VARIATION WITH EQUILIBRIUM CONDITION OF THE CALIBRATION
FACTORS FOR CONTINUOUS RADON PROGENY MONITORS
Phillip H.Jenkins
BowserMomer, Inc.
Dayton, OH
ABSTRACT
The calibration factor for a continuous monitor that uses gross alphaparticle counting for measuring radon
progeny concentration theoretically should vary as a function of the relative concentrations of the radon progeny;
therefore, an inherent error is introduced by using a constant calibration factor, regardless of the equilibrium
condition, as is the practice for most models of radon progeny monitor. An equation was derived describing the
calibration factor as a function of the concentrations of the radon progeny and was used to calculate values of the
calibration factor over the entire theoretical range of relative concentrations of radon progeny that comprise a
constant collective radon progeny concentration. The results of these calculations showed that the calibration factor
varies by approximately 10% over the entire theoretical range of relative concentrations of radon progeny. The
range of relative concentrations that typically exist in indoor air is a small subset of the entire range that is
theoretically possible; therefore, the calibration factor varies, in practice, due to this effect by less than 10% and the
inherent error introduced by the detection and analysis method is not serious. Loss of radon progeny, particularly
218~0,due to plateout on surfaces of the monitor before the progeny are collected on the filter has the effect of
lowering the value of the calibration factor. This effect can be significant at conditions of low equilibrium when the
fraction of radon progeny that are unattached to aerosols in the air is increased and plateout is more likely to occur.
Two types of continuous radon progeny monitor, Alpha Nuclear, Model 100 CIRAS and Thomson & Nielsen, Model
TNWL02, were exposed in BowserMomer's radon chamber under different conditions of radon progeny
equilibrium. A calibration factor was derived for each monitor from the data for each exposure. The results
indicated that the calibration factor for the Alpha Nuclear monitor varied from about 8 cpWmWL at low equilibrium
conditions to about 16 cphimWL at high equilibrium conditions, and that over the same range of equilibrium
conditions the calibration factor for the Thomson & Nielsen monitor varied from about 3 to 9 cph/mWL. This
variation in the calibration factor as a function of equilibrium condition is much more serious than the inherent error
in the detection and analysis method. These results indicate that measurements of radon progeny concentration could
be in error by as much as a factor of two or more if the equilibrium condition at the time of the measurement is
significantly different from the equilibrium condition at which the monitor was calibrated.
INTRODUCTION
The basis for the detection and analysis for most models of continuous monitors used for the measurement of
radon progeny concentration is gross alphaparticle counting of radon progeny collected on a filter. Typically, a
grossalpha count is made over a period of time, such as one hour, and a calibration factor is applied that converts
the net count rate to the radon progeny concentration. With this method alone, it is not possible to determine the
relative concentrations of the radon progeny, or the equilibrium condition. Even if one can assume that the
efficiencyfor the collection of radon progeny is constant, the calibration factor for this type of monitor theoretically
should vary as a function of the relative concentrations of the radon progeny; therefore, an inherent error is
introduced by using a constant calibration factor regardless of the equilibrium condition.
Another factor that affects the value of the calibration factor is loss of radon progeny due to plateout on
surfaces of the monitor before the progeny are collected on the filter.. If the fraction of each of the radon progeny
lost due to plateout were constant regardless of the equilibrium condition, then the value of the collection efficiency
and the value of the counting efficiency could be combined into one constant term. However,.plateout is more likely
1996 InternationalRadon Symposium IIP  5.1
to occur with radon progeny that are not attached to aerosols in the air, and the fraction of radon progeny,
particularly 2 1 8 ~ o that
, is unattached increases as the equilibrium ratio decreases. Therefore, there should be a
greater loss of radon progeny, particularly of 2 1 8 ~ o resulting
,
in a lower calibration factor, at a low equilibrium
condition that at a high equilibrium condition.
In order to gain an understanding of the magnitude of the variations in the calibration factor with the relative
concentrations of radon progeny, two approaches were used; one based on theory and the other based on
measurements made in a radon chamber. An equation was developed describing the calibration factor of a
continuous radon progeny monitor, using grossalpha counting, as a function of the individual concentrations of the
radon progeny, and the variation in the calibration factor with different relative radon rogeny concentrations was
investigated. The effect on this theoretical variation of different amounts of loss of 21$'o due to plateout was also
considered. The calibration factors for two models of continuous radon progeny monitor were measured by
exposing the monitors in a radon chamber at different conditions of radon progeny equilibrium.
