Feature Article - June 2013 |

by Do-While Jones |

Let’s try to clear up some “chronic” misunderstandings of radioactive dating.

Someone must have quoted some of our articles about radioactive dating on a blog somewhere, because we received two emails on the subject within a few days. The first came from Jason on May 9.

Hello Do-While, I came across your website while doing some research for a paper. In short, the premise of your page on the age of the moon seems to revolve around a lack of understand [ http://geology.csupomona.edu/jpolet/GSC307/Lectures/Wk7_Wed_GSC307/Wk7WedGSC307F11_web.pdf There are entire books on the subject, but this sums things up concisely, if not too much so. It also explains how/why Your website seems to attack the discrepancies in ages seen across individual lunar rocks, when, in reality, most lunar rocks are mingled breccias containing any number of differently-sources [ I'd read up on given aspects of the scientific methodology before discounting them. The work behind concordias is very well-grounded, even if you don't understand it. The creationwiki's biblical rationalization of concordias is much more...creative, and relies upon completely unfounded conjecture. To be frank, if you don't believe the scientific community's explanation of the observed characteristics of the rocks, believing in the religious account of events (which are relatively unsupported by data) makes significantly less sense. One might as well decide to not believe in dodos, but choose to believe in unicorns. Regards, |

The link he included went to a set of 34 PowerPoint slides, apparently from a college geology class. **As is the case with nearly all slides separated from an accompanying lecture, they don’t make much sense all by themselves.**

In the professor's slides, λ is the Greek letter "lambda," which represents the half-life. The half-life is the amount of time it takes for half of a radioactive substance to decay. λ238 is the half-life of uranium 238. λ235 is the half-life of uranium 235. The chemical symbol for lead is Pb, which comes from the Latin word *plumbum*, because lead pipes used to be used for plumbing (before lead was discovered to be toxic). He used "=>" as an abbreviation for "implies."

The third slide especially intrigued me because it said,

[ [ And their ratio: [ Present day uranium ratio is 1/137.88, independent of age and history of sample => Pb ratio is a function only of time => t can be estimated from lead ratio of a single sample (often zircon is used) |

These equations are full of math errors, and there were no references for the isotope ratios, so I responded with this short email.

*“The May newsletter is already done, but I think the issues you raise would make excellent material for the June newsletter. Do you have references for the isotope ratios stated in the slides?”*

It has been more than four weeks now, and Jason has not replied. So, I will have to address his professor’s slides without any background.

Translated into English, **the equation** “[^{206}Pb]_{now} = [^{238}U]_{now}(e^{λ238t} - 1)” **is supposed to mean, “The amount of lead 206 now present equals the amount of uranium 238 that has decayed since the uranium 238 was formed.”** That’s what is supposed to mean—but the equation is full of errors.

Actually, the professor probably meant to write,

“[^{206}Pb]_{now} = [^{238}U]_{initially}(e^{-λ238t} - 1)”

and

“[^{207}Pb]_{now} = [^{235}U]_{initially}(e^{-λ235t} - 1)”

He wrote "now" when he meant to write "initially" and left out a minus sign in the exponent. But, even correcting the typos, the equations are still wrong.

**Presumably, the professor might have said in his lecture that “t is a negative quantity” so the missing minus sign in his equation might not be an error. (But, in common practice, future time is generally specified as a positive, not negative number.)** Without the minus sign, the amount of lead will increase exponentially without limit, implying that a finite amount of uranium would eventually decay into an infinite amount of lead. He clearly didn’t mean that.

**The amount of lead produced by the decay of uranium depends upon the amount of uranium there INITIALLY, not the amount of uranium remaining now.** But, in his defense, since uranium decays so slowly, the amount of uranium today is essentially the same as the amount of uranium that would have existed when the Earth was created, so that mistake doesn’t really matter.

Since exponential decay is generally specified as “e^{-t/x}”, the professor must have said that “λ238” is actually 1/λ238.”

And, if one wants to be really picky, when computing radioactive decay, **it is the time constant τ ( Tau) not the half-life, λ, that must be used in exponential decay calculations.**

And, the professor must have been dyslexic because **he meant to write “1 minus the exponent,” not “the exponent minus 1.**” No doubt the professor caught that error when giving the lecture, and told his students to make the correction.

