<p>The uncertainty on the decay constant / half life is systematic. This means that, if the &quot;used&quot; value would be off the &quot;true&quot; value by 0.05%, then it would affect all the ages in the same way (e.g. either too old by 0.05% or too young by 0.05%, depending on which way the error is).</p>
<p>Effectively, if one is comparing differences between zircon U-Pb dates collected using the same decay constant, the systematic uncertainties such as half life can be ignored, as the duration does not change significantly. Just the absolute age value.
The reporting of uncertainties in the paper by Burgess et al. you describe is described in detail in the bottom of the second page. They clearly state:</p>
<blockquote>
<p>Uncertainties associated with weighted mean 206Pb/238U dates are
reported as ±x/y/z, where x is the analytical (internal) uncertainties
and y and z include the systematic uncertainties associated with
tracer calibration (0.03%) and 238U decay constant (0.05%),
respectively. If calculated dates are to be compared with other U-Pb
laboratories not using the EARTHTIME tracer, then ±y should be used
for each laboratory. If compared with other chronometers such as Ar-Ar
or astrochronology, then ±z should be used.</p>
</blockquote>

CC BY-SA 4.0
2022-03-16T09:56:37.430Z
2022-03-16T09:56:37.430Z
Geochron
<p>I can't be entirely sure but I'll make an informed guess:</p>
<p>That value doesn't come for a single measurement. Therefore, if the error in the age of a single sample is <span class="math-container">$\pm125$</span> kyr, you just need to average 16 samples to get it down to <span class="math-container">$\pm31$</span> kyr.</p>
<p>The uncertainty in the addition (or substraction) of two or more quantities is equal to the square root of the addition of the squares of the uncertainties of each quantity (assuming they arise from random errors). For example, if we have quantity A with uncertainty <span class="math-container">$\sigma_a$</span> and quantity B with uncertainty <span class="math-container">$\sigma_b$</span>, the error in the quantity <span class="math-container">$C=A+B$</span> would be:</p>
<p><span class="math-container">$\sigma_c=\sqrt{\sigma_a^2+\sigma_b^2}$</span></p>
<p>And if we call M to the average between A and B. The uncertainty in the average is</p>
<p><span class="math-container">$\sigma_m=\frac{\sqrt{\sigma_a^2+\sigma_b^2}}{2}$</span></p>
<p>So if we average 16 samples with <span class="math-container">$\sigma=125$</span> kyr, the uncertainty in the average would be</p>
<p><span class="math-container">$\sigma_m=\frac{\sqrt{16 \sigma^2}}{16}=\frac{\sqrt{16 \times 125^2}}{16}=31$</span> kyr</p>
<p>Uncertainty propagation can be seen in the abstract of the article you refer to:</p>
<blockquote>
<p>The extinction occurred between 251.941 ± 0.037 and 251.880 ± 0.031
Mya, an interval of 60 ± 48 ka.</p>
</blockquote>
<p>Where the ±48 ka comes from?</p>
<p><span class="math-container">$\sqrt{37^2+31^2}=48$</span></p>
<p>This treatment of uncertainties assumes that uncertainties are independent of each other. As @Mark pointed in the comments, this won't be the case if the uncertainty comes from &quot;the length of your measuring stick (the half-life of U-238)&quot;.</p>
<p>This is: if you measure something with a &quot;yard-stick&quot; that have the wrong size, you can't reduce the resulting error by just averaging many measurements.</p>
<p>I don't know enough of geochronology to understand all the different errors they report. But the simple example in the abstract cite I presented above shows that they are indeed treating those errors as independent. Otherwise the reported interval error (±48 ka) would not make sense.</p>
<p>If one significant source of error is indeed the uncertainty in the half-life of <span class="math-container">$^{238}$</span>U, it would be wrong to treat these errors as independent. Such an assumption would be right only if there exists an exact value for this half-life. Alternatively, maybe there is no exact value of the half-life, and what they meant is that the half-life value can truly vary a 0.05%. This is something to look into if you want to figure out if the treatment of errors they do is correct. However, after a quick google search I found that radioactive half-life can indeed vary by a small fraction due to environmental conditions, <a href="http://wtamu.edu/%7Ecbaird/sq/2015/04/27/can-the-decay-half-life-of-a-radioactive-material-be-changed/" rel="nofollow noreferrer">this article</a> explains pretty well the phenomena. Here a short excerpt:</p>
<blockquote>
<p>...radioactive half-life of an atom can depend on how it is bonded to
other atoms. Simply by changing the neighboring atoms that are bonded
to a radioactive isotope, we can change its half-life. However, the
change in half-life accomplished in this way is typically small. For
instance, a study performed by B. Wang et al and published in the
European Physical Journal A was able to measure that the electron
capture half-life of beryllium-7 was made 0.9% longer by surrounding
the beryllium atoms with palladium atoms.</p>
</blockquote>
<p>If the 0.05% uncertainty on the half-life of <span class="math-container">$^{238}$</span>U comes from random environmental factors, it would indeed be acceptable to consider them as an independent/random source of error for each sample.</p>

