Ken:

I’m not sure that I understand just what ____ is getting at, but I’ll have a go at introducing her to exponential decay.

She writes:

You said (above) that the decay rate has not changed in billions of years. How do you know that? Have you done experiments to prove it? If you have, please explain those experiments. If you haven’t done the experiments have you just accepted the words and the experimental work of evolutionary scientists who are seeking evidence by their methods to support their theory (hypothesis)?

The determination of the decay rates is done in a laboratory – that is it is done in present time. Therefore, there much be an extrapolation – a calculation based on information gained in the present backwards into the past. That must mean that uniformitarianism – what is happening in the present – has happened through the past (supposed) billions of years.

However, we know that even in the past – taking the Biblical dating – of about 6 000 years – that uniformitarianism did not occur. Some periods have been more stable than others; other periods have been less stable.

The most perplexing aspect of dating, for which I have not as yet found a wbsite which explains it, is that half of a substance decays in the first period of time, in the second period of the same length of time a quarter of the substance changes, continuing on for each period of the same duration a half of what is left changes until no more decay occurs. The answers that have been given me in other topics in aus.religion. christian have not answered this issue with conviction.

Ken:

If I understand you correctly, you’re happy with the idea that half the amount of some radioactive substance decays in a certain time, known as the half-life.

Now is your problem that you can’t see why the remaining half shouldn’t decay in one more half life, instead of just half of what is left?

If I have misunderstood you let me know, but what follows is an attempt to explain this as simply as I have managed to get, without introducing differential equations.

I take it that you are happy with the idea that the radioactivity of a lump of, say, uranium, is proportional to the size of the lump. In other words, if you halve the size of the lump, the radioactivity will also halve. If you cut off 1% of the lump, the radioactivity of this small piece will be only 1% of that of the original lump.

Now the rate of decay is clearly proportional to the radioactivity. If there was no radioactivity, there would be no decay – as with a lump of iron.

Now lets see just what this implies. After a certain lapse of time, due to radioactivity, half of the uranium atoms will have decayed, so that we have half of the original amount of uranium left.

This will have half the radioactivity of the original. Now atoms don’t have any memory – they couldn’t possibly have, since there is no structure which could possibly be used to store memories.

So with half the radioactivity, decay will take place at half the original rate. In other words, half the amount which decayed originally will decay in the same time, namely one half-life.

So after two half-lives, only a quarter of the original amount will be left, so it will have a quarter of the radioactivity of the original, so a quarter of the amount will decay in the same time, namely one half-life, leaving, after three half-lives only an eighth of the original amount, and so on.

If there is any step in the above which you don’t understand, Gladys, let me know, and I’ll see if I can explain that one to you.

Incidentally, about 15 years ago when I was on a committee revising the mathematics syllabus for the final two years of secondary education in Queensland, we were looking for simple examples to illuminate students’ understanding of exponential growth and decay. Several of my suggestions made it into the offiaial syllabus documents. One started with the formation of heavy elements in a supernova explosion – supernove 1987A had been in the news recently. The problem I set was: assuming that the two isotopes of uranium, U-238 and U-235 were formed in equal amounts in the supernova explosion which was the precursor to the formation of the solar system, use the known half-lives of these isotopes, and their present relative abundance, to estimate how long ago the explosion took place.

I had used the same example in an introductory class in differential equations at UQ, with some additional problems about fast breeder reactors and other things involving nuclear reactions.

It turns out that the explosion took place around 6,000 million years ago, comfortably between the 4,500 million years for the age of the Earth, and the 10,000 tp 20,000 million years for the age of the universe. The explosion must have taken place after the universe came into existence, but before the solar system, so everything ties in nicely.

Poster again:

If you begin with the idea that there is no God, or from the indoctrination that Evolution did occur you will reason from a different viewpoint than you will if you start with a conviction that God All-mighty created. Gladys

Salaam Ken Smith