PCM-2 Manual.pdf - Voss Associates

Eq. 8
EXAMPLE 2: An alpha CAM equipped with a multi-channel analyzer is set up to monitor for
plutonium contaminated particulates. Background counts (or count rates) are the result of the
presence of radon and thoron which produce a spectral distribution as illustrated in Figure 1 below.
SPECTRUM DISPLAY
10:42 13 Feb 88 10K
Sto.tus: Flow Fa. il 8K
Flow: 0,00 CfM 6k'
Region Counts 4K
Rm1~~Rm3 1~4
I 'I I I
I II I I
'"
I'
I II
"l
I
I
'I
II I I
J/N:) :
0 111285
I II I
2K
I II I
I I I
Cursor Counts oa
160 619 50 100 150 200 250
Figure 1, Alpha CAM Spectrum
Empirical data shows that counts collected in four regions of interest (ROls) have a consistent
relationship in the absence of plutonium. That relationship is expressed by Eq. 9 where the four
ROIs are identified as R, through R 4 and K is a constant.
R I = K R3 Eq. 9
R 2
R 4
Furthermore, when plutonium counts are present, they occur in R j , so that in order to maintain the
equality of Eq. 9, the plutonium counts, Pu, must be subtracted from R I
. This leads to the derivation
of the mean plutonium counts (or mean count rate) as expressed by Eq. 11.
R} - Pu R 3
---=---- = K - Eq. 10
R 2
R 4
Eq.11
Eq. 4 is applied to Eq. 11 by first dissecting it into small, easily managed parts that are illustrated by
Eq. 12 through Eq. 20 for the derivation of the Pu standard deviation. Eq. 21 is the result of
collecting all pertinent terms to solve for (JPt,.
PCM2.MAN