CC BY-SA 4.0
2019-03-02T20:48:06.817Z
As far as I know, this only applies if the uncertainties are independent.  If the uncertainty is in the length of your measuring stick (the half-life of U-238), the uncertainties are correlated and you can't reduce them by making more measurements.
Mark
CC BY-SA 4.0
2019-03-02T21:47:17.517Z
@Mark You are right. I've added something to my answer. Have a look.
Camilo Rada
CC BY-SA 4.0
2019-03-02T22:05:22.500Z
@Mark I just added something about the natural variation of radioactive decay half-life. I think that explain that they treat the errors as independent.
Camilo Rada
CC BY-SA 4.0
2019-03-02T22:24:46.340Z
The page you link to lists three potential mechanisms for changing the decay rate (and thus the half-life) of radioactive elements: time dilation, electron density change and bombardment with high-energy radiation. The first doesn't apply on Earth (well, technically it does, but the time dilation due to Earth's gravity is vanishingly small), the second only affects elements that decay via electron capture (Uranium doesn't), ...
Ilmari Karonen
CC BY-SA 4.0
2019-03-02T22:24:55.003Z
... and the last requires a high-radiation environment, e.g. due to a high concentration of radioactive elements. These _have_ actually [existed naturally on Earth](https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor), but they're rather rare and can be quite easily detected from the abundance and ratios of decay products they leave behind. To quote the conclusion at the end of the page: "*Therefore, outside of specialized labs, we can say that as a good approximation radioactive decay half-lives don't change.*"
Ilmari Karonen
CC BY-SA 4.0
2019-03-02T22:29:02.563Z
@IlmariKaronen Yes, but the OP doesn't seem to be content with just "a good approximation" as the whole question revolve around a 0.05% change in $^{238}$U half-life, a pretty tiny change.
Camilo Rada
CC BY-SA 4.0
2019-03-02T22:36:16.437Z
@IlmariKaronen The article also say: "*Other types of radioactive decay besides electron capture have also been found to have the decay half-life depend on the state of the surrounding electrons, but the effects are smaller.*" And that could fit the bill for a tiny 0.05%
Camilo Rada
CC BY-SA 4.0
2019-03-02T22:55:17.000Z
Well, I can't easily verify or refute that claim, since the page gives no sources or actual numbers, but I'd be _very_ surprised if the effect on the decay rate of uranium-238 was anywhere near 0.05%. In fact, I did find [this page](http://www.phys.ncku.edu.tw/mirrors/physicsfaq_old/ParticleAndNuclear/decay_rates.html), which says that "for a few alpha emitters, the change has been estimated to be of the order of 1 part in $10^7$ (!) or less, which would be unmeasurable in view of the fact that the alpha emitters' half lives aren't known to that degree of accuracy to begin with."
Ilmari Karonen
CC BY-SA 4.0
2019-03-02T20:00:09.693Z
2022-03-17T23:38:42.443Z
2022-03-17T23:38:42.443Z
Camilo Rada
<p>The uncertainty in the half life of uranium-238 is stated at 0.05% [1]. The same paper gives the date 251.941 myr ± 31 kyr. 
251.941 <span class="math-container">$\times$</span> 0.05% = 125 kyr. </p>

<p>How are the authors justified in claiming an accuracy of ± 31 kyr when the uncertainty in the half life alone is ± 125 kyr? On top of that, they list two other kinds of analytical uncertainties, which would only increase the overall uncertainty. </p>

<p>[1] ​ Burgess, S. ​et al​, "High-precision timeline for Earth’s most severe extinction", Proceedings of the National Academy of Sciences USA​, Volume 111, 2014.
<a href="https://www.pnas.org/content/pnas/111/9/3316.full.pdf" rel="nofollow noreferrer">https://www.pnas.org/content/pnas/111/9/3316.full.pdf</a></p>

<geophysics><measurements><mass-extinction><geochronology><uranium>
Unwarranted claim of higher degree of accuracy in zircon geochronology
sidharth chhabra
# Unwarranted claim of higher degree of accuracy in zircon geochronology

(Asked by: username_0 on 2019-03-02)

The uncertainty in the half life of uranium-238 is stated at 0.05% [1]. The same paper gives the date 251.941 myr ± 31 kyr.
251.941 $\times$ 0.05% = 125 kyr.

How are the authors justified in claiming an accuracy of ± 31 kyr when the uncertainty in the half life alone is ± 125 kyr? On top of that, they list two other kinds of analytical uncertainties, which would only increase the overall uncertainty.

[1] ​ Burgess, S. ​et al​, "High-precision timeline for Earth’s most severe extinction", Proceedings of the National Academy of Sciences USA​, Volume 111, 2014.
<https://www.pnas.org/content/pnas/111/9/3316.full.pdf>

**Tags:** geophysics, measurements, mass-extinction, geochronology, uranium


---

## 2 answers

### Answer by username_2 on 2019-03-02. Score: 10 | Accepted answer

I can't be entirely sure but I'll make an informed guess:

That value doesn't come for a single measurement. Therefore, if the error in the age of a single sample is $\pm125$ kyr, you just need to average 16 samples to get it down to $\pm31$ kyr.

The uncertainty in the addition (or substraction) of two or more quantities is equal to the square root of the addition of the squares of the uncertainties of each quantity (assuming they arise from random errors). For example, if we have quantity A with uncertainty $\sigma\_a$ and quantity B with uncertainty $\sigma\_b$, the error in the quantity $C=A+B$ would be:

$\sigma\_c=\sqrt{\sigma\_a^2+\sigma\_b^2}$

And if we call M to the average between A and B. The uncertainty in the average is

$\sigma\_m=\frac{\sqrt{\sigma\_a^2+\sigma\_b^2}}{2}$

So if we average 16 samples with $\sigma=125$ kyr, the uncertainty in the average would be

$\sigma\_m=\frac{\sqrt{16 \sigma^2}}{16}=\frac{\sqrt{16 \times 125^2}}{16}=31$ kyr

Uncertainty propagation can be seen in the abstract of the article you refer to:

> The extinction occurred between 251.941 ± 0.037 and 251.880 ± 0.031
> Mya, an interval of 60 ± 48 ka.

Where the ±48 ka comes from?

$\sqrt{37^2+31^2}=48$

This treatment of uncertainties assumes that uncertainties are independent of each other. As @username_3 pointed in the comments, this won't be the case if the uncertainty comes from "the length of your measuring stick (the half-life of U-238)".

This is: if you measure something with a "yard-stick" that have the wrong size, you can't reduce the resulting error by just averaging many measurements.

I don't know enough of geochronology to understand all the different errors they report. But the simple example in the abstract cite I presented above shows that they are indeed treating those errors as independent. Otherwise the reported interval error (±48 ka) would not make sense.

