Radiocarbon counting statistics

Vogel JS, OgnibeneT, Palmblad M, Reimer P. Counting statistics and ion interval density in AMS. Radiocarbon 2004 46(3) 1103—1109. 

Expression and Interpretation of Results. Archaeological interpretation of a radiocarbon age may depend critically on the error associated with that age. Errors are commonly expressed as a variance range attached to the central number (e.g., 2250 80 years). The 80 years in this example may correspond to the random error for a single analytical step. Both decay and direct-atom counting are statistical in nature, and lead to errors that vary as the square root of the number of counts. The error may also be expressed as the overall random experimental error (the sum of individual errors.) Overall random error can be determined only by analyzing replicate samples. 

Example To illustrate the capabihties of AMS, we compare carbon-14 determination by radioactive counting to AMS. A sanple of 1 g of environmental carbon contains 6 x 10 atoms of (and 1.2 x 10 times more atoms). Due to the 5730 years half-life of C, only 13 atoms will decay per minute. For a statistical precision of 0.5% as normally required in radiocarbon dating, decays from 1 g of carbon need to be counted for more than 48 h. AMS does not have to wait for the decays, it is more efficient because it uses the whole sanple. A sample of 1 mg carbon, only one thousandth of the material needed for decay counting, is completely sputtered in the ion source within 1-2 h and delivers about 6 x 10 atoms, which is 1% of the total content, to the AMS detector system Conventional mass spectrometers can not be used here, because the ions are superimposed by atomic and molecular isobars that are by orders of magnitude more abundant. These are and small fragments such as and Li2. Ab-... 

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