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Long-Term Measurements of Equilibrium Factor
and Unattached Fraction of Short-Lived Radon
Decay Products in a Dwelling - Comparison with
Praddo Model
C. Huet , G. Tymen & D. Boulaud
Published online: 30 Nov 2010.
To cite this article: C. Huet , G. Tymen & D. Boulaud (2001) Long-Term Measurements of Equilibrium Factor and
Unattached Fraction of Short-Lived Radon Decay Products in a Dwelling - Comparison with Praddo Model, Aerosol
Science and Technology, 35:1, 553-563
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Aerosol Science and Technology 35: 553–563 (2001)
c 2001 American Association for Aerosol Research
Published by Taylor and Francis
278-6826=01=$12.00 C .00
°
0
Long-Term Measurements of Equilibrium Factor
and Unattached Fraction of Short-Lived Radon
Decay Products in a Dwelling—Comparison
with Praddo Model
1
1
2
C. Huet, G. Tymen, and D. Boulaud
1
Laboratoire de Recherches Appliqu e´ es Atmosph e` re-Hydrosph e` re, Universit e´ de Bretagne Occidentale,
Brest Cedex, France
Service d’Etudes et de Recherches en A e´ rocontamination et en ConŽ nement, Institut de Protection
2
et de S uˆ ret e´ Nucl e´ aire, Gif-sur-Yvette Cedex, France
halation, it decays into a series of solid short-lived decay prod-
According to the United Nations ScientiŽ c Committee on the ucts, 218Po, 214Pb, 214Bi, and 214Po. According to the United
Effects of Atomic Radiation (UNSCEAR 1993), the dose due to
the inhalation of radon decay products represents almost 50% of
the total natural radiation dose to the general population. The sci-
entiŽ c community is interested in the assessment of the risk in-
duced by domestic radon exposure. The dosimetric models used
Nations ScientiŽ c Committee on the Effects of Atomic Radi-
ation (UNSCEAR 1993), the dose due to inhalation of radon
decay products represents almost 50% of the total natural radia-
tion dose to the general population. An association between an
to estimate the dose are very sensitive to unattached fraction and excess risk of lung cancer and exposure to radon and its decay
size distributions, which makes the characterization of the indoor
radon decay products aerosol necessary. For this purpose, long-
products has been demonstrated in uranium miners and other
miners (Lubin et al. 1994). The risk related to indoor domes-
tic exposure has been estimated from the risk projection from
underground miners data in association with measurements of
term measurements of unattached fraction ( f ) and equilibrium
p
factor (F) were taken in a dwelling under typical indoor domes-
tic aerosol conditions. An original device consisting of an annular
diffusion channel set in parallel with an open Ž lter was developed indoor radon concentrations. However, exposure conditions in
and calibrated to continuously measure the unattached fraction.
Moreover, radon activity concentration and particle concentration
were simultaneously monitored. With aged aerosol, particle con-
mines generally differ from those in dwellings, and thus the role
of radon domestic exposure in the occurrence of lung cancer
remains unclear.
¡
3
centration was found to be very low (between 500 and 5000 cm ),
¡
3
The last European program, RARAD (1996 –1999), was
radon activity concentration ranged from 240 to 2800 Bq m , and
the mean values of f
.16 (0.04–0.45). With aerosol sources, the high increase in particle
and F were, respectively, 0.31 (0.08–0.67) and aimed at assessing the risk induced by inhalation of short-lived
p
0
radon decay products under genuine living conditions. For this
purpose, a multidisciplinary approach was chosen, and the stud-
ies addressed Ž ve main topics: radioactive aerosol, modeling,
humans, animals, and retrospective assessment of radon expo-
concentration led to a negligible unattached fraction and raised
the equilibrium factor. A correlation relationship was determined
between these two parameters under different aerosol conditions.
Finally, our experimental results were compared to results obtained
with the PRADDO model; this comparison showed a good agree- sure. As part of the aerosol group, our objective was todetermine
ment between these two different approaches.
the properties and behavior of the radon decay products under
typical domestic conditions and to focus especially on the tem-
poral variability of unattached fraction and equilibrium factor.
As a matter of fact, a sensitivity analysis performed by Marsh
and Birchall (1998)using theRADEP model (Birchalland James
INTRODUCTION
222Rn is a noble, natural, and radioactive gas present at dif-
ferent concentrations in soils and building materials. After ex-
1
994) showed that the physical parameter that most affected the
weighted committed equivalent dose to lung per unit exposure
is the unattached fraction.
Our aim required us to Ž rst develop a device able to con-
tinuously determine the unattached fraction and equilibrium
factor over long-term periods. So the annular diffusion chan-
nel technique, which avoids the drawbacks of the screen
Received 1 November 1999; accepted 10 April 2000.
Address correspondence to G. Tymen, Laboratoire de Recherches
Appliqu e´ es Atmosph e` re-Hydrosph `e re, Universit e´ de Bretagne Occi-
dentale, 6 avenue Le Gorgeu, 29285 Brest Cedex, France. E-mail:
georges.tymen@univ-brest.fr
553

5
54
C. HUET ET AL.
technique, was implemented from May 1997 to April 1998 in
a typical house in Brittany, France. This French area is char-
acterized by a granitic subsoil; moreover, in some locations,
like the Northwest of Brest, houses with high indoor radon lev-
els are frequent. This is why the investigated dwelling seemed
to us a representative place to investigate the unattached frac-
tion, equilibrium factor, and size distributions of attached and
unattached radon decay products under realistic living condi-
tions (natural aerosol, cooking, cigar smoke, burning candles,
etc.).
Since long-term measurements are time-consuming and ex-
pensive, it was also of high interest to compare our experimental
data to that obtained with modeling in order to Ž nd an alterna-
tive to experiments for characterizing the radon exposure of the
general population.
The present report will Ž rst deal with the original system de- Figure 1. Alpha counts detected by our device versus 222Rn
signed in our laboratory to continuously measure the unattached activity concentration measured by an Alphaguard.
fraction and equilibrium factor, then we will introduce the re-
sults recorded for these two parameters over the long-term mea-
surements performed under different indoor domestic condi-
Annular Diffusion Channel
Most of the devices usually used to measure the unattached
tions. Finally, our experimental results, especially those about
fraction of radon decay products are based on screen techniques.
the nanometer radon decay products, will be compared to the
They have allowed one togetgood quality information on the po-
results obtained with the PRADDO model (Gouronnec 1995;
tential alpha energy concentration (PAEC) of unattached radon
decay products (James et al. 1972; Stranden and Berteig 1982;
Gouronnec et al. 1996).
Reineking et al. 1990; Cheng et al. 1997). Unfortunately, screen
techniques have two major drawbacks. These screens may col-
lect some attached radon decay products, which consequently
MATERIALS AND METHODS
Radon Activity Concentration Measurement Technique
overestimates the activity concentration of unattached radon de-
To continuously measure the radon activity concentration in cay products. Then a correction factor is needed (Reineking et al.
the air, we designed a system based on electroprecipitation of 1990). Moreover, some authors have noticed losses due to the
2
18
C
the positively charged Po ions on a surface barrier detector recoil of radon decay products collected on the screen (Knutson
PIPS Canberra 1700) carried out in a 9 kV electric Ž eld. The and George 1994). Therefore a technique previously developed
(
air was Ž rst Ž ltered to remove radon decay products, then con- in our laboratory for a speciŽ c application, i.e., the annular diffu-
3
tinuously sucked into a 0.035 m cylinder made of aluminium. sion channel (ADC) (Kerouanton 1996; Tymen et al. 1999), was
The alpha detector was isolated from the cylinder armature by improved to permit continuous measurements of the unattached
218
C
a piece of Te on. The Po ions formed consequently to the fraction.
disintegration of radon in the cylinder were then precipitated
Kerouanton et al. (1996) studied by analytical computation
on the alpha detector because of the electric Ž eld applied be- the diffusional behavior of ADC geometry; this showed that the
tween the cylinder armature and the alpha detector. The elec- annular diffusion channel has almost the same collection efŽ -
tronic card converting alpha counts into voltage pulses had been ciency as a  at rectangular channel of equivalent dimensions,
designed to only detect the alpha particles emitted with an en- considered as the most selective geometry. In the previous ap-
ergy range between 5 and 6 MeV, which permitted us to only plication, the ADC was equipped with a LR115 alpha track
detect the alpha particles produced by the decay of 2 Po . detector and calibrated in a radon chamber; it was used for the
18
C
2
18
Radon activity concentration was directly proportional to the measurement of the nanometer Po activity concentration and
alpha counts and was determined every 10 min. Data acquisi- size distribution averaged over time periods of several weeks in
tion was completely controlled by a PC. Because of the lack the environment (Tymen et al. 1999). We therefore designed a
of available radon standard at the time of our study, the re- system composed of two parallel sampling lines. The Ž rst one
sponses of different devices had to be compared to calibrate consisted of an ADC equipped downstream with a very high-
them; so our device was compared to an Alphaguard (Genrich efŽ ciency membrane Ž lter (Poretics, 0.45 ¹m). An alpha PIPS
1
994) based on the principle of the ionization chamber. The detector (Canberra 900) was inserted on the rear part of the in-
results recorded at different radon activity concentrations are ternal cylinder, the sensitive surface facing the Ž lter (Figure 2).