THEORETICAL EQUATION FOR THE CALIBRATION FACTOR
The first step in deriving an equation describing the calibration factor for a radon progeny monitor is to
develop expressions describing the activities of the two alphaemitting radon progeny, 21*Po and ^PO, collected
on the filter. It is assumed that the flow rate of the pump and the individual concentrations of the radon progeny are
constant during the measurement and that the efficiency for collection of the radon progeny from the air is 100%. A
further assumption is that after 2 i 8 ~ oand 2 1 4 ~ bare collected, their subsequent decay products are also collected on
the filter. The activities of ^PO and ^PO on the filter are described by the following equations:
F C3 [I  exp(A3t)] I A3
where
Al & A4 = Activity of 2 1 8 ~ and
o ^PO, respectively, on the filter (pCi);
F = Flow rate (Llmin);
= Concentrations of 2 1 8 ~ o2, 1 4 ~ &
b 2 1 4 ~ irespectively,
,
in air ( CiL);
Cl, C2, & C3
=
Decay
constants
of
^PO,
2
1
4
~
b
&
^
~
i
,
respectively
(min" ); and
A1, A2, & A3
t = Sampling time (min).
f
A farther assumption inherent to eqns (1) and (2) is that, because of its extremely short halflife, ^PO is
always in secular equilibrium with 2 1 4 ~ i ,and that the alphaparticle decay of each 2 1 4 ~ onucleus occurs
simultaneously with the betaparticle decay of its parent 2 1 4 ~ inucleus. This assumption is frequently used to
simplify the mathematics related to the decay and ingrowth of radon progeny, and its use introduces an insignificant
amount of error.
The exponential terms in eqns (1) and (2) indicate the exponential growth of activity on the sample filter
during the first few hours of sampling. These exponential terms become small when the sampling time exceeds four
hours. Under the condition of steady state the exponential terms can be replaced with zeroes, and eqns (1) and (2)
become:

1996 International Radon Symposium IIP 5.2
FC2\t{l/[A2(A3A2)] + l / [ A 3 ( A 2  W + F C 3 / ^
(4)
These equations can be simplified by first defining terms consisting only of the decay constants and then
substituting the constant terms into eqns (3) and (4).
Note that in eqn (10) the terms containing K2 and K3 describe the activity of 2 1 4 ~ on
i the filter due to the
,
from the air. It can be shown algebraicall that Kl and K2 are equal.
collection of ^PO and 2 1 4 ~ b respectively,
This makes sense physically, because at steady state the ortion of the activity of 2 1 1Po on the filter due to the
collection of 2 1 8 ~ 0from the air is equal to the activity of '^Po on the filter. The values of the halflives (tlI2) of
218Po,214Pb, and 2 ^ ~ iare 3.05 min, 26.8 min, and 19.7 min, respectively. The value for each decay constant is
calculated from the relationship that A = ln(2)/tl/2, and the values of Kl through K4 are calculated to be 4.40 min.,
4.40 min, 38.7 min, and 28.4 min, respectively.
Assuming that a single value can be used for the counting efficiency for the detection of alpha particles
emitted by 2 1 8 ~ 0and "'PO, the observed count rate is described by the following equation:
R = 133.2 E(A1 + A4)
where
R = Count rate (cph);
133.2 = Conversion factor, 2.22 dpmlpCi x 60 minh (dph/pCi); and
E = Counting efficiency (cld).
E in eqn (1 1) may also contain a constant factor for the efficiency of collection of radon progeny from the air.
Substituting the values of Al and A4 from eqns (9) and (lo),
1996 International Radon Symposium IIP  5.3
The collective radon progeny concentration is expressed as a function of the individual concentrations of the
radon progeny in the following equation:
where
RPC
=
Radon progeny concentration (mWL)
The calibration factor is the ratio of the net count rate, R, to the collective radon progeny concentration, RPC,
as expressed in the following equation:
THEORETICAL VARIATION IN CALIBRATION FACTOR WITH NO PLATEOUT LOSSES
The exact magnitude of the calibration factor is not important here, only the manner in which it varies as a
function of the relative concentrations of the radon progeny. In order to calculate values of the calibration factor, a
value of 0.125 Wmin was used for the flow rate, F, and a value of 0.143 c/d was used for the counting efficiency. A
set of values for the concentrations of the radon progeny were chosen to span the entire range that is theoretically
possible. A value of 1 WL for the collective radon progeny concentration was used in the calculations. The exact
value of the collective radon progeny concentration is unimportant, as long as it is constant.
