes which come only from supernovas can actually disappear from Earth entirely- they would become extinct. These extinct isotopes would stay extinct on Earth until a supernova redeposited the isotope.

Clarifying the Passage

As far as your question about an extinct isotope occurring on Earth- for the isotope to be extinct it cannot be currently occurring on Earth, but it was present in the past (logically, if an isotope never appeared on Earth it couldn't be part of the 308 isotope total, so for some of that 308 total to be extinct means they were present on Earth in the past). That question is sort of unrelated to the passage however, but the passage was written poorly enough that I think you misunderstood that they were trying to say that 121 isotopes should hypothetically be extinct, but that some of them are not actually extinct. To reduce the confusion the passage is causing, I have rewritten it to be far more clear: "Among all the elements that have have ever occurred or currently occur on Earth there are 308 total isotopes. Those isotopes are split into 150 stable isotopes and 158 unstable isotopes. Of the 158 unstable isotopes, 121 should be or currently are extinct, however, there are isotopes not actually extinct because they are constantly renewed, like carbon-14."

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  • $\begingroup$ Thank you for the thorough answer. I'm still confused about how one could determine that an isotope used to occur on Earth if it can't be detected today. $\endgroup$ – Austin Mohr Jan 17 '16 at 20:47
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    $\begingroup$ Because isotopes don't degrade to something random, they degrade to a specific substance. For instance, Carbon 14, it degrades to Carbon 12 at a certain rate- which is how carbon radio-dating works. So, say you know that there is a ton of a certain lead isotope that only comes from the degrading of a particular uranium isotope (which is a real phenomena- uranium eventually turns into lead) you can know that the uranium isotope was present in the past if you find the lead isotope. Even if the uranium isotope is extinct, the existence of the special lead isotope proves it used to occur on Earth. $\endgroup$ – Emily M Jan 17 '16 at 21:19
  • $\begingroup$ Your comment hits my oversight on the nose. It is not the case that radioactive isotopes decay and vanish without a trace. They decay to a stable substance that we can observe today. Thank you for bearing with me. $\endgroup$ – Austin Mohr Jan 17 '16 at 22:34
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As I pointed out in a comment, you have the right notion. The matter that makes the earth came from the big bang, or supernovas in the distant past. Our sun is thought to be a third generation star so the matter in our solar system could have come from the big bang, a first generation supernova, or a second generation supernova. Although we know about 3300 isotopes in total, no doubt more very short lived isotopes were produced in the big bang or supernovas.

I don't know how to determine which isotopes Dawkins thought to be the 150 stable ones, or the 158 unstable ones, nor which 121 of the unstable 158 that he determined were either extinct or exist only because they are constantly renewed. Dawkins numbers seem to be very out of date as well. For isotopes found/known on earth, a Wikipedia table lists:

That gives a total of 339 isotopes which have been detected on the earth out of the about 3300 known isotopes.

Primordial Radioactive Nuclides

The 34 primordial radioactive nuclides have half lives long enough to still survive from their creation in the big bang, or some supernova event, till the formation of the earth and also survive to the present day.

Let's take one isotope as an example of an primordial radioactive nuclide. In the second generation supernova some $\ce{^{244}Pu}$ (half life 80.8 million year) would have been created. If we assume that a billion years are needed for the matter from the second generation stars to form the third generation solar systems then that is 12.4 half-lives and 1.9E-4 of the plutonium formed in the supernova would survive enough to be detected on the newly formed earth. However the earth was formed about 4.54 billion years ago, so now an additional 56.2 half lives have passed and the original plutonium is mostly gone. So at this point it has been 5.54 billion years since the second generation supernovas which is 68.6 half-lives and only 2.3E-21 of the plutonium formed in the supernova would survive. That would seem to be just enough to yet be detectable.

Cosmogenic Radioactive Nuclides

The 21 cosmogenic radioactive nuclides are formed by nuclear reactions in earth's upeer atmosphere. I'll point out two such isotopes which have a short half life that they only exists because they are being renewed. Both $\ce{^3H}$ (half life 12.7 years) and $\ce{^{14}C}$ (half life 5,730 ± 40 years) are renewed in earth's upper atmosphere.

Extinct Isotopes

So with 51 short-lived isotopes known, and 21 of those being detected as cosmogenic radioactive nuclides, then we are left with 30 radioactive nuclides which have short half-lives and are as Dawkins puts it either (1) extinct or (2) exist only because they are constantly renewed like the cosmogenic radioactive nuclides. At this point the gist is that Dawkins seems to hedged his analysis and use an "or" to stop his analysis. In other words it isn't yet clear that all 30 of the renaming isotopes have been detected in nature. Some may just have been detected because they were made in a laboratory. If the isotope cannot ever be detected in nature (which seems unlikely if you really were determined to find such an isotope) then it would be an extinct isotope.

Thus one definition of an extinct isotope is:

an isotope which would have been created in the big bang or a supernova, but presently undetectable on earth.

This of course leaves an ambiguity if any particular atom of such an isotope survived from the big bang or a supernova long enough to actually be present when the earth formed, yet be undetectable today on earth. All in all this seems unlikely.

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  • $\begingroup$ Thanks for the detailed breakdown of the different isotope classes. As for Dawkins' numbers, he gives no reference, but the book is over six years old. Perhaps they were state of the art at the time, perhaps not. $\endgroup$ – Austin Mohr Jan 18 '16 at 3:17
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    $\begingroup$ I'd assume that Dawkins just used an relatively old reference for his research. Since Dawkins book was published in 2009 there is no way that 100 isotopes have been discovered in the last six years. I think overall Dawkins argument that the earth is billions of years old, is correct even though his isotope counts are wrong. $\endgroup$ – MaxW Jan 18 '16 at 4:47

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