Yes, thank you.
Then I have to ask:
If you're looking at this [sup]234[/sup]Thorium, why do you assume it was [sup]238[/sup]Uranium at one time?
Suppose God created them both ex nihilo (or ex materia) at the same time? or even the Thorium just before the Uranium?
Would you assume the Thorium came into existence after the Uranium?
Well, I'm glad you;ve learned what a half life is.
Well, we can tell by the particular ratios we see between uranium and thorium.
Let's use a simpler example instead of uranium and thorium to illustrate the concept, okay? Let's say we have a parent material P which decays to daughter material D. And then D decays into grandaughter material G. Now, P has a half life of 1000 years. D has a half life of 1000 years and G is stable, so it doesn't decay at all.
So, if I have a lump of P that weighs 100 kilograms, then after a thousand years, half of it will have decayed to D. But, since it doesn't happen all in one go (it happens constantly throughout that 1000 years), during that 1000 years, the D will have also been decaying into G.
So, we've had one half life period for P, so it has decayed by 50%. 50 kilos of the original lump will have decayed into D. So we have 50 kilos of P and 50 kilos that has decayed into D (assuming that the mass of all three materials is the same.)
But the D has passed through a half life period as well. It also has a half life of 1000 years, so half of all the D that was produced by the decay of P has now decayed into G.
So we have 50% P, and of the remaining 50%, half has decayed further to G while the other half has remained as D (and will decay in the future).
So looking at the whole lump, we have 50% P, 25% D and 25% G.
By looking at this ratio, we can conclude that either the D and G is a result of radioactive decay, or we can conclude that somehow the P is much younger and was somehow contaminated with just the right amount of D and just the right of G to make it appear much older than it actually is.
And we can check against this by examining other samples. If we find many samples of P in the particular layer, we know they are the same age (because they are in the same layer. You can't put rocks into a layer once it has formed, after all). So since we know that the samples are all the same age, we can check the ratios of P, D and G we find in each one. If the amount of D and G is a result of contamination, then we would see that the ratios would be different in each sample. After all, it strains credibility to think that contamination would produce IDENTICAL ratios in different samples and this contamination would be in just the right ratios to match what we'd expect to see. It would be like getting everyone on the planet to deal a deck of cards at the same time and everyone deals the cards out in the same order as everyone else. Just not going to happen. So we can discount that possibility. The only other option is to conclude that the sample has indeed been decaying for a thousand years.
In short, we can conclude that the daughter materials were the result of radioactive decay because it is practically impossible for the ratios we see in the real to have been formed by any other way.