The concentration of each of the radon progeny, 2 1 8 ~ o2, 1 4 ~ b and
, 2 1 4 ~ i in
, pCi/L that alone is equivalent
to 1 WL was determined from eqn (14) by setting RPC to 1000 mWL and solving for Cl, Cy, and C , assumin in
each case that the concentrations of the other two decay products is zero. These concentrations of "^Po, ^'6Pb,
and ^Bi were determined to be 952 pCi/L, 197 pCi/L, and 268 pCi/L, respectively. Values of the calibration
factor were calculated for every combination of Cl, C2, C3, in increments of 0.1 WL,that sum to 1 WL. The values
of Cl, C2, C3 were converted to the unit of pCiL before being used in eqn (15). The calculated values of the
calibration factor are listed in Table 1 and shown graphically in Fig. 1. Note that for constant values of the
concentration of 218 ~ othe
, calibration factor changes only slightly with changes in the relative concentrations of
14pb and 2 1 4 ~ i .
The graph in Fig. 1 shows the values of the calibration factor as a triangular surface. The comer of the surface
toward the upper left represents the condition where only 2 1 8 ~ ois present the comer toward the lower right where
only ^Pb is present, and the comer toward the upper right where only 2 f 4 ~ isi present. In the area of the surface
away from the edges all three of the radon progeny contribute to the collective concentration. From the values of CF
in Table 1, and from the surface in Fig. 1, it is seen that the calibration factor varies slightly with changes in the
relative concentrations of the radon progeny. The largest value occurs when only 2 1 8 ~ ois present, and the smallest
value occurs when only ^pb is present. The largest value is 10.1% greater than the smallest value.
The surface shown in Fig. 1 represents all possible combinations of the three radon progeny that contribute to
a constant collective radon progeny concentration. Combinations of the relative concentrations represented by
portions of the surface near the edges of the triangle are typically not found in an indoor environment. Therefore, the
variation in the calibration factor in practical situations is likely to be considerably less than 10%. This indicates that
the inherent error associated with using grossalpha counting for the continuous measurement of radon progeny
concentration is not seriously large.
1996 International Radon Symposium IIP  5.4
Table 1. Values of Calibration Factor, CF, for Various Relative Values of Radon Progeny Concentrations
Radon Pro~envConc. (WL)
Pb
% 2
L Bi
CF fcoh/mWL)
Radon Pro~envConc. (WL)
21 8 ~ o ^I4pb
 I4ei
EFFECT O F LOSS OF ^PO
DUE TO PLATEOUT
When the concentration of aerosols in the air is low, the percentage of radon progeny that are not attached to
particles is increased. This is particularly true for ^^PO whose halflife is so short that it may decay before it
contacts a particle on which to attach. In this condition, the radon progeny tend to migrate and attach to surfaces,
such as walls, floors, ceilin ,curtains, etc., thus depleting the collective radon progeny concentration in the air. The
relative concentration of ^Po in the air is increased; therefore, the region of the surface in Fig. I that is typical of
this condition is nearer the comer in the upper left.

1996 International Radon Symposium IIP 5.5
Continuous radon progeny monitors by necessity must pump air through some type of sampling head and
through a filter which is in close proximity to a detector. Some monitors are designed so that the air must pass
through a small opening in the case and into the interior of the monitor before reaching the filter. When unattached
radon progeny enter the interior of the monitor, there is a high probability that they will attach to some surface of the
monitor itself before they reach the filter where they should be collected and detected. This loss due to plateout is
more likely to occur with ^PO than with the other two radon progeny, simply because its unattached fraction is
likely to be larger than those of the other two radon progeny.
The calculation of the set of calibration factors plotted in Fig. 1 was repeated with the assumption that 10% of
the 2 1 8 ~ 0in the au is lost to plateout. This set of calibration factors is shown graphically in Fig. 2. In this case, the
10.1% variation of the calibration factor present in Fig. 1 is almost entirely eliminated. This set of data indicates that
if it were possible to design a monitor such that 10% of the 2 1 8 ~ owere consistently lost to plateout, the calibration
factor would be nearly constant over the entire range of relative concentrations of the radon progeny.
The calculation of the calibration factors was repeated twice more, assuming that 20% and 30% of the 2 1 8 ~ o
in the air is lost to plateout. These sets of calibration factors are shown graphically in Fig. 3 and Fig. 4. In
progressing from Fig. 1 through Fig. 4, the effect on the surface representing the calibration factor values is that the
upper left comer of the surface is lowered in increments of 10%. It is reasonable to expect that if the radon progeny
are in a high equilibrium condition, represented b a point of the surface somewhere in the vicinity of the middle of
the triangle, then there would be little loss of 2y8Po due to plateout and the surface shown in Fig. I would be
appropriate. If the aerosol concentration in the air is lowered, producing a lower e uilibrium condition, represented
by a location on the surface that is closer to the upper left comer, then the toss of ^Po due to plateout is increased
and a surface such as the ones shown in Fig. 2 through Fig. 4 would be appropriate depending on the magnitude of
the equilibrium condition and the amount of loss due to plateout. In the case of 30% loss of ^Po, the variation
across the entire surface shown in Fig. 4 is still only about 20%.
