<p>While a long half-life, hundreds or millions of years or more, favors a radioisotope being relatively common or even occurring in nature at all, it is not the only consideration.  Whether and how effectively the isotope can be regenerated also figures in.</p>

<p><a href="https://en.m.wikipedia.org/wiki/Isotopes_of_niobium" rel="nofollow noreferrer">Niobium</a>.   occurs as only one isotope, <span class="math-container">$_{41}^{93}\text{Nb}$</span>.  All other isotopes decay away much too quickly, including <span class="math-container">$_{41}^{94}\text{Nb}$</span> with a half-life of only about 20,300 years -- not enough to survive in the billions of years since primordial times when the Earth formed.</p>

<p>Now look at carbon.  The radioisotope carbon-14, <span class="math-container">$_{6}^{14}\text{C}$</span>, has a half-life of only 5730 years so surely it, too, is all gone, meeting the same end as <span class="math-container">$_{41}^{94}\text{Nb}$</span>.  In fact, as many readers know, carbon-14 is still with us (even if it's only trace amounts) and in use as a probe for dating organic matter.  The difference, of course, is there is a readily available mechanism for regenerating this isotope through <a href="https://en.m.wikipedia.org/wiki/Cosmogenic_nuclide" rel="nofollow noreferrer">the action of cosmic rays high above Earth</a>.  The availability of this mechanism means carbon-14 need not have enough half-life to survive billions of years since the Earth's formation, only enough to survive weeks of circulation time to get to the ground.</p>

<p>We can correlate half-life to abundance only when comparing isotopes that are <strong>formed by similar mechanisms.</strong></p>

CC BY-SA 4.0
2020-06-14T18:14:01.250Z
2020-06-14T18:21:02.233Z
2020-06-14T18:21:02.233Z
Oscar Lanzi
<p>In <a href="https://www.asa3.org/ASA/resources/Wiens.html" rel="nofollow noreferrer">Radiometric Dating: A Christian Perspective</a>, the author argues (persuasively, I think) in favor of the mainstream interpretation of radiometric dating (as opposed to the claims of young earth creationists). He says the fact that short-lives isotopes are generally not found on Earth is evidence showing that the Earth is billions of years old.</p>

<blockquote>
  <p>Just about the only radioisotopes found naturally are those with very long half-lives of close to a billion years or longer.... The only isotopes present with shorter half-lives are those that have a source constantly replenishing them...</p>
  
  <p>The Earth is old enough that radioactive isotopes with half-lives less than half a billion years decayed away, but not so old that radioactive isotopes with longer half-lives are gone.</p>
</blockquote>

<p>I would guess that some of these shorter-lived elements still exist in minute amounts because a decay curve has a long tail, but <strong>is the basic statement correct - that shorter-lived, non-replenished radioactive isotopes are absent (or nearly so) from Earth?</strong></p>

<p><strong>Where can I read more about this?</strong></p>

<hr>

<p><strong>Clarification</strong>: I didn't make it clear enough, but I'm specifically asking about the relative abundance of <strong>non-replenished</strong> radioisotopes - those that are not produced on Earth by natural processes. Eg, excluding carbon-14 (produced in the atmosphere by cosmic rays), excluding thorium-230 (produced by the decay of uranium-234), etc.</p>

CC BY-SA 4.0
2020-06-15T02:20:02.487Z
From "Promordial nuclides" on Wikipedia: "primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed...The shortest-lived primordial isotope, 235U, has a half-life of 704 million years, about one sixth of the age of the Earth and the Solar System." - https://en.wikipedia.org/wiki/Primordial_nuclide#Radioactive_primordial_nuclides
Nathan Long
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2020-06-15T14:54:32.497Z
@a_donda sorry, yes - I wasn't responding to your comment there, I was just noting that the article on primordial nuclides seems to support the idea that shorter-lived nuclides which aren't being replenished are not found on earth, since the shortest-lived primordial nuclide is 235U.
Nathan Long
CC BY-SA 4.0
2020-06-16T05:09:24.497Z
You also have to take into account just how much of any particular radioisotope originally existed.  They weren't all created in equal amounts, some might have segregated into different parts of the original solar nebula, or in different parts of the primordial Earth. E.g. if most of isotope X segregated into the core, how would we know its abundance?
jamesqf
CC BY-SA 4.0
2020-06-16T17:49:53.713Z
@jamesqf That's true, but wouldn't it be awfully coincidental if all the short-lived radioisotopes just happened not to be created, or to be located in inaccessible locations?
Nathan Long
CC BY-SA 4.0
2020-06-25T11:01:57.500Z
I found where Wikipedia says the standard atomic weight of each element is determined by the terrestrial abundance of its isotopes as determined by CIAWW. https://www.ciaaw.org/isotopic-abundances.htm lists the isotopes by abundance, though it doesn't seem to include them all (eg carbon-14 is not there).
Nathan Long
<radioactivity>
Does the relative abundance of radioactive isotopes reflect their half-lives?
Nathan Long
# Does the relative abundance of radioactive isotopes reflect their half-lives?

