Answer to Question #11973 Submitted to "Ask the Experts"

I have some questions regarding the answer to Q10245 submitted to the Health Physics Society (HPS) Ask the Experts. You indicate in Section (A) that assuming 7,000 hours spent indoors per year at home, 1 becquerel per meter³ (Bq m^-3) is equal to 0.0044 working level month (WLM). Could you please provide a worked calculation and a more detailed rationale with all the assumptions (e.g., dwelling occupancy factor) for the conversion of Bq m^-3 to WLM?

The US Environmental Protection Agency (EPA), for example, provides conversion factors for radon units, which states that "1 WL [working level] corresponds to radon progeny concentration in equilibrium with 100 pCi L^-1 [picocuries per liter] radon (3,700 Bq m^-3)."¹ What would be considered a typical WLM expressed in Bq m^-3 for a residential indoor radon exposure setting?

In addition, please can you clarify how to convert WL to WLM (or vice versa) directly in occupational/residential settings? How can an occupational WLM measurement be applied and converted to Bq m^-3 for a long-term residential exposure to indoor radon gas?

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¹ The radon concentration units are given here in pCi L^-1 (called traditional units), as well as WL and WLM (called special units), because these are the units used by the EPA. However, the Health Physics Society has adopted the International System (SI) units, which are given in parentheses (where appropriate).

This is a very timely concern as more and more people are testing their homes for radon and need help interpreting the results. The units are confusing with the international units (Bq m^-3) interspersed with conventional units (pCi L^-1) and then confounded by the special units (WL and WLM).¹

While radon had been identified as the cause of lung cancer in underground miners in the early 1900s, it was not until the 1950s that the decay products of radon, not radon itself, were determined to be the primary cause. The WL was introduced in the 1950s or thereabouts to address radon decay product concentrations in underground mine air. The relatively recent concern about indoor radon has resulted in use of the units for estimating exposure to members of the public derived from occupational radon exposure. (Note: There are several naturally occurring isotopes of radon. I use the term “radon” when referring to the gas, but I use the specific isotope radon-222 [²²²Rn] in the calculations because it is the radon isotope of concern for indoor exposures.)

Since I'm not sure how much background you have in radiation, please let me review the process y which ²²²Rn and its decay products (daughters) are generated. Radium-226 (²²⁶Ra) is produced by the radioactive decay of uranium-238 (²³⁸U), a natural constituent of the earth’s crust, through a series of decay products. ²²⁶Ra decays to a noble (inert) gas, ²²²Rn. Because it is a noble gas, radon diffuses through the soil to reach the atmosphere and is mostly breathed in and breathed out. ²²²Rn rapidly decays to solid decay products (polonium-218 [²¹⁸Po], lead-214 [²¹⁴Pb], bismuth-214 [²¹⁴Bi], and polonium-214 [²¹⁴Po]) that can be deposited in the lung. Because they have short half-lives, the decay products build up to the same radioactivity concentration in air as the ²²²Rn (that is, they are in equilibrium). The radioactivity concentrations of the short-lived decay products in air depend on the time since the radon was released into the atmosphere. In a closed environment, it takes about four hours for the decay products to reach 100% of equilibrium with the ²²²Rn.

When estimating the potential risk from radon, it is important to know the activity concentration of radon decay products. The WL unit was defined initially to express the ²²²Rn decay product concentration. One WL is the concentration of the short-lived decay products in equilibrium with 100 pCi L^-1 (3,700 Bq m^-3) of ²²²Rn; that is, 100 pCi L^-1 (3,700 Bq m^-3) each of ²¹⁸Po, ²¹⁴Pb, ²¹⁴Bi, and ²¹⁴Po.¹ (One WL is more precisely defined in international units as 2.08 × 10^-5 joules of alpha energy per meter³ of air [J m^-3], the amount of energy emitted by the short-lived decay products of ²²²Rn in equilibrium with 3,700 Bq m^-3 of ²²²Rn.) Thus, the concentration of radon decay products in WL depends on the "age" of the air; in other words, the time since the radon entered the atmosphere. The fraction of equilibrium can range from near zero immediately after the radon is generated to 100% after about four hours. The average equilibrium fraction for residences is approximately 0.4 (NCRP 2009) based on the ventilation rate but can be higher for energy-efficient homes that have a low air-exchange rate associated with energy-saving construction (tight homes).