**The correct equation for the amount of lead at time t is**

**Pb _{t} = Pb_{initial} + U_{initial} * (1 - e^{-t/τ})**

where the value of τ depends on the half-life of the isotope of uranium involved.

You can check this at t=0, t=λ, and t=5λ.

When t=0, e to the 0 power equals 1, so Pb_{t} equals Pb_{initial} (the amount of lead initially in the rock).

When t=λ, the exponent equals -0.69315, so half the uranium has decayed to lead, so Pb_{t} equals Pb_{initial} plus half the amount of uranium initially in the rock.

When t=5λ (or greater), the exponential term is essentially zero, so the number of lead atoms after time t=5λ is equal to the number of lead atoms initially there plus the number of uranium atoms initially there because all the uranium has decayed to lead.

Of course, **the big unknown** (which the professor ignored) **is, “What was Pb _{initial}?”** One can’t just assume it was zero because we don’t know what it was.

When computing the ratio of ^{207}Pb to ^{206}Pb, he apparently thought that A^{X}/B^{Y} = A/B * X/Y. Rather than go through a messy mathematical proof, let’s just say 5 squared divided by 3 cubed is not equal to 5/3 times 2/3. 25 divided by 27 is not equal to 5/3 times 2/3. (0.926 does not equal 1.11.)

The lead isotope ratio is NOT "a function only of time." The lead isotope ratio does change with time; but it also depends upon the initial amounts of the led isotopes and the uranium isotopes.

We would have loved for Jason to have given us a reference so we would know the basis for the statement, “Present day uranium ratio is 1/137.88, independent of age and history of sample.” We would also like to know where the unnamed professor got the data for the concordia diagrams on the subsequent slides. He didn’t just make it all up, did he?

In the first paragraph of Jason’s email, he said I have, “a lack of understand of what a concordia is and how it works. If partial melting of a rock occurs, one expects a resulting concordia to show the age of the heating event, from which one can still extrapolate the age of the rock, or at least the rock[’]s last major melting event.” That’s true. **I do not understand how melting a rock will change the ratio of isotopes in any way.**

**If a rock had a certain ratio of uranium to lead when it melted, and then solidified again when it cooled, that would not make all of the lead disappear from the solid rock, causing all subsequent lead to be the product of radioactive decay.**

Potassium-argon dating of lava is based on the semi-plausible idea that all the previously existing argon gas escapes from lava when it is molten, and so all the argon gas trapped in the lava after it solidified came from the decay of potassium. The well-known “excess argon” discoveries in historically documented lava flows have shown that not all the argon escapes, resulting in ages that are wrong by millions of years, so the potassium-argon method isn’t reliable. But at least it is reasonable to think that heating can make gas escape from a hot rock on the surface of the Earth.

**What’s the logic behind believing that melting a rock deep inside the Earth will make the amount of lead in it change?** Where does the lead go? Does all the lead float on top of the uranium like oil on top of vinegar in a salad dressing? Does all the liquid lead 205 float on top of all the liquid lead 207 until the rock cools and freezes them in place? If so, the lead isotope ratios would be 0 or infinity depending upon where the sample was taken.

Jason says, “It also explains how/why **you might get anomalously high or low ages**, depending on the thermal history of the individual mineral grain you're looking at.” In other words, “The method doesn’t always work. Sometimes **the ages are too high or too low because of something you don’t know** about the thermal history of the rock.” If that is true, **what good is the method?**

It is really just this simple: **The ratios of elements and isotopes in rocks depend entirely upon how much of each isotope was in the rock when the rock formed. If you make the erroneous assumption that the ratios are the result of different initial values and the passage of time, you will come to erroneous conclusions.**

Jason said, “Your website seems to attack the discrepancies in ages seen across individual lunar rocks.” **We did not “attack” the discrepancies—we simply reported them.** Furthermore, **the elite scientists who were chosen to analyze the Apollo 11 moon rocks should understand breccias and dating methods better than Jason does.** (After all, Jason didn’t catch all the errors in the professor’s slides.) **If they thought that their analyses were invalid, why did they report them?**

On one hand, evolutionists like to claim that their rock-dating methods are accurate. Then, on the other hand, they come up with excuse after excuse to explain why they don’t give the correct results!

