Understanding Carbon Dating: Assumptions, Ratios, and Half-Life

[nabeel17]

Before I start, I'm not some young Earth believer or anything, just want to understand how it works and if the assumptions are fair.

So my understanding of carbon dating is that the ratio of C14 to C 12 is known (About 1 trillion to 1) and it is the same in the atmosphere as it is in organic material. Sicne C14 is not stable, it decays and the ratio in the organic compound becomes smaller and smaller since no more C14 is being produced. Using this you can estimate how old the thing was.

Questions

Once something dies, it can no longer produce an C12 or C 14 correct?

How do we know the ratio of C14 to C12 to be constant. Has it always been 1 to 1 trillion. It seems to me if this is wrong, the whole thing falls apart. What assumptions do we base that this ratio is constant on?

How doe we determine the half life of Carbon in the first place, or any element at that?

 

[Nugatory]

How doe we determine the half life of Carbon in the first place, or any element at that?

That question came up in another thread recently: www.physicsforums.com/showthread.php?t=750944

Once something dies, it can no longer produce an C12 or C 14 correct?

The organism isn't "producing" carbon of either type. As long as the organism is alive, it's continuously cycling carbon through its body (by eating, absorption, or photosynthesis), so the ratio of carbon-12 to carbon-14 in its body will match the ratio in its environment. As soon as it dies it stops bringing carbon into its body, so the ratio of C12 to C14 will diverge from the ratio in the environment as the C14 decays.

How do we know the ratio of C14 to C12 to be constant. Has it always been 1 to 1 trillion.

There is a tremendous amount of observational evidence and some very compelling theoretical arguments that it has been constant across the time span for which we use carbon dating. Among the evidence:
- We can look at the ratios of C12 to C14 in objects whose age is known through other means. after correcting for the known amount of C14 decay over the known age of the object, we find the expected ratio.
- The ratio of C12 to C14 in the atmosphere is determined by the rate of C14 production, largely by cosmic-ray interactions with atmospheric nitrogen. There's no remotely plausible way that this mechanism could have dramatically changed over the past few tens of thousands of years (a geological blink of the eye) without leaving all sorts of obvious evidence elsewhere.

 

[jtbell]

How doe we determine the half life of Carbon in the first place, or any element at that?

Take a sample of the element (actually, an isotope of it) and calculate the number of atoms in it by dividing its mass by the mass per atom.

Count how many decays you get in a certain time period, long enough to make the statistical uncertainty small, but short enough to be much shorter than the half-life.

Divide the number of decays by the number of atoms and the time period. This gives you the decay constant, λ, for that isotope, which is the probability that a single atom decays in one time unit (e.g. second). As far as we know, this has the same value for any undecayed atom of that isotope. It leads to the exponential decay law, and is related to the half-life by
$$t_{1/2} = \frac{\ln 2}{\lambda}$$

This works for very long half-lives, so that the number of decays per second (which is proportional to the number of undecayed atoms) is practically constant for the duration of a lab experiment. For short half-lives, we observe the number of decays per second to decrease as time passes, and we can simply wait for it to decrease by 1/2 and note how long it took.

 

[jtbell]

How do we know the ratio of C14 to C12 to be constant.

There is a tremendous amount of observational evidence and some very compelling theoretical arguments that it has been constant across the time span for which we use carbon dating.

Actually it does vary slightly. This has been studied by using samples from tree rings, and the results are incorporated into a calibration curve.

http://en.wikipedia.org/wiki/Radiocarbon_dating#Atmospheric_variation

 

[nabeel17]

Thank you all! So there is a slight variation in the carbon ratio over the last couple thousand years and it is non negligible?

 

[dauto]

It is small but not entirely negligible. The fact that it is taken into account shows that
a) Scientists don't simply blindly follow untested assumptions. All assumptions are tested very carefully to the level of obsession
b) The final results are very accurate because even small effects are taken into account.

 

[Nugatory]

Actually it does vary slightly. This has been studied by using samples from tree rings, and the results are incorporated into a calibration curve.

http://en.wikipedia.org/wiki/Radiocarbon_dating#Atmospheric_variation

Yes, I should have said "constant enough". Error bars are important.

 

[Vanadium 50]

Before I start, I'm not some young Earth believer or anything,

Carbon dating is not used to date the age of the earth. As you've read from other posts, it dates when an object dies, and the Earth was never alive. Furthermore, C-14 has a half life of 5730 years. That means the technique starts to run out of steam at about 50,000 years.

It's important to understand the range of validity of the test. C-14 is a very good technique to date when a shoe worn by Cleopatra was made. It's not so good in dating a shoe worn by Imelda Marcos or one by Fred Flintstone.

 

[nabeel17]

Carbon dating is not used to date the age of the earth. As you've read from other posts, it dates when an object dies, and the Earth was never alive. Furthermore, C-14 has a half life of 5730 years. That means the technique starts to run out of steam at about 50,000 years.

It's important to understand the range of validity of the test. C-14 is a very good technique to date when a shoe worn by Cleopatra was made. It's not so good in dating a shoe worn by Imelda Marcos or one by Fred Flintstone.

Yes but young Earth believers don't believe in carbon dating, so I didn't want to seem skeptical or seem like a young Earth theorist by asking about it. Carbon dating effectively disproves that the Earth is younger than 10000 years so it blows my mind how many people still believe this

 

[mfb]

Yes but young Earth believers don't believe in carbon dating, so I didn't want to seem skeptical or seem like a young Earth theorist by asking about it.

There is nothing wrong with questions to understand how something works :).