2002 International Radon Symposium Proceedings

Accurate measurement of Rn decay product concentration ratios for
determining air exchange rate and Rn source in rooms
R. Rolle
Isotope Laboratory, Institute of Physical Chemistry, University of Goettingen
37077 Goettingen, Germany
<rrolle@gwdg.de>

MEASUREMENT RELEVANCE
The lung cancer risk from the (potential) alpha emission of inhaled radon decay products is
considered the main radiation burden of man. Mostly in situations of elevated potential alpha
energy concentrations (PAEC - working level WL) mitigation can bring meaningful long-term
exposure reduction. The exposure dynamics involve the rate constants
of the variabilit of the sources of ^ ~ nand " O h (+ external sources of decay products),
^Rn,(%
^pb, 2 1 2 ~ i
- decay ~ f ' ~ ~ R2n1,8 ~ o2,1 4 ~ 21413i,
b,
56s, ('17s), 10.6h, 60min
at ti/,: 3.8d, 3min, 27min, 20min
- attachment of the decay product unattached clusters to aerosol (@ size distribution),
- room air exchange (variable - 0.1 to 10 air changes per hour),
- inhalation rate and retention in the lung,
lung clearance rates of retained decay products.

-

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When attempting to relate measurements to relevant exposure conditions more detailed
information can be most useful and cost saving near or above prescribed action levels,
particularly for more critical or problematic mitigation decisions.
The lung concentrates the decay products continuously and this can be more realistically
simulated by concentrating and differentiating the individual decay products for measurement,
rather than by a sometimes poorly related gas measurement. When continuously concentrating at
a flow-rate f and efficiency ef a radionuclide with decay constant 1n2/ty:,then the concentrated
activity in the sample is equivalent to the activity in an effective source volume of air
ESV =f ef ty, 1.44 . For breathing rates and at a conventional sampling rate of e.g. ~ 2 l . m i n - l ,
this ESV, for the five decay products listed above, is far greater than the detection volume of a
non-concentrating gas monitor or the lung. Thus the sensitivity for continuous decay product
measurement is usually far greater than for gas measurement. In decay product measurement, as
for the lung, the sensitivity for ^PO, due to the short t&/7 s, is insignificant, while in gas
measurement P O within a second is in equilibrium with ^ ~ nand usually has the equivalent
gas monitor detection volume.

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A measurement is complete only when the measurement uncertainty is available. For
interdependent species the covariance matrix is required and allows uncertainty calculation of

2002 International Radon Symposium Proceedings
derived values. Good calibration is a prerequisite to obtain accurate results. Few available
measurement systems fulfil the needs for critical mitigation decisions and an attempt is made
below to indicate a way to better measurement.

FLOW STRING EVALUATION
The vast majority of 'PAEC' measurements are made with long-term integrating passive Rn gas
n
providing only a very coarse estimate of PAEC
detectors and charcoal 2 2 2 ~samplers,
exposures. From PAEC exposures of the individual decay products, split into (two or more)
aerosol size ranges, more realistic internal doses can be assessed. Conventionally with electronic
instruments only an approximated, combined PEAC external exposure is measured. In some of
the earliest methods of Rn decay product measurement for electronic instruments only a single
gross alpha measurement (SGAM) was converted to PAEC. With current technolow raw pa
spectral data, measured online, while concentrating decay products on a screen (or several
screens) and a filter, can readily be logged, together with ancillary data, at short intervals with
small portable equipment. The (offline) computational evaluation of this data, provides optimal
differentiation of varying individual decay product PAE concentrations or exposures, and
associated covariance matrix. Subordinate to this self-evident system, and not necessarily
ranking above optimised SGAM, lie any number of systems cum methods that use practically
comparable electronic instrumentation and computational power, yet deliver far inferior
exposure information and rarely provide statistical uncertainty.
The calculations involved in assessing sources, sinks and exposure situations are readily set up
from string equations for flow (or decay) systems as follows:
For a constant source Q (e.g. flux in atoms.~")to a single string with branching(*) flow/decay ^1

+--> N,, " + , and A,+ A*, =Ai
^'

N~ k~~

q

' - I

a;

- all string members at equilibrium (observation time t

ti/,of all string members) have -

-InNn -1)
(for a non-branching string Ai = A , :- @,,,+e

In a single tunnel the ventilation may be regarded as plug flow with negligible mixing across
plug boundaries and the concentrations in a plug are described without ventilation-branching
strings. In a room the air can be approximated as a well-mixed plug with ventilation (and surface
plate-out) branches.
Non-equilibrium string flows Nili for a steady flux
given by:

(I>]

starting at t=0 when all

......(&j = 1 for i=j, SIJ = 0 for i#j],

= 0 are

2002 International Radon Symposium Proceedings
0:
while in the absence of a flux and Ni>i,i=o=

The response, i.e. the integral flow or decays along the string, of member n over a period ta Ñ
for a constant flux <P\ from t = 0 to t b , starting with Ni* = 0 at t = 0, is :

&,

tb

4

- A , +6#,,
'

while the response of member n after terminating the flux at t b during time tc to t d is:

The above equations can, with stepwise time shifts, be cumulatively applied to step changes in
source fluxes and rate constants, and can thus, at adequately short time steps accommodate
arbitrary progressions. For a network of flows the individual string responses, divided by their Xi
to derive the Ni, are summed at the nodes and weighted proportionally for duplication of
common leading string sections. A measured response, that is the counts Ni in a particular
spectral regions of interest (ROI) and counting interval is related, by the (large number of) above
string calculations to all the relevant foregoing flux steps.
Shown in Fig. 1. is a simplified flow- or string scheme indicating relevant parameters in a Rn
(single) source 'room'. For consecutive rooms or with significant Rn and decay product activity
in the air intake, the decay product sources also need to be taken account of. They can usually be
measured independently at the transition location. For a measurable activity space profile in a
room the room can be evaluated as separate compartments.
Typically data from a continuous room measurement need to be evaluated as follows. A data set
is obtained from sampling ^PO, ^Pb and ^ ~ iconcentrations continuously and recording
spectral data, over a time period where these concentrations possibly vary significantly, i.e. the
fluxes @,, (onto a filter) vary with time. A plot of the 6 MeV spectral peak window, i.e. ROI
counts, vs. time will indicate the time steps over which the concentrations should be separately
evaluated; alternately regular short concentration intervals could be chosen. For presumably nonchanging concentrations the data could be evaluated for only a single concentration step as in
batch-, or grab-sampling measurement. In the evaluation of the data, every individually recorded
(ROI) count N is related, via filtration rate and efficiency, detection efficiency in ROI and either
of the last two response equations above, by a factor k to all the individual activity
concentrations in every concentration [ j] time step up to the end of that count:
Ni + ~i = k i , l ~ [ 2 1 g+~k ~i ,l2] ~ [ ~ ~ +.
~ ~..0+2ki,20x[~~~pbl]
]
+ ki.21~ [ ~ ' ~ P+..
b 2+] k i , ~ ~ x [ ~ ' ~ ~ i ~ ] + . .
= ? kiJxCj ,
(with possible additional components j, such as background ( 2 i 0 ~ ocount
)
rate, ^ ~ band ^ ~ i
concentrations). A weighted least squares calculation of all available Ni equations yields the

2002 International Radon Symposium Proceedings
individual concentrations for all the time steps, and the appropriate uncertainty evaluation yields
the covariance matrix. Other parameters, such as PAE concentrations, can then be derived from
these results.

OBSERVATIONS ON MEASUREMENTS AND SYSTEMS
In Fig. 2 the strong concentration dependence on air exchange rate of ^ ~ nand the lungexposure-relevant decay roducts for a room with a flux from a 10 kBq (emanating) ^ ~ aand a
lOkBq ^ ~ asource.vol' is shown. In Fig. 3, for the same air exchange range, the (potential
alpha ener ) equilibrium factor F for ^Rn is shown, as well as the activity ratios of 2 1 8 ~ o / 2 2 2 ~ n
and ^ ~ i 2/ 7 rPo. Estimation of PAE from a measurement of 222Rngas and a presumed F factor is
thus coupled with a substantial (systematic) uncertainty range at unknown air exchange rate. The
indicated measurement of individual Rn decay product concentrations, using almost comparable
electronic instrumentation to gas measurement, does not include this uncertainty for PAE, and
since the effective source volume is far greater than for gas measurement, the statistical
uncertainty is also far better than in gas measurement. Conversely, for the calculation of ^Rn
concentration from individual decay product measurements, for instance the two decay product
ratio curves in Fig. 3 show that the air exchange rate can readily be assessed form the measured
2 H ~ i / 2 i 8ratio.
~ o The 222Rnconcentration is then obtained via the ^PO concentration at this
exchange rate - probably at better accuracy than direct gas measurement.

f

The simplified example above can be extended, with more appropriate calculation and extension
of the string model, to the evaluation of the effective " ' ~ a source(s) and air exchange rates and
their time dependence in various environments. Using e.g. an inline screen and filter instrument,
the individual unattached and attached Rn decay product concentrations can be measured and the
attachment time-constants can be determined. Having assessed prevailing sources of Rn and
ventilation, and their time dependence, then the string calculations indicated above can be used
to model the effect of various choices of mitigation measures, and to choose the most cost
effective ones, and in stepwise implementation to verify their effectiveness. Mere Rn
concentration measurement would allow only far less objective mitigation.
In the a determination of Pb and Bi concentrations simultaneously, both are measured via
the same a emissions of Po and differentiation of the two concentrations is only feasible on the
basis of their sequential buildup and decay behaviour. With the halflife of Bi shorter than that of
Pb, when differentiating them by sequential a-measurement, the statistical precision of a
determination is seriously impaired. With current technology of Si-detectors and signal
amplification stable P-measurement can readily be included in the conventional a-spectrometric
measurement, improving the differentiation of individual decay product concentrations about
tenfold (Rolle and Lettner, 1998). When significant concentrations of only ^PO, ^ ~ band ^ ~ i
are present, then measurement by pa-spectrometry offers good differentiation of these, even
without the sequential buildup-decay manipulation of a measurement procedure, i.e. evaluation
of 3 unknowns from 3 ROIs (partially overlapping). Time sequences of the three concentrations
could be evaluated from continuously sampled and sequentially recorded pa-spectraROIs.
When in addition also significant concentrations of ^ ~ band ^ ~ iare present, then essentially

2002 International Radon Symposium Proceedings
only 4 spectral pa-ROIs are available for the 5 concentrations. Here quasi-continuous sampling
(%h on, !hh off) with sequential recording of pa-spectral data is a good choice for many
applications.
CALIBRATION O F RADON DECAY PRODUCT MONITORS
A measurement is no better than the underlying calibration permits.
Conventional calibration for Rn decay product concentration measurement may have sufficed in
the past for the applications used, but would not meet the accuracy requirements for the more
demanding measurement applications proposed here.
Airflow can normally be adequately controlled within a few percent while the aerosol retention
efficiency for prescribed filters usually exceeds 99%. Conventional a-detection efficiency
calibration was normally carried out using a metal disc with a thinly lated, Ion -lived a-emitter
of certified activity and matching active diameter. In a few instances '14Pb and 8 4 I3i activities on
measurement filters (and screens) were measured in both the monitor and by y-spectrometry
(traceable to national standards).
For an optimised filter and detector combination the a spectrum shows substantial, variable
spectrometric peak tailing. This results from energy loss of the emitted a-particles from the
collected activity to the active volume of the detector - roughly '13 each in the filter, the airgap
and the detector window. The aerosol particles partly penetrate the filter to depths that, in
continuous sampling, change with filter loading and aerosol consistency, thus modifying the
tailing and relative detection efficiency in adjacent spectrometric ROIs. This behaviour cannot be
accommodated with conventional fixed calibration factors.
An accurate a-calibration for filter and detector geometry has been developed, based on
analytical calculation of fractional solid angles for every sample element, as shown in Fig. 4, and
residual energy calculation in penetrating successive layers of filter, air and detector window.
Adjusting an initially unknown exponential depth distribution parameter for optimal fit to
measured spectral profiles provides the per channel or ROI detection efficiency for each emitted
a-energy calculated. Spectral tail shape matching over 4 decades of intensity has substantiated
the correctness of the computation. The a-absorption curves for different materials are available
from a SRIM package (the Stopping and Range of Ions in Matter Ziegler ef al. 198Y2000).
This calibration has been extensively used for measurement data sets with presumed nonchanging spectral tail shapes - incorporation with automated shape matching into the evaluation
of continuously recorded spectral data with progressive 'filter loading' is the next step.

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The p-detection efficiencies, in a common ROI above a lOOkeV threshold, for Rn-decay
products on a filter have to date been derived in measurement sequences where the a-calibration
and a-activities have been accurately determined. Experience with the computational a-

2002 International Radon Symposium Proceedings
calibration has provided inspiration to proceed also with the computation of p-detection
efficiencies, excluding the energy region below 1OOkeV.
To date for wire mesh screens, used for aerosol size-differentiating measurement, the p- and adetection efficiencies for ' " ~ b and ' " " ~ ihave been scaled from filter detection efficiencies (or
y-measurement). The ventilation applications outlined in this paper point out the need also for
more accurate calibration for screens. The considerably more cumbersome computation of
detector-subtended, solid angles for all the surface elements of a woven wire screen cell is in
progress. Additional impetus for this task has come from a very similar need, i.e. to determine
the recoil loss factor for screen collected ''*PO that a-recoil on decay to ^Pb. The neglect of this
factor has resulted in underestimating the concentration of unattached ^ ~ b , a species with
enhanced lung deposition.

CONCLUSIONS
Important metrology applications in Rn radiation protection are locating 'buildings' with
(potentially) high indoor (Rn) Rn decay product levels and making proper mitigating decisions.
A major application requires cost-effective screening measurements of adequate PAEC
precision. Another is in critical situations with a need, instead of mere ^ ~ nlevel measurement,
for cost-effective determination of Rn sources and air exchange rate, evaluated via room
modelling with input of decay product measurements of enhanced accuracy. Subsequently
mitigating options can be modelled more objectively for the most cost-effective reduction of
concentrations, and can be re-evaluated after (stepwise) mitigation. The instrumental requisites
for this decay product measurement are only marginally above those of commercially available
active monitors for Rn and/or decay products, and have been implemented on a batch of
instruments. A software package for concentration evaluation of the sequentially logged spectral
data has been developed, as well as a program for accurate a-calibration of filters. Forthcoming
software will extend the enhanced accuracy calibration to screens and for P-calibration. Beyond
this, a range of software to simplify the more elaborate combination of strings for system
evaluation is foreseen.

2002 International Radon Symposium Proceedings

REFERENCES
R. Rolle and H. Lettner: 'An analysis of efficient measurement procedures for radon progeny.'
Environment International, Vol. 22 Suppl. 1, pp. S585-S593, 1996.
Ziegler, J. F., Biersack, J.P., Littmark, U., 1985. The Stopping and Range of Ions in Solids,
Pergamon Press, New York.

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Figures -Note to editor: (The figure titles of figures 2 - 4 are in separate, transparent text
boxes). Figures 2 and 3 are screen copy-and-paste from an APL+win application. Please email
<rrolle@gwdg> if better resolution or different type size is required. Figure 4 is also available in
the attached Powerpoint File - renoppt2.ppt

Figure 1. Simple model string (flow) scheme showing transformation rate constants effective in a
room with a Rn source J^ and air exchange (short arrrows); Xu.= -attachment rate to aerosol, Xu.,v
to wall; ra, rw - recoil fractions. The sampling or 'breathing' section (left of dotted line) can
normally be treated independently, and the wall section would normally be considered a
refinement.

2002 International Radon Symposium Proceedings

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2

4

8

6

10

Air changesfh
Fig. 2. Effect of air exchange rate at a ^Rn and 22uRn
flux from lOkBq ^ ~ aand 1OkBq ^ ~ ainto a volume.
1

0.8
0.6

ratio
0.4
0.2

-

I

0

LI I I

0

I

2

I

I

I

4

I

I

I

6

I

I

I

8

-

I

1

IJ

10

Air changesk
Figure 3. Effect of air exchange rate in a room on the
Rn PAE equilibrium factor F, and on activity ratios
of ^ ~ n ,^PO and ^ ~ i .

2002 International Radon Symposium Proceedings

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Source

Figure 4. Solid angle and absorption path for calculation of a detection efficiencies.