F14Crun Calculation

We calculate the F14C value of a single run of an unknown with the following quantities: avgSR0 and avgSR1 refer to the R0 and R1 values of the selected Standard runs which bracket, in time, the run of the unknown. Since we use online 13C/12C ratios there is no need to calculate a d13C value for normalization, and we use avgR1 directly. avgR12 refers to the average of R1 squared rather than the square of avgR1. avgBR0 is the average 14C/12C ratio for all designated background cathodes.

It is worth pointing out here that the fractionation correction is made to the background corrected value of the unknown's R0. The philosophy of the fractionation correction is that dividing by the 13C/12C ratio models a physical process. The background correction, on the other hand, is subtracting out the contribution to the sample of contamination due to chemistry in the laboratory and noise in the AMS. So we only fractionation correct that portion of the activity which occurred in nature.


Propagation of errors gives

having used

The statistical uncertainty of each run is used to compute the uncertainty in the 14C/12C ratio:

There is no per-run uncertainty associated with R1 so sigR1run is taken as zero at this stage. Not until the runs have been averaged for a cathode is it possible to calculate a variance on the 13C/12C ratios. It is possible, however, to calculate a variance on SR1 for bracketing standards. The number of standards bracketing each run of a cathode is referred to as nstandards. The formulae for bracketing standards are: