Athro, Limited Gubik Field Trip Section 20 Karmuk

You collect a sample of wood from the section, return from the field, and send it to an accelerator mass spectrometer (AMS) lab for carbon 14 dating.

The lab returns the following value:

This is an infinite radiocarbon age. This sample is older than about 38,000 years, but its exact age cannot be determined, and no further statement can be made about its age.

[NOTE: This result is fictitious. It is a reasonable value for what you might find if you did this analysis, but is not based on any real data collected at this location]

How carbon dating works

So what does all this mean? Radiocarbon dating measures the ratio between the unstable isotope of Carbon C¹⁴ and the stable isotope of Carbon C¹². Most Carbon is in its normal Carbon 12 form (6 protons, 6 neutrons). Carbon 14 is produced in the upper atmosphere as cosmic rays bombard Nitrogen atoms. In this reaction Nitrogen 14 (7 protons, 7 neutrons) captures a neutron and looses a proton to make Carbon 14 (6 protons, 8 neutrons). As a result of this process the atmosphere contains a small proportion of Carbon 14. Plants, in building sugars from Carbon dioxide, capture Carbon atoms from the atmosphere and incorporate it into their tissues. Thus a living plant will contain carbon atoms (in sugars and other metabolic products) with a ratio of C¹⁴ to C¹²that reflects the ratio in the atmosphere. Once the plant dies, new carbon is not added from the atmosphere and the particular set of carbon atoms in the plant at the time of its death remain there. Since C¹⁴ is unstable and gradually decays to N¹⁴ (by beta decay in which a neutron decays releasing an electron and converting to a proton), while C¹² is stable, the quantity of C¹⁴ in the remains of the plant gets less over time. Thus the ratio of C¹⁴ to C¹² in the remains of the plant changes over time. C¹⁴ decays in a regular clock like manner with a half life of 5730 years. The ratio of C¹⁴ to C¹² is thus a result of the original ratio of C¹⁴ to C¹² at the time of the death of the plant, and the amount of time that has elapsed since then. The uncalibrated radiocarbon age is calculated by measuring the ratio of C¹⁴ to C¹² in organic remains, and calculating how many years it would have taken the C¹⁴ to decay from the ratio found in the modern atmosphere to that found in the sample. Measurement of the amount of carbon 14 in a sample has some error, thus a standard deviation is given for the age results. In a case such as this one, too little carbon 14 remains in the sample to make a meaningfull measurement - almost all of it has decayed to Nitrogen 14. This is reported as an infinite radiocarbon age - the sample is something over 40,000 years old, but how much older it is not possible to tell.

The flux of cosmic rays hitting the upper atmosphere appears to have fluctuated over time, therefore the ratio of C¹⁴ to C¹² in the atmosphere has not been constant. Therefore, it has been necessary to find independent ways of calibrating Carbon 14 ages. The standard calibration (which gives good carbon dating ages up to about 14,000 years ago) is dendrochronology - counting tree rings. A more recent method that offers the prospect of calibration back to some 38,000 years is dating organic matter from varves - yearly layers in lakes. Both of these are consistent with results obtained by simultaneous C¹⁴ and Uranium-Thorium dating of corals. By by counting growth rings in trees back to some known age, and then measuring the C¹⁴ to C¹² ratio in a tree ring of that age, it is possible to produce a correction curve to the raw C¹⁴ age. This is the Dendrocalibrated age - it corrects the uncalibrated age for changes in the original amount of C¹⁴ in the atmosphere over time.

The value for del 13C is a measure of the amount of the other stable isotope of Carbon C¹³ found in the sample. It can be used to evaluate the value of the carbon dating.