depicted in Figure 1, which permitted us to determine a conver- The size parameters of our system were governed by the fol-
sion factor from alpha pulses to radon activity concentration of lowing two criteria: the establishment length of the  ow had to
¡3
1
.127 Bq m
.
be as short as possible and the cut-off diameter had to allow the

MEASURED INDOOR RADON PRODIGY PROPERTIES
555
Figure 2. Annular diffusion channel equipped with an alpha detector.
separation of the unattached fraction from the attached one. With be counted in the 218Po energy peak. The Ž lter-detector distance
¡1
the dimensions given in Figure 2 and a  ow rate of 7 l min
the ADC had a cut-off diameter of 3.2 nm, which was close to efŽ ciency while minimizing the overlap of the two energy peaks.
the cut-off diameter recommended by Ramamurthi and Hopke
The two alpha detectors were connected to a PC via two
1989), i.e., 4 nm, to optimize the collection of the unattached
,
was then set to 5 mm, which allowed an optimum geometric
(
(
)
preampliŽ ers and two ampliŽ ers Canberra 2012 . A program
fraction. The unattached fraction was then deposited by diffu- was written for both the acquisition of the alpha spectrum and
sion on the walls of the ADC, whereas the attached radon decay the pump control so that the sampling and counting procedure
products were collected on the downstream Ž lter facing the al- was completely controlled by the computer and the measure-
pha detector. The second sampling line consisted of a reference ments were performed every 3 h. In such a case, the previous
Ž
lter equipped with an alpha detector (PIPS Canberra 900) fac- cycles do not exert any in uence on the cycle in progress. The
ing a very high-efŽ ciency membrane Ž lter (Poretics, 0.45 ¹m). experimental set up used is depicted in Figure 3. The attached
¡1
The  ow rate through the reference Ž lter was set to 20 l min
.
and total radon decay products activity concentrations were de-
As our reference Ž lter had been designed to let the air pass termined by alpha spectroscopy using the method of Tremblay
through a slot between the detector and membrane Ž lter, some et al. (1979) according to the following sequence: 0–15 min
aerosol particles could have been removed from the air stream, sampling, a Ž rst 0–15 min counting sequence, and a second 20–
which thus required us to estimate the inlet losses. So the dif- 75 min counting sequence. The way our device had been de-
fusion losses were Ž rst estimated using the formula given by signed permitted us to simultaneously sample and count, which
Mercer and Mercer (1970), and second our reference Ž lter was improved accuracy on the calculated activity concentrations. In
compared with a classical open-face Ž lter of the same character- order to validate our device, it was compared to a screen tech-
istics (diameter,  ow rate) under different conditions (particle nique throughout an intercomparison campaign conducted in a
concentration and radon activity concentration). The difference radon chamber (Huet 1999; CEC Report 1998).
between the two devices was of the order of the counting statis-
tics uncertainty, which thus made us sure that we collected the
total radon decay products.
Aerosol Measurements
In order to improve the system detection, we developed an
During the experiments, particle concentration was continu-
expression of the geometric efŽ ciency applicable to different ously measured using a diffusion battery TSI 3040 associated
Ž
Ž
lter-detectorconŽ gurations. For adistanceof 5mm between the with a condensation particle counter, TSI 3022A. The diffusion
lter and detector, the geometric efŽ ciency calculated according battery was composed of 11 stages. The particle concentration
241
to our expression and veriŽ ed with a standard source of Am was only measured after 0, 1, 6, 15, 28, and 55 screens. The  ow
¡1
was equal to 24% for the two sampling lines. Moreover, energy rate through the diffusion battery was 4 l min . Knowing the
losses of 6 and 7.7 MeV alpha particles were determined as a kernel matrix of the diffusion battery and the particle concentra-
function of their path in the air; it showed that for a 5 mm Ž lter- tion at the outlet of the six stages previously mentioned permit-
detector distance, only the 7.7 MeV particles emitted between ted us to reconstruct the number size distribution of the ambient
±
9.5 and 81.5 from the perpendicular of the Ž lter surface could aerosol using the EVE algorithm (Paatero 1990; Tapper 1995).