MEASUREMENTS OF CALIBRATION FACTORS
Measurements of calibration factors were made under different conditions of radon progeny equilibrium using
two types of continuous radon progeny monitors; Alpha Nuclear, Model 100 CIRAS and Thomson & Nielsen,
Model TNWL02. The monitors were exposed in BowserMomer's radon chamber for a minimum of 24 hours after
allowing four hours to achieve a steadystate condition. Both monitors were capable of printing or storing gross
alphaparticle counting data on an hourly basis. The background count rate for each monitor was determined by
exposing it to an atmosphere of nitrogen for a minimum of 24 hours, after allowing four hours to achieve a steadystate condition.
During each exposure, several grab sample measurements of the radon progeny concentration were made
using the modified Tsivoglou method (Thomas 1972). BowserMorner's use of this method has been verified over a
range of equilibrium conditions through intercomparisons exercises at the Department of Energy's Environmental
Measurements Laboratory (EML). Each grab sample measurement was paired with a monitor's net count for the
hour in which the grab sample was made. A least squares procedure was applied to the paired data to select the
value of the calibration factor that produced the best fit of the monitor's hourly data to the grab sampling data. This
value of the calibration factor was applied to all of the hourly measurements from the monitor to produce hourly
average radon progeny concentrations. The hourly measurements of radon progeny concentration were averaged to
produce the radon progeny concentration for the entire exposure period. Hourly radon measurements were made
during the same time period using a continuous monitoring system consisting of three detectors. This system is
calibrated by comparisons with grab scintillation cells, which in turn are verified through intercomparisons with
EML and with the radon laboratories of the U. S. Environmental Protection Agency in Montgomery, Alabama and
Las Vegas, Nevada. The average radon progeny concentration and the average radon concentration were used to
determine the equilibrium ratio for the exposure period.

1996 International Radon Symposium IIP 5.6
This procedure was used to determine the calibration factor for the two monitors at several conditions of
radon progeny equilibrium. The equilibrium condition was held as constant as possible during each exposure, and
was changed between exposures by varying the concentration of aerosols in the chamber air. The results of these
measurements are presented in Table 2 and shown graphically in Fig. 5. The results indicated that the calibration
factor for the Alpha Nuclear monitor varied from about 8 cph/mW at an equilibrium of 14.5% to about 16
cph/mWL at an equilibrium condition of 45.0%. Over the same range of equilibrium conditions, the calibration
factor for the Thomson & Nielsen monitor varied from about 3 cph/mWL to about 9 cph/mWL.
These results indicate a much greater variation in the calibration factor than predicted by the theoretical
investigation discussed above. This implies that, at a very low equilibrium condition, the loss of 2 1 8 ~ odue to
lateout is much greater than 30%. Perhaps also at a very low equilibrium condition there is loss of unattached
514Pb andor ~ ~ f f i .
Table 2 . Measured Values for the Calibration Factors of Two Types of Monitor
Eauilibrium (%)
Calibration Factor (cvh/mW)
Alnha Nuclear
Thomson & Nielsen
CONCLUSIONS
The inherent error associated with using gross alphaparticle counting as the basis for a continuous radon
progeny monitor was shown to be less than 10% and is not a serious concern. The variation of the calibration factor
for a continuous radon progeny monitor was shown theoretically to vary by no more than 20% if the loss of *^PO
due to plateout is no more than 30%. Measurements of the calibration factors for two types of continuous radon
progeny monitor, however, indicated that the calibration factor can vary by a factor or two or more depending on the
equilibrium condition. More measurements should be made to verify these conclusions, since a small number of
measurements of the calibration factor for each monitor was made. Also, this study should be expanded to include
equilibrium conditions greater than 45%, additional models of continuous radon progeny monitor, and more than one
instrument of each type. If the results of this study are typical, however, then a measurement using a continuous
radon progeny monitor could be in error by as much as a factor of two or more if the equilibrium condition at the
time of the measurement is significantly different from the equilibrium condition at which the monitor was
calibrated.
REFERENCE
Thomas, J. W., "Measurement of Radon Daughters in Air," Health Physics;23:783, 1972.
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4
d
0
N
tin
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