The second email came to us from Matt via Michael. Matt wrote to Michael to tell him what an idiot I am, and why he should not pay any attention to me. He begins by saying,

What baffles me about this is that Pogge clearly misunderstands how isochrons work. For your own benefit, I highly recommend that you read about the method and really try to understand how it works (to the point of being able to calculate things) so that you can fact-check these guys yourself. Some good resources: http://www.talkorigins.org/faqs/isochron-dating.html and http://en.wikipedia.org/wiki/Isochron_dating. |

Matt thinks TalkOrigins and Wikipedia are “good resources.” Let’s just leave it at that.

Matt then says,

OK let’s discuss the article: Pogge: “In other words, the assumption is that when the moon rocks solidified (“chemical closure”), the amount of strontium 87 (the “uniform initial 87Sr/86Sr ratio”) was 0.69784 ± 0.00012 regardless of how much rubidium 87 there was in the rock.” This statement is incorrect. Pogge misread the paper. The researchers in the paper say very clearly that they assume a uniform initial ratio of Sr-87/Sr-86. They *do not* say that they assume the ratio to be 0.69784. This number is calculated based on the slope of the isochron. It is derived, not assumed. The beauty of the isochron method is that you do not need to make any assumptions about how much the original ratio was. Your only assumption is that if all eight rocks were produced at the same time, they should have the same initial isotope ratio. Then you can calculate what that ratio was. |

**The “derivation” is actually the result of a collection of assumptions.** First, **it is assumed that if all eight rocks were produced at the same time they should have the same initial isotope ratio.** Observation of rocks quickly reveals that they generally aren’t homogenous. The minerals in a single rock aren’t even distributed equally. There is no reason to believe that isotopes will be evenly distributed in an individual rock, let alone different rocks created at the same time. The **second assumption is that there has been sufficient time for the isotope ratio to change.**

Ironically, after saying, “The beauty of the isochron method is that you do not need to make any assumptions about how much the original ratio was,” Matt makes this statement later in his email:

The assumption underlying isochrons is that 8 different rocks with the same origin must have the same isotopic starting ratio Sr-87/Sr-86 and, regardless of what that ratio is, the only way for them to have different isotope ratios is for the Rubidium-87 to decay into Sr-87. |

**After saying there are no assumptions, he said what the assumptions are.** Did he even read what he wrote?

Furthermore, even if they had different Sr starting ratios, there is no reason why these isotopic ratios would be proportional to elemental abundance of Rubidium except that nuclear decays of Rubidium-87 to Sr-87 would precisely predict such a linear relationship! |

No, the nuclear decay explanation depends on equal starting ratios.

Matt says,

So why should the initial Sr-87/Sr-86 ratio be the same in all eight rocks? The answer to this question gets at the heart of Pogge’s failure to understand radiometric dating. You will notice that throughout this article Pogge talks interchangeably about the ratio of different elements and the ratio of different isotopes. These are two very different things. Chemistry is about how electrons are shared and exchanged between elements. Elements are pure materials consisting of atoms with a certain number of protons (and an equal number of electrons). Isotopes are atoms of the *same element* with different numbers of neutrons (neutral particles). Because the number of protons and electrons is the same, ***isotopes are chemically indistinguishable from each other*** to an extremely high degree of accuracy. This is a testable fact. Rocks form by chemical processes. Since isotopes are chemically indistinguishable, there is no mechanism why rocks formed at the same time will have different isotopic ratios. Again, we observe this directly in nature. It is repeatable. |

It is true that “Isotopes are atoms of the *same element* with different numbers of neutrons (neutral particles). Because the number of protons and electrons is the same, ***isotopes are chemically indistinguishable from each other*** to an extremely high degree of accuracy.” Unfortunately Matt fails to recognize that **what he says is irrelevant.**

**Carbon 12 combines with oxygen to form carbon dioxide equally as well as carbon 14** combines with oxygen to form carbon dioxide. The two extra neutrons in carbon 14 do not affect the ability of the carbon to combine with oxygen. **The vast majority of carbon dioxide gas in the atmosphere contains carbon 12. Very little contains carbon 14. That’s simply because there is a whole lot more carbon 12 than there is carbon 14 in the atmosphere.** The fact that both isotopes react identically doesn’t have anything to do with the relative amounts of carbon 12 and carbon 14 in CO_{2} gas. There should not be equal amounts of carbon 12 and carbon 14 in CO_{2} gas just because they react identically.

