Isnt Carbon 14 Dating based on probability Formula rather than deterministic?

Question

lamda constant based on determined results?

Answer 1

Definitely probabilistic, but it uses deterministic processes.

First of all, it has some significant assumptions:
- Carbon dating assumes the dead object was in carbon equilibrium with the surroundings. This is fine.
- It assumes the amount of carbon in an object 1000's of years old is the same as an object today. Maybe fine if there are existing specimens. Not so good with dinosaurs.
- It assumes the ratio of C-14 to normal Carbon is exactly the same as it is today. Probably not so fine (think ozone layer).

Radioactive decay is deterministic and measuring it is deterministic (you can conclusively point to a number that directly relates to decay rate), but radioactive dating (of which carbon dating is just one type) is based on the probability of carbon decay. It assumes C-14 will decay at a specific rate. The likelihood of this probability is very high to about 50,000-100,000 years, at which point there is too much uncertainty in the assumption and too little decay to measure accurately. This is why they do not use carbon dating for dinosaur fossils, for example.

Answer 2

Yes and no.

Radioactive decay is a statistically random process, just like a roulette wheel in a casino is. For a given isotope there is a fixed probability per unit of time that an atom will decay. Of course, the atom may decay in a second, a day, a year or a millenium.

But what you have to consider is this probability averge over all of the atoms in a sample. In a mole of atoms there are some 6 x 10^23 atoms. So if I now calculate the average time for 1/2 of those atoms to decay based on the average rate of decay above and its standard deviation, I will get a very, very precise number with almost no variation at all. This number is called the half life, and is what is measured. For carbon 14 it is about 5568 years (the error in knowing it is that it is hard to take measurements for 5568 years, so we have to estimate from shorter observations!).

The rate at which carbon 14 is produced is not constant, and this is an issue for carbon dating. This is overcome by calibrating against items with a known date. So trees whose rings can be counted are really useful, as are objects found with archaeological artifacts whose dates are known.

Answer 3

Yes, carbon dating is based on probabilty.

If you have 10 C^14 atoms sitting together there is no way to tell which will decay first. They could all decay within a few minutes, or they could all decay in 10,000 years. But, if we look at a very large amount of atoms (a few mols), we can see that about half of the atoms will decay after about 5700 years.

Answer 4

First off, this should probably be in Geology, but
If your asking what I think your asking...
C14 dating is based on an assumption that the amount of C14 in the atmosphere has stayed at about the same amount throughout history. This assumption fixes the timeline so that people have a fixed point of reference. However, it is very possible and quite likely that the amount of C14 in the atmosphere has been decreasing in a sqrt shaped curve.