7

5
56
C. HUET ET AL.
Figure 3. Schematic diagram of our continuous system.
i
Air Exchange Rate
where c (1) is the constant activity concentration and ¸ is the
0
0
Radon exhalation and the ventilation rate of a room can be decay constant for radon.
derived from both the increase of the radon concentration by the
radon exhalation and the steady-state condition between exhala- RESULTS
tion and air exchange with the free atmosphere as described by
Porstend o¨ rfer et al. (1980). Once the room has been ventilated,
the increase of radon concentration can be written as
The house where our measurements were carried out con-
sisted of a ground  oor and a Ž rst  oor; it was equipped with
electric heating. Our experimental apparatus was placed in the
3
6
7 m furnished living room (ground  oor) whose surface-to-
¡1
E
volume ratio was about 1.95 m . This room had two large
windows and a door opening directly to a corridor.
c (t) D (1 ¡ e¡vt ) C c ;
i
a
0
[1]
0
v
i
a
where is c the indoor radon concentration, c is the outdoor
0
0
Air Exchange Rate
¡
3
¡1
radon concentration, E is the exhalation rate (Bq m
and v is the ventilation rate (h ). When t < 1=v, the radon
emanation is given by
h
),
The air exchange rate was determined according to the pro-
cedure described above. Figure 4 depicts a typical example of
the growth of radon activity concentration as a function of time
¡
1
after ventilation of the room. The slope of this curve gave us
i
1
c (t)
¡3 ¡1
0
an exhalation rate around 150 Bq m
h , corresponding to an
E D
:
[2]
¡
1
1
t
air exchange rate of 0.15 h . Additional measurements were
carried out and allowed us to determine that the air exchange
Considering a steady-state condition in the room, the venti-
lation rate can be determined using
¡1
¡1
.
rate was within 0.1 and 0.4 h for a mean value of 0.25 h
Although these results are in agreement with the range of values
¡
1
(
between 0.1 and 2 h )reported inthe literature (Grot and Clark
i
0
E ¡ ¸0c (1)
v D
;
[3] 1981; Grimsrud et al. 1983; Knutson 1988), the ventilation rate
in this room can be considered low.
i
0
a
0
c (1) ¡ c

MEASURED INDOOR RADON PRODIGY PROPERTIES
557
concentration could be explained by a pressure gradient from
inside toward outside that leads to a leak of radon.
Without artiŽ cial aerosol production, the particle concentra-
tion was quite low in this house. Usually, it ranged between 500
¡
3
¡3
and 5000 cm with a mean particle concentration of 1200 cm .
This low particle concentration can be attributed to both the low
air exchange rate, which does not bring particles from the out-
side, and the reduced human activity in the house. With aerosol
sources such as cigar and cooking smokes, fumigating sticks (in-
censesmoke), and burning candles, particleconcentration highly
¡3
increased to sometimes reach values around 1000000 cm
.
Unattached Fraction and Equilibrium Factor
With aged aerosol i.e., particle concentration between 500
¡
3
and 5000 cm , the unattached fraction of PAEC ranged between
.08 and 0.67 with a mean value of 0.31 (Table 1), calculated
from a series of 1000 data. The mean unattached fractions of
Figure 4. Increase of 222Rn activity concentration versus time
after ventilation.
0
2
18
214
Po ( fPo) and Pb ( fPb) were equal to 0.69 and 0.23, respec-
tively. Only 8% of the Bi was found unattached. The mean
2
14
Radon and Particle Concentrations, Ambient Conditions
Throughout the 12 month measurements, we noticed that the value of fp determined in the present study ishigh in comparison
±
room temperature remained stable at 20 C and the relative hu- to most of the data reported in the literature and the value of 0.08
commonly used in dosimetric models. Indeed, the unattached
fraction in indoor air is usually below 0.15 (Kojima and Abe
midity around 50%; these two parameters were both measured
with a Pt probe (SOLOMAT Ltd). All throughtout the year, we
observed variations of radon activity concentration within 240
1
988; Reineking and Porstend o¨ rfer 1990; Hopke et al. 1995).
