Division of Compensation Analysis and 

Support Technical Information Bulletin

Document Number: 

DCAS-TIB-011 

Effective Date: 5/1/2013 

Revision No. 4

Lung Dose Conversion Factor for Thoron WLM Page 1 of 10 

Approval: Signature on file 

 J.W. Neton, Associate Director for Science 

 Date: _5/1/2013__ 

 

Supersedes: Rev 3 

RECORD OF ISSUE/REVISIONS

ISSUE 

AUTHORIZATION 

DATE

EFFECTIVE 

DATE

REV. NO. DESCRIPTION

3/16/2005 3/16/2005 0

New document to provide a basis for the 

conversion factor. 

4/15/2005 4/15/2005 1 Correction factors added for ET1 and ET2 regions 

1/13/2006 1/13/2006 2

Correction factors added for ET1 and ET2 regions 

for Radon 222 

1/4/2008 1/4/2008 3

Correction factors added for Radon 219 and 

calculation errors corrected. Minor editorial 

changes to text.

5/1/2013 5/1/2013 4

Added conversion factor for Radon 222 lung dose

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). It also 

provides conversion factors for Rn-222 and Rn-219. 

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. 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 2 of 10 

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 

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 66

1

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 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 3 of 10

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. 

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 66

1

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 

Birchall

2

describe an evaluation while Nikezic

3

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 James

4

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

5 

Nikezic et. al.

3

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.

6

performed a theoretical calculation that showed the unattached fraction 

for Rn-220 decay products to be approximately 1.6% for indoor air. 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 4 of 10

Porstendorfer

7

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. 

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.

3

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. 

Porstendorfer

7

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 James

4

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.

5

considering the best estimate to be 0.25 micron. 

ICRP 32

8

indicates the value between 0.2 and 0.3 micron. 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 5 of 10

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

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

Bi-212 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. 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. 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 6 of 10

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 32

8

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

9

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. 

6.0 Thoron Results 

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

default assumptions used in this report, a dose of 6.20 rem to the lungs will be assigned 

per WLM of Rn-220 decay products inhaled. Similarly, the default doses to the ET1 

region will be 943.83 rem and 0.45 rem to ET2. 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 

7.0 Radon 

A direct risk-based Rn-222 exposure model is available for lung cases in NIOSH-IREP. 

However the chronic lymphocytic leukemia (CLL) model requires the calculation of a 

lung dose from all sources including Rn-222. Table 3 provides the conversion factor but 

it should only be used for CLL dose calculations. This direct exposure model should 

continue to be used for Rn-222 exposures for lung cases. 

The LNet compartment was determined but not listed here. Due to the fact that there is 

no direct deposition in the lymph nodes and the short half-life of the radon progeny, no 

significant dose is received by the lymph nodes. The progeny undergoes significant 

decay before any of the material can reach the lymph nodes. 

% equilibrium 

(Bi212/Pb-212)

Lung dose (rem) 

per WLM

ET1 dose (rem) 

per WLM

ET2 dose (rem) 

per WLM

20% 5.77 913.92 0.23

40% 5.92 924.25 0.31

60% 6.06 934.21 0.38

80% 6.20 943.83 0.45
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 7 of 10

The Po-214 decay was not modeled separately. The energy emitted from this decay was 

added to the Bi-214 decays. This is due to the very short half-life of Po-214 

(approximately 0.16 msec). 

a) Model Parameters 

The absorption rate and particle size used for radon 220 were again used for radon 222. 

The unattached fractions used were 0.18, 0.021, and 0.0007 for Po-218, Pb-214, and Bi214 respectively. This was taken from a formula in NCRP Report 78

10

that equates 

unattached fractions to dust particle concentrations in the air. The particle concentration 

used was 1x10

4

particles per cm

3

, which equate to an overall unattached fraction of 8%. 

This fraction is the same reported by Nikezic et. al.

3

for indoor air. By comparison, 

Birchall and James

4

reported an unattached fraction of 1% for mine air. The dose 

conversion factor was determined to be higher for higher unattached fractions. Since the 

dust concentration is difficult to determine and the difference is not large (~15%) the 8% 

assumption was used. This should be an overestimate for most work sites. 

The equilibrium of the various radon 222 progeny also affects the conversion factor. 

However, this also affects the number of working levels the activity in the air will 

represent. These tend to be competing factors and cause the affect on this conversion 

factor to be relatively small. Three equilibrium fractions were investigated. Two from 

NCRP Report 78

10

and the third from Domanski

11

. The factors along with the associated 

overall equilibrium factor are shown in the table below. 

