Office of Compensation Analysis and Support Document Number: OCAS-TIB-011

Technical Information Bulletin Effective Date: (3/16/2005)

Revision No. 0

Lung Dose Conversion Factor for Thoron WLM Page 1 of 7 

Approval:______________________ Date: ____________ 

 J.W. Neton, Associate Director for Science 

Supersedes: None 

RECORD OF ISSUE/REVISIONS 

ISSUE 

AUTHORIZATION 

DATE 

3/16/2005

EFFECTIVE 

DATE 

3/16/2005 

REV. NO. 

0 

DESCRIPTION 

New document to provide a basis for the 

conversion factor. 

1.0 PURPOSE

This Technical Information Bulletin provides the conversion factor for calculating lung 

dose from Rn-220 decay products measured in working level months (WLM). 

 

2.0 Background

EEOICPA uses the Interactive RadioEpidemiological Program (IREP) to determine the 

Probability of Causation (POC) that a cancer was caused by occupationally related 

radiation exposure. Annual radiation dose is the normal IREP input but in the case of 

radon, a direct exposure model is also included for lung cancers. The exposure model 

was based on studies performed at uranium mines and thus applies to Rn-222 and its 

associated decay products. Rn-220 (also known as thoron) decay products have 

characteristics that are sufficiently different from Rn-222 so that the exposure model is 

not applicable to thoron. However, thoron decay products are often measured in units of 

working levels. This requires the development of a conversion factor to express thoron 

working level exposures in terms of lung dose in rem. 

3.0 Working Level Definition

The majority of dose received from radon is actually derived from energy emitted by the 

decay products rather than the gas itself. Because of this, the dose per unit radon gas 

activity is greatly dependent on the state of equilibrium of the decay products. To better 

describe the hazard associated with radon, worker exposure has historically been 

expressed in terms of the decay product activity. The unit developed for this is the 

Working Level. A Working Level is described as the amount of short lived radon decay 

products in one liter of air that will ultimately decay with 1.3E5 MeV of alpha energy. 

When the decay chain reaches 100% equilibrium, one Working Level is equivalent to 

approximately 100 pCi/L of Rn-222 or 7.5 pCi/L of Rn-220. While this is a significant 
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Document Number: OCAS-TIB-011 Technical Information Bulletin

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difference in the gas concentrations, by definition of the working level, the decay 

products will ultimately emit the same amount of alpha energy. This, however, does not 

lead to the same lung dose. This is caused largely by the difference in the half-lives of 

the decay products. Since Rn-220 products have longer half lives, the body has longer to 

transport the activity from one compartment to another and thus deliver dose to different 

areas of the lung. 

Since the working level is an air concentration, it is analogous to an exposure rate. To 

describe exposure, the unit working level month (WLM) is normally used. A WLM is 

described as the exposure equivalent to breathing one WL for 170 hours (one working 

month). 

4.0 Calculation Method

The ICRP 664 lung model was used to determine the proper conversion factor of dose per 

WLM Rn-220. The model consists of 14 compartments. Material deposited in the lung 

is moved among these compartments as well as removed to the blood stream, the GI tract, 

and via extrinsic means. No absorption occurs in one compartment, (ET1). 

Default absorption rates are described as a combination of two rates, a rapid rate and a 

slow rate as well as the fraction of material that is absorbed rapidly. This requires the 

model to use 2 compartments for each of the 13 lung compartment from which absorption 

occurs. Therefore, the mathematical model consists of 13 rapid absorbing compartments, 

13 slowly absorbing compartments, and one other compartment for a total of 27 

compartments. 

To further complicate the model, Rn-220 decays to 5 important decay products and the 

model must be solved for each. This then requires a total of 135 mathematical 

compartments in order to solve the model. 

Each compartment can be solved analytically using simple first order differential 

equations. The solution to these equations becomes tedious when the compartment 

receives material that has passed through several compartments previously or has 

decayed through a chain of several nuclides to reach that point. Therefore, several 

simplifying assumptions have been made. Two of the decay products (Po-216 and Po212) have very short half-lives (<1sec). Po-216 was considered to be in equilibrium with 

Rn-220 gas. Po-212 is produced in 64% of the Bi-212 disintegrations and was therefore 

each Bi-212 decay was considered to also immediately produce a Po-212 decay. 

5.0 Model Parameters

The choice of parameters for the model is an important issue. There are numerous 

parameters to define. The ICRP defines default parameters for the majority and these are 

to be used unless more specific information is known about the particular situation. 
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Parameters chosen specifically for Rn-220 decay product inhalation are discussed in 

more detail below. The remaining parameters used the ICRP defaults. 

a) Absorption 

The ICRP 664 lung model defines three default categories for particulate lung absorption. 

These defaults are to be used unless more specific information is known about the 

situation at hand. In the case of radon decay products, a number of references are 

available indicating an absorption half-life of approximately 10 hours. Marsh and 

Birchall5

 describe an evaluation while Nikezic6 lists four separate references to this value. 