¡
3
¡3
and 2800 Bq m with a mean value of 1420 Bq m . They were But one should note that in the places where these previous
induced by changes in atmospheric conditions. As a matter of measurements had been carried out, the particle concentration
was higher than in the dwelling mentioned above where the low
particle concentration obviously explains the high fp recorded.
As a matter of fact our measurements gave a mean equilibrium
factor of 0.16 (variation between 0.04 and 0.45), indicating an
fact, low radon activity concentrations were observed during
rainy and windy periods. Figure 5 illustrates the variations of
radon activity concentration and atmospheric pressure recorded
over a 5 day period. It clearly shows that high activity concen-
trations were obtained under high pressure conditions, i.e., with important disequilibrium between radon and its decay products.
an anticyclonic weather, whereas radon activity concentration With a low particle concentration it is rare to have attachment,
so radon decay products were mainly free and thus plated out on
surfaces, leading toa small equilibriumfactor. A typicalexample
of the variations of the unattached fraction, equilibrium factor,
and particle concentration is presented in Figure 6. For a particle
decreased with the arrival of a depression, usually accompanied
in Brittany with rain and wind. The decrease of radon activity
¡
3
concentration between 800 and 2800 cm , fp and F are in the
ranges 0.14 – 0.43 and 0.15– 0.34, respectively. This remarkably
illustrates the inverse behavior of these two parameters. More-
over, ithighlightsthat the amount of unattached fraction depends
more on particle concentration than on the equilibrium factor.
Table 1
Mean, maximum, and minimum values of unattached fractions
218
214
214
of PAEC, Po, Pb, and Bi and equilibrium factor
obtained with aged aerosol
Mean Maximum Minimum
Equilibrium factor
Unattached fraction of PAEC 0.31
Unattached fraction of Po
Unattached fraction of Pb
0.16
0.45
0.67
0.86
0.61
0.37
0.04
0.08
0.37
0
2
18
0.69
0.23
0.08
2
14
Figure 5. Variations of 222Rn activity concentration and at-
mospheric pressure.
2
14
Unattached fraction of Bi
0

5
58
C. HUET ET AL.
Figure 6. Variations of F, fp, and Z with aged aerosol.
Figure 8. Unattached fraction of PAEC versus particle con-
centration.
However, our resultsconcerning fp were comparable tothose
found by Li and Hopke (1991) in indoor air and Cheng et al.
1997) in caverns, where particle concentrations were in the
(
and 214Bi, but there was some free 218Po. Results analysis high-
lighted a possible distinction between the different aerosol sour-
ces: on the one hand, cooking activities and burning candles
and on the other hand, cigar smoke and fumigating sticks. As
a matter of fact, although cooking and candles produced a lot
of particles, the equilibrium factor was comparable to the one
found with aged aerosol when the particle concentration was
218
same range. A plot of the unattached fraction of Po versus
particle concentration (Figure 7), displaying their results and
ours, showed a good agreement between allthese measurements.
A deeper analysis of our fp measurements with aged aerosol
allowed us to establish the following relationship between the
unattached fraction of PAEC and the particle concentration (Z ),
fp D 400=Z; it is in agreement with previous suggestions by
Porstend o¨ rfer (1996) (Figure 8). This curve shows that between
¡
3
around 5000 cm . With cigar smoke and fumigating sticks, it
reached higher values. These data therefore suggest that cook-
ing and/or burning candles induce a production of particles in
the nucleation mode where attachment is lower than in the accu-
mulation mode. On the other hand, cigar and fumigating sticks
would produce particles in the accumulation mode, leading to a
greater attachment of nanometer radon decay products to these
particles. These hypotheses were conŽ rmed by the analysis of
the number size distributions obtained through the combination
of thediffusionbattery and CNC. As illustratedinFigure9, burn-
ing candles, like cooking, produced particles in the nucleation
range, whereas those produced by cigar smoke and fumigating
sticks were in the diameter range 160–200 nm. The in uence
¡
3
0
and 2000 cm a small change in the particle concentration
causes a high variation of unattached fraction. On the other hand,
¡3
when the particle concentration is above 3000 cm , the varia-
tions of the unattached fraction become negligible.
With aerosol sources, the unattached fraction became neg-
ligible (<5%) whereas the equilibrium factor was increased to
sometimes reach 0.75 depending on the source used (Table 2).
