Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

and is often expressed as a percent:
HEALTH PHYSICS INSTRUMENTATION 491
%CV = σ
× 100. (9.41b)
mean
Thus, in the case illustrated above, where a mean count rate of 1000 cpm was
determined by a 10-minute count and a 1-minute count, the precision of the
10-minute count was ±1% while that of the 1-minute count was ±3.2%.
Standard Deviation of a Sum or a Difference
The square of the standard deviation, σ 2 , is called the variance. When two quantities,
each of which has its own variance, are either added or subtracted, the variance of
the sum or difference is equal to the sum of the variance of the two quantities:
(A ± σA) ± (B ± σB) = (A ± B) ± σA±B, (9.42)
σ 2 A±B = σ 2 A + σ 2 B , (9.43)
σA±B =
σ 2 A + σ 2 B . (9.44)
When making radioactivity measurements, we must usually account for background,
and are thus interested in the net counting rate; that is, the difference
between the gross counting rate of the sample, which includes background, and
the background counting rate. Each of these counting rates has its own standard
deviation. The standard deviation of the net counting rate is given as
σn =
where
σ 2 g + σ 2 b =
rg
tg
+ rb
, (9.45)
tb
σg = standard deviation of gross counting rate,
σb = standard deviation of background counting rate,
rg = gross counting rate,
rb = background counting rate,
tg = time during which gross count was made, and
tb = time during which background count was made.
W Example 9.10
A 5-minute sample count gave 510 counts, while a 1-hour background measurement
yielded 2400 counts. What is the net sample counting rate and the standard deviation
of the net counting rate?