(Asked by: username_0 on 2020-06-14)

In [Radiometric Dating: A Christian Perspective](https://www.asa3.org/ASA/resources/Wiens.html), the author argues (persuasively, I think) in favor of the mainstream interpretation of radiometric dating (as opposed to the claims of young earth creationists). He says the fact that short-lives isotopes are generally not found on Earth is evidence showing that the Earth is billions of years old.

> Just about the only radioisotopes found naturally are those with very username_0 half-lives of close to a billion years or longer.... The only isotopes present with shorter half-lives are those that have a source constantly replenishing them...
>
> The Earth is old enough that radioactive isotopes with half-lives less than half a billion years decayed away, but not so old that radioactive isotopes with longer half-lives are gone.

I would guess that some of these shorter-lived elements still exist in minute amounts because a decay curve has a username_0 tail, but **is the basic statement correct - that shorter-lived, non-replenished radioactive isotopes are absent (or nearly so) from Earth?**

**Where can I read more about this?**

---

**Clarification**: I didn't make it clear enough, but I'm specifically asking about the relative abundance of **non-replenished** radioisotopes - those that are not produced on Earth by natural processes. Eg, excluding carbon-14 (produced in the atmosphere by cosmic rays), excluding thorium-230 (produced by the decay of uranium-234), etc.

**Tags:** radioactivity

> **Comments:**
> **username_0**: From "Promordial nuclides" on Wikipedia: "primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed...The shortest-lived primordial isotope, 235U, has a half-life of 704 million years, about one sixth of the age of the Earth and the Solar System." - https://en.wikipedia.org/wiki/Primordial_nuclide#Radioactive_primordial_nuclides  
> **username_0**: @a_donda sorry, yes - I wasn't responding to your comment there, I was just noting that the article on primordial nuclides seems to support the idea that shorter-lived nuclides which aren't being replenished are not found on earth, since the shortest-lived primordial nuclide is 235U.  
> **username_1**: You also have to take into account just how much of any particular radioisotope originally existed.  They weren't all created in equal amounts, some might have segregated into different parts of the original solar nebula, or in different parts of the primordial Earth. E.g. if most of isotope X segregated into the core, how would we know its abundance?  
> **username_0**: @username_1 That's true, but wouldn't it be awfully coincidental if all the short-lived radioisotopes just happened not to be created, or to be located in inaccessible locations?  
> **username_0**: I found where Wikipedia says the standard atomic weight of each element is determined by the terrestrial abundance of its isotopes as determined by CIAWW. https://www.ciaaw.org/isotopic-abundances.htm lists the isotopes by abundance, though it doesn't seem to include them all (eg carbon-14 is not there).  

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## 1 answers

### Answer by username_2 on 2020-06-14. Score: 1

While a username_0 half-life, hundreds or millions of years or more, favors a radioisotope being relatively common or even occurring in nature at all, it is not the only consideration. Whether and how effectively the isotope can be regenerated also figures in.

[Niobium](https://en.m.wikipedia.org/wiki/Isotopes_of_niobium). occurs as only one isotope, $\_{41}^{93}\text{Nb}$. All other isotopes decay away much too quickly, including $\_{41}^{94}\text{Nb}$ with a half-life of only about 20,300 years -- not enough to survive in the billions of years since primordial times when the Earth formed.

Now look at carbon. The radioisotope carbon-14, $\_{6}^{14}\text{C}$, has a half-life of only 5730 years so surely it, too, is all gone, meeting the same end as $\_{41}^{94}\text{Nb}$. In fact, as many readers know, carbon-14 is still with us (even if it's only trace amounts) and in use as a probe for dating organic matter. The difference, of course, is there is a readily available mechanism for regenerating this isotope through [the action of cosmic rays high above Earth](https://en.m.wikipedia.org/wiki/Cosmogenic_nuclide). The availability of this mechanism means carbon-14 need not have enough half-life to survive billions of years since the Earth's formation, only enough to survive weeks of circulation time to get to the ground.

We can correlate half-life to abundance only when comparing isotopes that are **formed by similar mechanisms.**


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