2
14
Under these conditions, there were nearly no unattached Pb
of aerosol sources on the unattached fraction and equilibrium
factor is illustrated in Figure 10.
Finally, Figure 11 shows a plot of the unattached fraction
versus the equilibrium factor with and without source. The con-
tinuous line corresponds to the correlation curve obtained be-
tween the two parameters mentioned above. One should note
a low dispersion on both sides of the line. Since the formula
¡
1:47
fp D 0:0195 £ F
expresses the relationship between fp
and F, it can now be used as a calculation model for dwellings
under typical domestic conditions. This formula was established
from a large set of data covering the whole range of variations
of the equilibrium factor (0.04–0.74) in opposition to the previ-
ous relationships established by Stranden and Strand (1986) and
Tokonami et al. (1996), which were restricted to a small number
of data and/or a short range of variations. Vargas et al. (2000) had
Figure 7. Comparison of unattached fraction of 218Po versus previously obtained a similar relationship from measurements
particle concentration.
performed in several Spanish houses.

MEASURED INDOOR RADON PRODIGY PROPERTIES
559
Table 2
Mean, maximum, and minimum values of particle concentration, unattached fractions of PAEC, 218Po, 214Pb, and 214Bi, and
equilibrium factor obtained with aerosol sources
Unattached
fraction of
PAEC
Equilibrium
factor
3
¡3
Z £10 cm
fPo
fPb
fBi
Cooking
250
80–500)
0.046
(0.01– 0.09)
0.18
(0.03 – 0.3)
0.017
(0– 0.09)
0
0.27
(0.15 – 0.4)
(
(0– 0.02)
Fumigating
sticks
100
(60– 450)
0.02
(0.01– 0.05)
0.069
(0.047– 0.17)
0.017
(0– 0.075)
0
0.49
(0.3– 0.59)
Burning
390
(100 –1,000)
0.032
(0.022– 0.047)
0.10
(0.01– 0.16)
0.023
(0.014 – 0.06)
0
0.31
(0.26 – 0.35)
candles
Cigar smoke
80
60–300)
0.024
(0.012– 0.039)
0.10
(0.07– 0.15)
0.001
(0– 0.007)
0.001
(0– 0.007)
0.56
(0.26 – 0.74)
(
MODEL-EXPERIMENT COMPARISON
period of concern; the variations of attachment rate and radon
Field measurements and physical process modeling consti- activity concentration are depicted in Figure 12. Free and at-
¡
1
tute two complementary approaches to study the behavior of tached deposition rates were set at 20 and 0.2 h , respectively,
radon decay products in indoor air. Unfortunately only few these values being recommended by Knutson (1988) for indoor
theory-experiment comparisons have been performed to check conditions. Following the hypotheses of a permanent regime and
models. The PRADDO model (Gouronnec 1995), an extension homogeneous atmosphere, the differential equations taking into
of the room model (Jacobi 1972; Porstend o¨ rfer et al. 1978), has account radioactive decay, deposition, attachment, recoil, and
already been tested in a town hall basement with a high particle ventilation processes were solved; new values of unattached,
concentration (Gouronnec et al. 1996). But this model was not attached, and deposited activity concentrations for each radon
validated for the nanometer radon decay products. That is why decay product, potential alpha energy concentration, unattached
we tried to check performance of the PRADDO model under fraction, and equilibrium factor were then obtained and com-
conditions of low ambient aerosol particle concentration.
For this purpose, the time period shown in Figure 6 was ex-
pared to the corresponding experimental ones.
The results dealing with total, attached, and free PAEC are
amined. The model input data were either Ž eld measurements depicted in Figure 13. During the analyzed period of time, the
¡
3
(
radon activity concentration, attachment rate, ventilation rate) total measured PAEC ranged between 1.5 and 2.8 ¹J m . One
218
or literature data (recoil probability of Po, free and attached should notice, Ž rst, that the calculated values follow the vari-
deposition rates, radioactive decay constants). Using the attach- ations of the experimental data. The model is thus capable of
ment theory we determined the attachment rates from the num- reproducing the changes in ambient conditions due to variations
ber size distributions obtained, as previously mentioned. Table 3 of radon activity concentration and/or particle concentration. It
gives the values of the input data used in our calculations for the
Figure 9. Example of number size distribution obtained with
burning candles.
Figure 10. Variation of F, fp, and Z with aerosol sources.

5
60
C. HUET ET AL.
Figure 11. Unattached fraction versus equilibrium factor un-
der domestic conditions.
