Page 582 - Instrumentation Reference Book 3E

564 Measurements employing nuclear techniques

two soft beta particles (Emax = 0.156MeV), one Anthracite coal, with an estimated age of
can appreciate that the counting is, indeed, very 2 x lo9 yr, can be used to provide the dead car-
“low-level.’’ The natural counting rate bon background. Corrections must also be made
(unshielded) of a typical gas proportional counter for isotopic fractionation which can occur both in
15 cm diameter x 60 cm long would be some 75.6 nature and during the various chemical proced-
counts per second, whereas the signal due to ures used in preparing the sample.
1 atm of live modern CO? or CH4 filling the
counter would be only 0.75 count per second. In Statistics of carbon dating The standard devi-
order to achieve a standard deviation of 1 percent ation u of the source count rate when corrected
in the measurement, 10,000 counts would have for background is given by
to be measured, and at the rate of 0.75 count
per second the measurement would take 3.7 days.
It is immediately apparent that the natural back- (23.10)
ground must be drastically reduced and, if possible,
the sample size increased to improve the counting
characteristics (Watt and Ramsden 1964). where S is the gross count of sample plus back-
Background is due to many causes; some of the ground, B the background counted for a time tb
most important being: and T the total time available.
In carbon dating S N 2B and the counting
(1) Environmental radioactivity from walls, air, periods for sample and background are made
rocks, etc.; equal, usually of the order of 48h. Thus if
(2) Radioactivities present in the shield itself; tl = tb = TL and S = D + B we have
(3) Radioactivities in the materials used in the
manufacture of the counters and associated
devices inside the shield; (23.1 1)
(4) Cosmic rays;
(5) Radioactive contamination of the gas or The maximum age which can be determined by
liquid scintillator itself; any specific system depends on the minimum
(6) Spurious electronic pulses, spikes due to sample activity which can be detected. If the “2g
improper operation or pick-up of electromag- criterion” is used, the minimum sample counting
netic noise from the electricity mains supply, rate detectable is equal to twice the standard
etc. deviation and the probability that the true value
of D lies within the region &20D is 95.5 percent.
Calculation of a radiocarbon date Since the mea- Some laboratories prefer to use the “4u criterion,”
surement is to calculate the decay of 14C, we have which gives a 99.99 percent probability that the
the relation true value is within the interval k4u. If Dmin =
200, then
I = I, exp -(At) (23.8)
where I is the activity of the sample when meas- (23.12)
ured, IO the original activity of the sample (as
reflected by a modern standard), A the decay then the maximum dating age Tmax which can be
constant = 0.693/T~ (where rri= half-life) and t achieved with the system can be estimated as
the time elapsed. Ir‘ T; = 556dyr (the latest best follows. From equation (23.9)
value found for the half-life of 14C is 5630 yr, but
internationally it has been agreed that all dates
are still referred to 5568 yr to avoid the confusion
which would arise if the volumes of published
dates required revision) then equation (23.8)
may be rewritten as
S, - B (23.13)
t = 8033 log, __ (23.9)
So - B As D,,, <( 2B the equation can be simplified to
where S, is the count rate of sample, SO the count
rate of modern sample, and B the count rate of
dead carbon. A modern carbon standard of oxalic
acid, 95 percent of which is equivalent to 1890 where DO is the activity of the modern carbon
wood, is used universally, and is available from sample, corrected for background. The ratio
the National Institute of Standards and Testing DoJB is considered the factor of merit for a
(NIST) in Gaithersburg, Maryland. system.