Therefore, the 10 hour half-life is used in this calculation. 

b) Unattached Fraction 

Radon decay products are normally electrically charged. This causes the products to 

quickly attach to particles normally in the air. This greatly affects the aerodynamic 

characteristics of these particles which in turn affects the deposition of the particles in the 

lungs. While unattached fraction is not specifically a parameter of the ICRP 66 lung 

model, the aerodynamic parameters are. 

Birchall and James1

 used an unattached fraction of 1% based on a report by Samet et. al.9 

Nikezic et. al.6 used 8% apparently based on the same report. The largest difference 

appear to be that Birchall and James attempted to describe typical mine air while Nikezic 

attempted to describe typical household air. It should also be noted that both reports were 

describing Rn-222 decay products. The unattached fraction of Rn-220 decay products 

can be different due to the greatly different half-lives of the products. The Rn-220 

products have longer half-lives and thus a longer period of time for the attachment to 

occur. 

Yamasaki et. al.10 performed a theoretical calculation that showed the unattached fraction 

for Rn-220 decay products to be approximately 1.6% for indoor air. 

Porstendorfer8

 demonstrated showed the unattached fraction depends on the 

concentration of particulates in the air. He also showed that the unattached fraction of 

Rn-220 decay products is smaller than that of Rn-222 decay products. His values match 

well with each of the references above therefore, this calculation will use a value of 2%. 

It is likely that the dust concentration in a work environment is higher than in a dwelling 

and thus the unattached fraction should be lower for the work environment. Therefore, 

when Yamasaki’s value of 1.6% is considered, the 2% unattached fraction should be 

slightly high for a standard work environment. This can be shown to be a slight 

overestimate of dose conversion factors but with the percentages so low, it appears to be 

a reasonable. 
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c) Particle Size 

The ICRP recommends a default particle size of 5 micron for a working environment and 

1 micron for members of the public exposed to environmental releases. In both cases, 

these particle sizes are the median of a lognormal distribution of particle sizes. The 

default geometric standard deviation (GSD) is 2.5, the default density is 3 g/cc and the 

default shape factor is 1.5. This calculation uses all these defaults with the exception of 

the particle size. 

The particle size distribution affects the regional deposition of the aerosol in the lungs. 

This size is greatly affected by the unattached fraction. The fraction that is attached to 

other particulates can exhibit the aerodynamic characteristics of the larger particle to 

which it is attached. The unattached fraction, on the other hand, represents very small 

particles produced from the noble gas (radon). 

Nikezic et. al.6

 indicated a particle size distribution for the attached fraction of 0.2 micron 

with a GSD of 2.35 while the unattached fraction was 0.0015 micron with a GSD of 1.1. 

Porstendorfer8 indicated particle sizes for various environments. The unattached median 

particle sizes ranged from 0.00013 micron to 0.0013 micron with GSDs ranging from 1.1 

to 1.3. For the attached fraction, the major contribution (~86%) exhibited median particle 

sizes of 0.33 micron for outdoor air and 0.217 micron for indoor air. Most of the 

remaining distribution exhibited a median size of ~0.040 micron. The GSD for these 

distributions varied from 1.5 to 2.2. 

Birchall and James1 indicated that the available data of attached aerosol size in 

underground uranium mines indicates a particle size between 0.15 micron and 0.5 micron 

with Samet et. al.9

 considering the best estimate to be 0.25 micron. 

ICRP 323

 indicates the value between 0.2 and 0.3 micron. 

Based on the references above, this calculation will use a median particle size of 0.25 

micron for the attached fraction. A size of 0.0015 micron will be used for the unattached 

fraction. The ICRP 66 default value of 2.5 will be used for the geometric standard 

deviation. 

 

d) Equilibrium 

The last major factor to consider is the state of equilibrium exhibited by the decay chain 

inhaled. The decay chain of Rn-220 is shown below. 

Rn-220 55.6 sec Alpha decay 

Po-216 0.15 sec Alpha decay 

Pb-212 10.64 hours Beta decay 
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Document Number: OCAS-TIB-011 Technical Information Bulletin

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Bi-212 60.6 min Alpha decay (36%), Beta dcay (64%) 

Po-212 304 nsec Alpha decay 

Tl-208 3 min Beta decay 

When the chain is in 100% equilibrium, the activity of each generation is equal. 

However, the number of atoms required to reach this equilibrium activity varies 

depending on the half-life. Since the working level is defined by the ultimate energy 

released, it is affected by the number of atoms more than the total activity in a mixture. 

The alpha energy is emitted only by Po-216 and essentially Bi-212. In reality Bi-212 

emits an alpha only 36% of the time but the other 64% of the time it emits a beta then an 

alpha almost immediately through the decay of Po-212 (304 nsec half-life). The average 

alpha energy released by a Bi-212 decay is then 7.8 MeV (6.07 Mev * 0.36 + 8.785 MeV 

* 0.64). Since Po-216 ultimately decays by two alphas (Po-216 and Bi-212) the alpha 

energy released per Po-216 atom is 14.6 MeV. Pb-212 and Bi-212 both decay with an 

effective alpha energy of 7.8 MeV. Po-212 decays with an energy of 8.785 MeV and Tl208 decays by beta decay only. 

