Valentine Pontifex

There is a rather nice piece on radiometric dating by Chris Stassen in the latest Talk.Origins feedback which was posted a few days ago as I mentioned in the post mentioning the feedback. Here is the feedback in question:

http://www.talkorigins.org/origins/f...may03.html#f13

He gives the following two equations (though I will replace the Greek lambda with a k for the two decay constants). The x's and i's are subscripts to indicate the a measured sample and i being for the initial conditions.

[Pb207/Pb204]x - [Pb207/Pb204]i = [U235/Pb204]x * (e^kt-1)
[Pb206/Pb204]x - [Pb206/Pb204]i = [U238/Pb204]x * (e^k't-1)

These two equations are easily derived from the basic equation of exponential decay.

Stassen fills in the intial lead (Pb) ratios from iron meteorites which lack uranium (U) which decay into lead. With that Stassen counters the creationist claim that radiometric dating has more variables than equations which would be, of course, unsolvable. With other samples it becomes many equations with only one unknown (time) which is fairly simple to solve.

If the creationist who Stassen responded to a reply actually has some wits about him he might object that filling of the initial lead ratios via iron meteorites is an assumption. This is why I was a bit surprised that Stassen did not mention that one does not need to make that assumption for the date. (Though a sharp eyed reader might figured out this is the case by noticing the isochron diagram.)

Take the two equations above and combine them into a single equation by dividing one into another. Set the x-axis to Pb206/Pb204 and the y-axis to Pb207/Pb204 and the new equation is in the form of (y-yi)/(x-xi)=Constant which is another way to express y=mx+b which is a straight line. (If you don't see that recall that U235/U238 is same measured the same everywhere in the Solar System with the exception of nuclear reactors, etc.) And thus the age can be computed from the slope though the calculation is a bit more complicated then is the case for Rb-Sr isochrons. Another difference between Pb-Pb isochrons and the Rb-Sr type is that the y-intercept does not give any initial quantities. Of course Stassen did show a graphic of a Pb-Pb isochron.

(And even without the isochron it should also be obvious that for multiple samples from a single lava sample that the initial lead ratios whould be the same and thus with multiple points one will have more equations than variables.)

Kevbo

He actually did mention that in the feedback, Valentine, maybe it was added later:

Valentine Pontifex

I saw that. He discussed the isochron's data and showed the graphic of the isochron, but he really did not discuss the isochron itself in any real detail. Though rereading that paragraph I see that a really smart person could have figured it out from that. Maybe I should say that my surprise is that he did not more clearly state that one does not need to make an assumption about the initial lead ratios.

Also one rather minor nitpick: it would be better to say that the constant uranium ratios found today is substituted into the isochron equation as opposed to it cancelling out:



Still a very good and useful feedback. I saw the problem in a bit different light. There is more than one way to get the (correct) date with the same data.

Kevbo

I agree, I learned a lot from that feedback.