Radiometric Dating

I think I’m missing a key concept about Isochron dating. What is the relationship between the the amount of daughter isotope (D) and the amount of non-radiogenic isotope of the same element (Di)?

The talk.origins FAQ says:

Why is this?

As the talk.origins page points out, as isotopes of the same element they have the same chemical properties, i.e. the atoms may be a percent or two different in mass, but they’ll have the same number of electrons, form the same ions, bind to the same other elements etc. Thus if you start off with some sample of, say, primordial uranium that’s been around from the formation of the Earth, pretty much regardless of what’s been done to the sample that won’t change the ratio of the different uranium isotopes (U235 and U238 in this case). The only thing that is changing the ratio is differential radioactive processes: either one isotope will be formed and/or decay faster than the other. Isoschron techniques exploit this independence from chemical processes (and the inter-relation between ratios for different elements) to turn the problem into an entirely nuclear one. And the nice thing about eliminating any chemical effects from the problem is that nuclear effects really don’t get altered by anything on Earth. Hence the reliabilty of the answers.

Thanks bonzer. I think I’m getting it.

One more question.

Isochron dating seems to require multiple samples that are “formed at the same time from a common pool of materials”. So am I correct in saying that this dating method assumes that all the samples had the same original D/Di ratio? If so, why is this assumption made?

Careful investigators don’t make this assumption. They take a geologist along to try to insure that the samples in fact do come from a common pool of materials. This wasn’t always done in the past and it led to mistaken dates.

But what about D/Di ratios? Is it assumed that all the samples had the same original D/Di ratio if they truly did come from a common pool of materials?

There’s no assumptions involved. Here’s an example:

There are at least two naturally occurring isotopes of Potassium (K), K-40 and K-39. K-40 is stable and comprises almost all (something like 99%) natural K. K-39 is radioactive and decays to stable Ar-39. This reaction has a half-life of ~1.38 billion years.

All K, whether stable K-40 or radioactive K-39, behaves chemically in the exact same way, so when a K-bearing mineral (like alkali feldspar or muscovite) forms, it will incorporate K-40 and K-39 in proportions identical to those found in nature. However, what this ratio (K-40/K-39) is dosen’t matter. When radiometrically dating K-rich minerals, all that maters is the proportion of K-39 to Ar-39. And further, no assumption needs to be made on the original content of Ar-39 in the mineral (when calculating the ratio) because the answer is: NONE. Inert Ar doesn’t participate in chemical reations, and is besides disimilar enough from K to substitute for it, anyway, in these minerals. So ANY Ar found in a K-rich mineral turns out to be radiogenic Ar-39. And the ratio of K-39 / Ar-39 can then be used to determine the date of the mineral.

Of course, a different problem occurs if the mineral being tested is not fresh and weathered: an altered mineral can lose that Ar, which will result in erroneously young radiometric dates.