The largest number of atoms associated with the chain in equilibrium are Pb-212 and Bi212 due to the relatively long half-lives. The remaining nuclides contribute little to the 

WL measurement or the lung dose. 

Since Pb-212 has a half-life approximately 10 times larger than Bi-212, the number of 

Pb-212 atoms in an 100% equilibrium mixture is approximately 10 times that of Bi-212. 

This causes Pb-212 to be the primary contributor to the WL measurement regardless of 

the degree of equilibrium. On the other hand, Pb-212 atoms inhaled have more time to be 

removed from the lungs prior to emitting all energy that will ultimately be emitted by the 

remainder of the decay chain. This causes Pb-212 to produce less lung dose per unit 

activity inhaled than that of Bi-212. Therefore, while the amount of Pb-212 in air drives 

the WL measurement, the amount of Bi-212 in air is a large contributor to lung dose. 

This causes the degree of equilibrium to be an important parameter. A good 

measurement of this degree of disequilibrium is the ratio of Bi-212 to Pb-212. 

The degree of equilibrium depends entirely on the circumstances surrounding the 

production and movement of the Rn-220 gas in the breathing zone. This cannot be easily 

predetermined but a range of likely values can. 

ICRP 323

 indicates this ratio (Bi-212 to Pb-212) is between 0.2 and 0.8. Pillai and Paul7

indicate the ratio is between 0.11 and 0.37 in a monazite mine and 0.24 to 0.84 in open 

air. This calculation will use 0.8 as a default value but also provide values for a range of 

equilibrium values. This will allow the most appropriate value to be used for the 

particular circumstances. 
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Document Number: OCAS-TIB-011 Technical Information Bulletin

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6.0 Results

The ICRP 66 lung model was solved using the assumptions described above. Under the 

default assumptions used in this report, a dose of 7.61 rem to the lungs will be assigned 

per WLM of Rn-220 decay products inhaled. This value should be considered to be 

received entirely in the year the material was inhaled. 

The values for different degrees of equilibrium were also calculated and are provided in 

the table below. The degree of equilibrium is specified by the ratio of Bi-212 activity to 

Pb-212 activity. These values can be used is information for the specific situation is 

available. 

Table 1 - Dose per WLM inhaled for various degrees of Equilibrium

% equilibrium (Bi-212/Pb-212) Lung dose (rem) per WLM 

20% 4.04

40% 5.27

60% 6.46

80% 7.61
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Document Number: OCAS-TIB-011 Technical Information Bulletin

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7.0 References

1. Birchall A., James A. C., Uncertainty Analysis of the Effective Dose per Unit 

Exposure from Radon Progeny and Implications for ICRP Risk-Weighting 

Factors. Radiation Protection Dosimetry vol. 53, pp 133-140 (1994) 

2. Hursh, J. B., Schraub, A., Sattler, E. L. and Hofmann, H. P. Fate of 212Pb Inhaled 

by Human Subjects. Health Physics 16, 257-267 (1969) 

3. ICRP Publication 32, Limits for Inhalation of Radon Daughters by Workers. 

ICRP Vol. 6 No. 1 (1981) 

4. ICRP Publication 66, Human Respiratory Tract Model for Radiological 

Protection. ICRP Vol. 24 No. 1-3 (1994) 

5. Marsh J. W., Birchall A., Determination of Lung-To-Blood Absorption Rates For 

Lead and Bismuth which are Appropriate for Radon Progeny. Radiation 

Protection Dosimetry vol. 84, No. 4, pp 331-337 (1999) 

6. Nikezic D. Haque A. K. M. M., Yu K. N. Effects of Different Deposition Models 

on the Calculated dose Conversion Factors for 222Rn Progeny. Journal of 

Environmental Radioactivity vol 61, issue 3, pp. 305-318 (2002). 

7. Pillai, P. M. B., Paul, A. C. Studies of the Equilibrium of 220Rn (Thoron) and its 

Daughters in the Atmoshphere of a Monazite Plant and its Environs. Radiation 

Protection Dosimetry vol. 82, No. 3, pp 229-232 (1999) 

8. Porstendorfer J., Physical Parameters and Dose Factors of the Radon and Thoron 

Decay Products. Radiation Protection Dosimetry vol. 94, No. 4, pp 365-373 

(2001) 

9. Samet, J. M., Albert, R. E., Brain, J. D., Guilmette, R. A., Hoopke, P. K., James, 

A. C., and Jaufman, D. G. Comparative Dosimetry of Radon in Mines and Homes. 

National Academy Press (1991). 

10. Yamasaki, T., Guo, Q., Jida, T. Distributions of Thoron Progeny Concentrations 

in Dwellings Radiation Protection Dosimetry vol. 59, No. 2, pp 135-140 (1995)