Figure 12. Variation of 222Rn activity concentration and at-
tachment rate during the examined period.
appears also that the input values of 20 and 0.2 h 1, respec-
tively, for free and attached deposition rates are representative
of the considered dwelling. Moreover, there is a good agree-
ment between the two types of values with a mean deviation of,
respectively, 6, 5, and 11% for total, attached, and unattached
PAEC. As a consequence, the agreement for unattached fraction
and equilibrium factor is also quite satisfactory, as illustrated
in Figure 14. The mean deviation of experimental results from
theoretical data for the unattached fraction and the equilibrium
factor was 6 and 5.5%, respectively.
¡
It is then obvious that, with an aged aerosol, the PRADDO
modelfaithfullyreproduced our experimental resultsand demon-
strated its capability to satisfactorily describe the behavior of
nanometer radon decay products.
In a second step, the model was tested under all the conditions
investigated in the dwelling, i.e., with and without sources. So
Figure 13. Model-experiment comparison for total, attached,
and free PAEC with aged aerosol.
2
7 situations covering the whole range of variations observed
for unattached fraction and equilibrium factor were extracted
from our database. (i) Free and attached deposition rates and re-
2
18
coil probability of Po were identical to the values previously
¡
1
taken. (ii) Ventilation rate was either 0.2 or 0.25 h . (iii) At-
tachment rate and radon activity concentration ranged between
¡ ¡3
1
9
30 and 1.5 h and 400 and 1800 Bq m , respectively, as
illustrated in Figure 15.
The results of the model-experiment comparison for total ac-
218
214
214
tivity concentration of Po, Pb, and Bi are depicted in
Table 3
Input values of the PRADDO model with aged aerosol
Parameter
Value
222Rn activity concentration
Ventilation rate
Figure 12
¡1
0.15 h
20 h
0.2 h
0.83
¡
1
Free deposition rate
Attached deposition rate
Recoil probability of 18Po
Attachment rate
¡
1
2
Figure 14. Model-experiment comparison for unattached
fraction and equilibrium factor with aged aerosol.
Figure 12

MEASURED INDOOR RADON PRODIGY PROPERTIES
561
Figure 15. Variations of 222Rn activity concentration and at-
tachment rate for the 27 situations examined.
Figures 16, 17, and 18, respectively. For the three radon de-
cay products, there is good agreement between the calculated
218
and experimental data. However, the values calculated for Po
are greater than the experimental data, with a mean deviation
of 9.4% for a range of variations between 0.4 and 32%. The
most signiŽ cant deviations were obtained with high particle con-
Figure 17. Model-experiment comparison for total 214Pb ac-
tivity concentration.
centration, especially under cooking conditions. For 214Pb, the and the mean deviation was 6% for a variation within 0 and
calculated values were usually equal or below the experimen- 21%.
tal ones. The mean deviation was 10.7% for a variation range
On the whole, satisfactory results between calculated and
within 0 and 52%. Bi had the same behavior as the one ob- experimental values under different aerosol conditions were ob-
214
2
14
served for Pb, which means that the PRADDO model tends tained. Input parameters, particularly those taken from the liter-
to underestimate the experimental data; there was a mean de- ature, seem to be representative of the conditions of the dwelling
218
viation of 13.4% between experimental and calculated values. of concern. Nevertheless, overestimation of total Po activity
Finally, the results dealing with equilibrium factor are given concentration could be explained by an underestimation of the
in Figure 19. For the 27 experiments analyzed, it ranged be- free deposition rate with aerosol sources, which will conŽ rm
tween 0.08 and 0.75. A very good agreement was observed the observations made by Porstend o¨ rfer et al. (1987) and Li and
Figure 16. Model-experiment comparison for total 218Po ac- Figure 18. Model-experiment comparison for total 214Bi ac-
tivity concentration.
tivity concentration.

5
62
C. HUET ET AL.
sition rate with aerosol sources may be higher than the value
¡
1
of 20 h recommended by Knutson. However, the PRADDO
model is a good alternative to long-term measurements to cal-
culate the exposure required to assess the dose received by the
general population from input data like radon concentration,
particle concentration and size, and ventilation rate.
ACKNOWLEDGMENTS
This work was partially funded by the European Union under
contract FI4P-CT95-0025. We wish to thank Dr. Friocourt for
her assistance in the writing of an English manuscript.
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