**Strontium 87 and strontium 86 will react equally well with other elements in rocks; but that’s irrelevant to the ratios of those isotopes in rocks. How much of each isotope reacts depends upon how much of each isotope is present.**

The cover story in the June 2013 issue of *Scientific American* is titled, “Tiny Engines of Evolution.” The cover proclaims, “Millions of years ago phytoplankton powered the explosion of life.” We were going to review it; but it turned out not to be worth writing about. The article just claimed that abundance of nutrients caused accelerated evolution. It was all speculation.

Fortunately for us, the article contained the graph below which is relevant to our discussion of strontium isotope ratios.

We know the whole chart is based on bogus assumptions; but **all we care about is the time scale at the top and the graph at the bottom.** According to this chart, **the ^{87}Sr/^{86}Sr ratio does not increase linearly with time** over 500 million years as rubidium 87 decays to strontium 87, as Matt says it should.

*Scientific American*’s chart claims to show the ^{87}Sr/^{86}Sr ratio of fossils of different ages. The truth is that it shows the ^{87}Sr/^{86}Sr ratio of fossils found in different places. **The erroneous assumption is that the rocks in certain places are hundreds of millions of years older than rocks in other places**, so the age is naďvely inferred from the place where the fossils were found. **What the data really shows is that the ^{87}Sr/^{86}Sr ratio of fossils found in a variety of places is typically 0.708 +/- 0.14%.**

By comparison, the ^{87}Sr/^{86}Sr ratio of the Apollo 11 moon rocks ranged from 0.69876 to 0.70704 (which is 0.7029 +/- 0.6%). **All this really means is that the natural abundance of strontium 87 is about 70 percent of the abundance of strontium 86 both on the Earth and on the Moon. No other conclusion can really be reached.**

In our article ^{1} that Matt found objectionable, we plotted Apollo 11 data showing that the correlation between potassium and rubidium is much stronger than the correlation between strontium 87 and rubidium. Matt’s reaction was,

Pogge: “The data also tells us that the rocks that are richer in rubidium are richer in potassium. The data doesn’t tell us why that is true—it simply tells us that it is true.” Actually the data *does* tell us why its [ |

Matt is wrong. **The data does not give a reason. The reason is supplied by scientists who interpret the data.** The data shows a correlation between rubidium and strontium, and **Matt thinks it is a result of radioactive decay.** The data shows a correlation between rubidium and potassium and **Matt thinks it is because of a chemical reaction.** The data shows similar correlations, but Matt thinks it shows different reasons.

Matt reacted rather emotionally to our criticism of the isochron dating method.

Pogge: “The isochron dating method rests entirely on the unsubstantiated assumption that the amount of strontium 87 was entirely independent of the amount of rubidium 87 when the moon rocks solidified.” No!!! The isochron method rests on the very substantiated observation that the initial ISOTOPIC ratio of Sr-87/Sr-86 should be independent of the ELEMENTAL abundance of Rubidium. |

Matt’s conclusion is,

Pogge: “We know that the amount of potassium wasn’t independent of the amount of rubidium when the moon rocks solidified. We know that the amount of barium wasn’t independent of the amount of rubidium when the moon rocks solidified. Why should we assume that the strontium 87 was independent?” Because (1) the ratio of potassium/rubidium and barium/rubidium is driven by chemical processes and (2) since strontium 87 and strontium 86 are chemically indistinguishable, they will not vary according to chemical processes. Again, Pogge doesn’t understand the difference between isotopes and elements. |

I certainly do understand the difference between isotopes and elements. What Matt doesn’t understand is that **the amount of material (isotopes or elements) now in a rock depends upon how much of that material was available to be incorporated in the rock when it was formed.**

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Footnotes:

^{1}
*Disclosure*, May 2008, “Timeless Isochrons”