Quote:
Originally Posted by Backwoods Presbyterian  Not to get to technical Todd but can you flush that out for us? |
basically (and i need to get to bed soon or i won't get up in the morning sufficiently early
) it's this:
Lifetimes of radioactive elements are easily measurable by looking at the change of the rate of decay of a given sample of that substance. The decay rate changes according to an exponential function, so if you measure the rate of decays for identical short intervals over some period of time, you'll see the rate changing - and the function looks like Rate = Rate(t=0) * e^(t/lifetime). (here, e is the base of natural logs - 2.718blahblahblah) The quantity Rate(t=0) is something you don't know a priori, but it is a fact that the rate at any one time is proportional to the number of atoms of the radioactive isotope present. As these atoms decay, the number decreases - and hence so does the rate.
For carbon, there is a well known natural abundance of the radioactive isotope C-14, as compared to the normal isotope, C-12. I forget the actual number but it's something like 1 C-14 for every 10^18 C-12's. Don't panic - those aren't large numbers. 10^18 C-12 atoms is about the amount of C-12 atoms in 2 micrograms of carbon.
Anyway, in living organisms, this ratio is maintained as the organism eats, always taking in a fresh supply of C-14 along with the C-12 in its diet, and effectively balancing out the C-14 that is lost through decay. (you and I are radioactive - did you know that!?)
Now the organism dies. No more fresh C-14. The proportion of C-14 in the organism's body starts to decay away - from its mass, you can tell how much C-14 there was at "t=0" from the 10^-18 proportionality I mentioned. From its current rate of C-14 decays, you can then make the rate calculation Rate(t=now)/Rate(t=0). This ratio is just e^(-t/lifetime). Since we know the lifetime of C-14, we can from the ratio of rates find out what t, or the time since t=0; that is, the age of the organism since its death.
So far so good - for once living organisms, you have an easy way of dating them, and it's pretty reliable (though uncertainties might be significant, just due to the facts of scientific analysis which always have uncertainties).
For longer-timeframe measurements, the exact same method applies - the same radioactive decay laws (same form of the equation) holds.
Difference is, though, we don't have a simple way to get the "original rate" of anything, because we don't have a simple way to get the original proportion of radioactive to non-radioactive isotopes in the object.
But if we make assumptions - (you know what those do) we can get the original rate, and hence from an analogous analysis, the age of the object.
Problem is, those assumptions are grounded on - you guessed it, since I'm a card-carrying Van Tillian - PRESUPPOSITIONS.
Those presuppositions may or may not line up with the truth - and in fact if you don't make presuppositions in the case of long-timebase radioactive decay dating measurements, you can't do anything.
So there you have it...
much too much detail, but finals have been over for a couple of days and I haven't lectured since last Thursday, so I was itching to do it, apparently
