# Mount St. Helen’s Radioactive Dating

I’ve been hoping to visit Mount St. Helens this summer if we ever get a weekend when it’s not either raining or hot enough that I’m concerned about my shoes melting walking on volcanic rock. So I’ve been reading a bit about YEC Steve Austin’s research out there. I had done a bit of research into him about a decade ago when I met him while he was in Edmonton, but I’m not really into geology so I haven’t looked into him much since.

One of the things Steve Austin did at Mount St. Helens was to take rock samples for radiometric dating. As described in his paper in Creation Ex Nihilo Technical Journal, he collected samples from rock that formed in 1986, and received data back from the lab corresponding to dates ranging from 350,000 to 2,800,000 years old.

These results are widely cited in YEC literature to this day, as well as being circulated widely in social media.

Naturally, there are tons of articles written by people far more knowledgeable than me explaining the discrepancies and ridiculing Dr. Austin’s methodology. And while I have no doubt that these criticisms are valid, they are incredibly boring and quite difficult to explain to the average YEC on social media.

So I’d like to try a different question. What would it mean if Dr. Austin’s results were accurate, and everyone was convinced they were accurate? What if Mount St. Helens erupted again tomorrow, and a completely impartial group of scientists went out and took samples that they could somehow guarantee were completely free of all previously formed minerals and contamination and the lab equipment was cleaned to standards that allow more recent materials to be dated and got exactly the same results? How would that affect our use of radiometric dating? What scientific discoveries would that bring into question? Would we throw out radiometric dating altogether? Would updated calculations reveal that the earth is actually less than 10,000 years old?

To figure this out, all we need is some math we all learned in Jr High. In fact, I’m going to simplify it a little bit. In Jr High you probably had to calculate the number of atoms of parent and daughter isotopes in a sample. In this case, all we need is the ratios. This simplifies the equation down to:

R* = R_{0} + e^{λt} − 1

Where:

t is age of the sample,

R* is the ratio of atoms of the daughter isotope to atoms in the parent isotope[1] in the sample now,

R_{0} is the ratio of atoms of the daughter isotope to atoms of the parent isotope when the sample formed,

λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2, which for potassium-argon is 5.543 x 10^{-10}/year.

With potassium-argon dating, R_{0} is traditionally assumed to be negligible – there was no argon in the sample when it formed. If Dr. Austin’s results were correct, it would show that assumption is inaccurate. We can calculate the new value for R_{0 }(the ratio of Argon to Potassium to expect in a newly formed sample) based on his data. We’ll use his worst case sample, which gave the highest date at 2.8 million years.

We know that they calculated the 2.8 million years assuming R_{0} was equal to 0. So can easily calculate the ratio of argon to potassium they found in the sample like this:

R* = 0 + e^{λt} – 1 = e^{(0.0000000005543 x 2,800,000)} – 1 = 0.00155

We could also get this value from Dr. Austin’s paper, which has the parts per million of potassium and argon used to calculate the dates, which works out to 0.00156.

We know the actual time t is 10 years, so we can calculate the new R_{0} as

R_{0} = R* – (e^{λt} − 1) = 0.00155 – (e^{(0.0000000005543 x 10)} – 1) = 0.00155

Which is the same as D*/N(t) above, because the radioactive decay in 10 years is negligible.

Now let’s use this new value for R_{0} to find the age of one of the meteorites they used to estimate the age of the earth to be 4.543 billion years. First we back-calculate the ratio of argon to potassium they found in the meteorite:

R* = e^{λt} – 1 = e^{(0.0000000005543 x 4,543,000,000)} -1 = 11.4

Now the new age of the earth would be:

t = ln(R*-R_{0} + 1)/λ = ln(11.4-0.00155+1)/( 5.543 x 10^{-10}/year) = 4.543 billion years

Well, that was anticlimactic. There are not enough significant digits than the age of the earth to actually see the difference from Austin’s data, so it is completely unchanged. Note the R* value, at this stage there is 11.4 times as much argon as potassium left. The tiny bit of argon Dr. Austin found is completely insignificant compared to all of the Argon that has been produced over 4.5 billion years.

However, having a significant R_{0} will matter more for more recent dates. So let’s try something much more recent, like the end of the Cretaceous 66 million years ago, when the dinosaurs went extinct.

R* = e^{λt} – 1 = e^{(0.0000000005543 x 66,000,000)} -1 = 0.0373

t = ln(R*-R_{0} + 1)/λ = 63.2 million years

If you were a paleontologist, a 3 million year difference might be significant. Particularly if there are other dating methods used that don’t require the same adjustment, some details might have to be reconsidered. But we don’t exactly need to rewrite the history of life on earth over it. As far as the big picture debates go, this is also insignificant.

The dates that would really be affected by this discrepancy are the really recent ones. For example, the stone tools in Olduvai gorge were dated at 1.7 million years by potassium-argon dating. Obviously, we can’t adjust those for a starting argon level equivalent to 2.8 million years. Similarly, the three examples listed in Dr. Austin’s paper, the basalt of Devils Postpile in California, the basalt of Toroweap Dam at the bottom of Grand Canyon and the Keramim basalt in Israel are all dated at 1 million years or less, and would be affected if his results were accurate. However, I suspect that anyone interested in any of these formations is probably capable of reading a paper by a geochemist detailing all the flaws in Dr. Austin’s methodology. For the typical internet debate where this research is brought up, the rocks being dated are hundreds of millions or billions of years old. And for those rocks, Dr. Austin’s research confirms that the starting argon in the rock was negligible.

[1] Technically only about 10% of ^{40}K decays to ^{40}Ar. That’s built into the ratio, so it shouldn’t matter unless you actually try to get back to the ppm numbers in Dr. Austin’s paper.

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