Table 2 – Equilibrium Factors for Radon 222 

NCRP 78 outdoor NCRP 78 indoor Domanski 

Po-218 0.9 0.5 0.656 

Pb-214 0.7 0.3 0.446 

Bi-214 0.7 0.2 0.259 

Overall 0.72 0.28 0.40 

The highest conversion factor for the ET2 compartment was produced by the NCRP 78 

outdoor factors. Given the small difference in factors, these fractions will be used as a 

slightly favorable assumption for all values of equilibrium. 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 8 of 10

b) Radon Results 

As a result of these parameters, the radon 222 conversion factors are listed in the table 

below. 

Table 3 – Dose Conversion Factors for Radon 222 

Conversion Factor

(Rem/WLM)

ET1 compartment 1793

ET2 compartment 6.09

Lungs a

15.69

a. Direct exposure model in NIOSH-IREP should be used for lung cases. The lung conversion factor should 

only be used for CLL cases. 

7.0 Radon-219 

Radon 219 conversion factors were determined only for the ET1, ET2, and lung 

compartments. The LNet and LNth compartments were determined but not listed here. 

Due to the fact that there is no direct deposition in the lymph nodes and the short half-life 

of the radon progeny, no significant dose is received by the lymph nodes. The progeny 

undergoes significant decay before any of the material can reach the lymph nodes. 

The Po-211 decay was not modeled separately. The energy emitted from this decay was 

added to the Bi-211 decays. This is due to the very short half-life of Po-211 

(approximately 0.516 sec). 

a) Model Parameters 

The absorption rate and particle size used for radon 220 were again used for radon 219. 

No specific information was found for the unattached fraction of radon 219. This 

fraction appears to be related the time the particles have to attach to dust particles and so 

is related to the half life. The unattached fraction for Po-218 was 0.18 due to its short 

half life of 3.05 minutes. Its progeny (Pb-214) has a half-life of 26.8 minutes leading to 

an unattached fraction of 0.021. The first progeny of radon 219 is Po-215 which has a 

half-life of 1.7 microseconds. Therefore the unattached fraction of Po-215 should be 

considered to be 1.0. The next progeny is Pb-211 with a half life of 36.1 minutes. This is 

slightly longer than Pb-214 which should result in a lower unattached fraction. Since the 

unattached fraction used for radon 220 progeny was 0.02 and this is slightly lower than 

Pb-214, this fraction was used for all the radon 219 progeny. 

The equilibrium of the radon 219 progeny has little affect on the conversion factor. The 

initial progeny (Po-215) has a very short half-life and therefore represents very few atoms 

in on working level. The next progeny (Pb-211) drives the composition of progeny in a 

working level. This decays to Bi-211 which has a 2.13 minute half-life then to Po-211 
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 9 of 10

which has a 0.516 sec half-life. Give the short half-lives of the progeny produced after 

Pb-211, it is reasonably to assume they are in 100% equilibrium with Pb-211. 

b) Radon-219 Results 

As a result of these parameters, the radon 219 conversion factors are listed in the table 

below. 

Table 4 – Dose Conversion Factors for Radon 219

Conversion Factor

(Rem/WLM)

ET1 compartment 1066

ET2 compartment 2.92

Lung 14.66
Division of Compensation Analysis and 

Support Technical Information Bulletin Document Number: DCAS-TIB-011 

Effective Date: 5/1/2013 Revision No. 4 Page 10 of 10

References 

1 ICRP Publication 66, Human Respiratory Tract Model for Radiological 

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

2 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) 

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

on the Calculated dose Conversion Factors for 

222

Rn Progeny. Journal of 

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

4 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) 

5 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). 

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

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

7 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) 

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

ICRP Vol. 6 No. 1 (1981) 

9 Pillai, P. M. B., Paul, A. C. Studies of the Equilibrium of 

220

Rn (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) 

10 NCRP (National Council on Radiation Protection and Measurements) Report No. 

78, Recommendations of the National Council on Radiation Protection and 

Measurements, Evaluation of Occupational and Environmental Exposures to 

Radon and Radon Daughters in the United States, Bethesda, Maryland, (1984) 

11 Domanski, T., “Correlation between the equilibrium factor F and the relative 

concentration of radon daughters in mine air”, Health Physics, Vol. 137, 177 

(1979)