If one significant source of error is indeed the uncertainty in the half-life of $^{238}$U, it would be wrong to treat these errors as independent. Such an assumption would be right only if there exists an exact value for this half-life. Alternatively, maybe there is no exact value of the half-life, and what they meant is that the half-life value can truly vary a 0.05%. This is something to look into if you want to figure out if the treatment of errors they do is correct. However, after a quick google search I found that radioactive half-life can indeed vary by a small fraction due to environmental conditions, [this article](http://wtamu.edu/%7Ecbaird/sq/2015/04/27/can-the-decay-half-life-of-a-radioactive-material-be-changed/) explains pretty well the phenomena. Here a short excerpt:

> ...radioactive half-life of an atom can depend on how it is bonded to
> other atoms. Simply by changing the neighboring atoms that are bonded
> to a radioactive isotope, we can change its half-life. However, the
> change in half-life accomplished in this way is typically small. For
> instance, a study performed by B. Wang et al and published in the
> European Physical Journal A was able to measure that the electron
> capture half-life of beryllium-7 was made 0.9% longer by surrounding
> the beryllium atoms with palladium atoms.

If the 0.05% uncertainty on the half-life of $^{238}$U comes from random environmental factors, it would indeed be acceptable to consider them as an independent/random source of error for each sample.

> **Comments:**
> **username_3**: As far as I know, this only applies if the uncertainties are independent.  If the uncertainty is in the length of your measuring stick (the half-life of U-238), the uncertainties are correlated and you can't reduce them by making more measurements.  
> **username_2**: @username_3 You are right. I've added something to my answer. Have a look.  
> **username_2**: @username_3 I just added something about the natural variation of radioactive decay half-life. I think that explain that they treat the errors as independent.  
> **username_4**: The page you link to lists three potential mechanisms for changing the decay rate (and thus the half-life) of radioactive elements: time dilation, electron density change and bombardment with high-energy radiation. The first doesn't apply on Earth (well, technically it does, but the time dilation due to Earth's gravity is vanishingly small), the second only affects elements that decay via electron capture (Uranium doesn't), ...  
> **username_4**: ... and the last requires a high-radiation environment, e.g. due to a high concentration of radioactive elements. These _have_ actually [existed naturally on Earth](https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor), but they're rather rare and can be quite easily detected from the abundance and ratios of decay products they leave behind. To quote the conclusion at the end of the page: "*Therefore, outside of specialized labs, we can say that as a good approximation radioactive decay half-lives don't change.*"  
> **username_2**: @username_4 Yes, but the OP doesn't seem to be content with just "a good approximation" as the whole question revolve around a 0.05% change in $^{238}$U half-life, a pretty tiny change.  
> **username_2**: @username_4 The article also say: "*Other types of radioactive decay besides electron capture have also been found to have the decay half-life depend on the state of the surrounding electrons, but the effects are smaller.*" And that could fit the bill for a tiny 0.05%  
> **username_4**: Well, I can't easily verify or refute that claim, since the page gives no sources or actual numbers, but I'd be _very_ surprised if the effect on the decay rate of uranium-238 was anywhere near 0.05%. In fact, I did find [this page](http://www.phys.ncku.edu.tw/mirrors/physicsfaq_old/ParticleAndNuclear/decay_rates.html), which says that "for a few alpha emitters, the change has been estimated to be of the order of 1 part in $10^7$ (!) or less, which would be unmeasurable in view of the fact that the alpha emitters' half lives aren't known to that degree of accuracy to begin with."  

---

### Answer by username_1 on 2022-03-16. Score: 3

The uncertainty on the decay constant / half life is systematic. This means that, if the "used" value would be off the "true" value by 0.05%, then it would affect all the ages in the same way (e.g. either too old by 0.05% or too young by 0.05%, depending on which way the error is).

Effectively, if one is comparing differences between zircon U-Pb dates collected using the same decay constant, the systematic uncertainties such as half life can be ignored, as the duration does not change significantly. Just the absolute age value.
The reporting of uncertainties in the paper by Burgess et al. you describe is described in detail in the bottom of the second page. They clearly state:

> Uncertainties associated with weighted mean 206Pb/238U dates are
> reported as ±x/y/z, where x is the analytical (internal) uncertainties
> and y and z include the systematic uncertainties associated with
> tracer calibration (0.03%) and 238U decay constant (0.05%),
> respectively. If calculated dates are to be compared with other U-Pb
> laboratories not using the EARTHTIME tracer, then ±y should be used
> for each laboratory. If compared with other chronometers such as Ar-Ar
> or astrochronology, then ±z should be used.


---

