Okay, so I understand that calendrical dates and C14 dates don’t match up exactly, because the concentrations of C14 have varied over time. But why does that mean C14 dates aren’t the same as calendrical ones? Also, how exactly do calibration curves work? I kind of get it, but even Wikipedia is beyond my understanding.
Thank you very much.
C14 is (usually) the product of solar radiation acting on carbon(12) dioxide in the atmosphere. It’s produced, and decays, at a fairly steady rate, so the amount in the atmosphere is ~constant. Living creatures absorb it directly (plants) or indirectly (animals eating plants). When they die, they don’t absorb it anymore, so the C14 decays at a precise exponential rate. Measuring how much C14 is left in previously living tissue can establish how long the previously-alive whatever has been dead.
There are a million caveats: different metabolic rates for different ceatures, natural (and lately human made) differences in the CO2 content of the atmosphere (less CO2 gives less C14), time of year the deceased croaked (winter has less sunlight, so less C14, and hibernation could be there too), contamination of sample sources from who-knows-where.
And NONE of this matters for anything that died after 1945. The radiation spewed into the atmosphere since then has raised the C14 level to where death dates seem to be well into the future.
[sup]14[/sup]C is produced in the atmosphere at a rate that depends on a number of factors, the one that is of longterm significance is solar radiation levels (I say longterm to avoid short term events like nuclear tests which swamp the longer term fluctuations). What this means is that a basic linear* extrapolation (based on a constant [sup]14[/sup]C production rate) will introduce errors in dating, causing [sup]14[/sup]C dates to not match up with the calendar.
So the [sup]14[/sup]C dates need to be calibrated. The calibration curves rely on obtaining dates from known objects. Tree rings provide a good start - they rely only on atmospheric carbon and can be dated, and can also contain confirming data from significant dates (poor summers, volcanic events). Layered ice cores trap CO[sub]2[/sub], and annually layered sediments trap organic material that can be carbon dated. All these sources can be combined to give calibration data for 30000-50000 years, to the limits of [sup]14[/sup]C detectability. However, there is some uncertainty in the calibration curves. Also, the older the sample, the larger the uncertainties are (due to the exponential nature of the decay).
So a sample gets dated. The [sup]14[/sup]C/[sup]12[/sup]C ratio is determined. This ratio is plotted on the calibration curve, and a line dropped down to identify the age. It is possible that the determined ratio actually crosses the calibration curve at multiple points (this is more likely with recent dates impacted by nuclear tests) - this produces uncertainty in the date that may be resolved by context, but may not be.
Context must also be used to determine if a sample can be accurately sampled. Oceanic carbon is older than atmospheric carbon, so human remains from near the sea and fed on fish/shellfish can date older than they are. A creationist canard is that a living mollusk was dated as being 10000 years old, so carbon-dating is unreliable - but the experiment was carried out to confirm the theory that carbon-dating is inappropriate for sea-living creatures, and strengthened the basis for appropriate carbon-dating. Fire pits can contain carbon from much older forests than the inhabitants who made the fire. Building materials can be much older than the builders. So sampling techniques and selection are as important as the calibration.
Si
*By linear, I actually mean a plot using a logarithmic scale to make the exponential decay curve a straight line - the phrase exponential extrapolation just does not seem right.
Missed the Edit window :smack:
Also, there were issues about the accepted figure for the half-life of [sup]14[/sup]C. The currently accepted figure (Cambridge) is slightly different to the one originally used (Libby), but for radiometric dating, the Libby value is still used, as the calibration curves are based on the Libby values.
So, to answer the OP - based on a constant level of [sup]14[/sup]C production, a radiometric date can be determined using a basic logarithmic* extrapolation. This is an ideal figure if the earth was static. Due to natural variations, radiometric dates are not quite the same as calender dates, so a calibration curve is used to determine the actual calender date. From the sample and the calibration curve, an age can be determined. However, the calibration curve may introduce more uncertainty into the date of the sample. This is how science works.
Si
exponents, logarithms :smack: two sides of the same coin. It’s an exponential decay function, so logarithms get involved, and I am mixing the terms depending on which side of the equation I am looking. So sue me, I’m not a mathematician. Or consistent.
Nitpick: C-14 is the result of cosmic ray neutrons on atmospheric nitrogen. A nitrogen atom (atomic mass 14) absorbs a neutron and then emits a proton. So essentially, the N-14 is turned into C-14.
dtilque, you got it right.