For environmental atmospheres (indoor and outdoor), ²²²Rn gas is commonly measured and the concentration expressed in Bq m^-3. These measurements can be converted to WL if the equilibrium fraction is known or an average equilibrium fraction can be assumed. In the example that you gave, 1.0 Bq m^-3 can be converted to WL assuming an equilibrium fraction of 0.40 as follows:

Concentration in WL = (1.0 Bq m^-3)(0.40)(1 WL/3,700 Bq m^-3) = 0.00011 WL (2.2 × 10^-9 J m^-3)

The exposure to radon decay products is expressed in working level months (WLM). Initially, when this unit was derived, it was assumed that a miner would work for 170 hours per month (h month^-1). Thus the WLM is the exposure you would receive at a concentration of 1.0 WL for 170 h. Residential exposure times are much greater than 170 h month^-1. If you assume an individual spends 7,000 hours per year (h y^-1) indoors, approximately 80% of the year, at a radon concentration of 1 Bq m^-3, the exposure in WLM would be as follows:

Exposure in WLM = (0.00011 WL)(7,000 h y^-1)/(170 h month^-1) = 0.0045 WLM y^-1(1.6 × 10^-5 J h m^-3)

(Note that the comparable SI unit for WLM is J h m^-3, and 1 WLM = 0.0036 J h m^-3.)

The slight difference between the initial value you received of 0.0044 and the above calculation is due to rounding. The occupancy factor used in the calculation is dependent on the activity of the individual and is quite variable. For example, if a person works outside the home for the normal 2,000 h y^-1 and spends a reasonable amount of leisure time outdoors or away from home, the occupancy factor would be significantly lower. The 80% indoor occupancy is assumed by the U.S. Nuclear Regulatory Commission (NRC) in its draft guidance on calculating radon doses to members of the public (NRC 2014).

The US EPA estimates that the average US residential indoor radon concentration is 1.3 pCi L^-1 (48 Bq m^-3) (EPA 2016)¹. Assuming an average equilibrium factor of 0.40, a typical indoor radon decay product concentration would be as follows:

Concentration = (48 Bq m^-3)(0.40)(1 WL/3,700 Bq m^-3) = 0.0052 WL (1.1 × 10 ^-7 J m^-3)

A typical annual exposure would be as follows:

Exposure = (0.0052 WL)(7,000 h y^-1)/170 h month^-1 = 0.21 WLM y^-1 (0.00076 J h m^-3)

Health Canada published a report on a survey of Canadian homes but did not list an average concentration, just the percentage of homes that were below the guidance of 200 Bq m^-3 and in increments above that level (HC 2012). The Canadian guidance level is somewhat higher than the US EPA guidance level of 4 pCi L^-1 (150 Bq m^-3).¹

In doing the exposure calculation, it's important to remember how the WLM was initially derived using an assumption of 170 h month^-1 in the working environment.

If you are interested, the HPS has a position paper and a background document on indoor radon.

Jan Johnson, CHP, PhD
 

References
Health Canada. Cross-Canada survey of radon concentrations in homes—final report. 2012. Available on the Health Canada website.

National Council on Radiation Protection and Measurements. Ionizing radiation exposure of the population of the United States. Bethesda, MD: National Council on Radiation Protection and Measurements; Report 160; 3 March 2009.

Environmental Protection Agency. A citizen's guide to radon. Washington, DC: Environmental Protection Agency; EPA 402/D-12/002/2016; 2016.

Nuclear Regulatory Commission. Evaluations of uranium recovery facility surveys of radon and radon progeny in air and demonstrations of compliance with 10 CFR 20.1301.Washington, DC: Federal Register 79:17194–17195; 27 March 2014.
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¹ The radon concentration units are given here in pCi L^-1 (called traditional units), as well as WL and WLM (called special units), because these are the units used by the EPA. However, the Health Physics Society has adopted the International System (SI) units, which are given in parentheses (where appropriate).