Answer to Question #10245 Submitted to "Ask the Experts"

I'm a little bit confused with the calculation of working level month (WLM). Would you explain it to me?

In the early days of uranium mining, a radon concentration of 100 picocuries per liter (pCi L^-1) was adopted as a limit value (note that pCi is a traditional unit; today the Health Physics Society uses International System [SI] units of becquerels per cubic meter [Bq m^-3]). When it was realized that most of the lung dose came from the radon progeny (called daughters in those days), not the gas, a new limit value was introduced, the working level (WL). This was based on the energy that inhaled progeny would deposit in the lung.

In old uranium mines, the ventilation was often poor, and the radon progeny were close to equilibrium with the radon. The progeny in equilibrium with 100 pCi L^-1 (3,700 Bq m^-3) radon gas would release approximately 130,000 megaelectronvolts (MeV) of alpha energy in decay, so the WL was defined as:

1 WL = 130,000 MeV alpha energy per liter of air = 0.0208 millijoules (mJ) alpha energy per cubic meter (m³) air (mJ m^-3)

The nominal working hours per month for a miner at that time was 170, so the working level month (WLM) was introduced to simplify record keeping.

WLM = 1 WL exposure for 170 hours

1 WLM = 170 x 0.0208 = 3.54 mJ h m^-3 

17,000 pCi h L^-1 radon = 629,000 Bq h m^-3 radon = 1 WLM

1 pCi h L^-1 = 37 Bq h m^-3 = 59 microWLM (µWLM)

If measurements are made of radon progeny concentration, the average concentration over time can be directly converted to WLM. However, if radon gas is the measured quantity, then the question of progeny equilibrium affects the estimate. In many buildings the progeny concentration is only about 40% of the equilibrium value, so the conversion factor there would be 1 pCi h L^-1 = 37 Bq h m^-3 = 24 µWLM.

In addition, most radon measurement devices measure over the entire day, so in the case of workplaces that are only occupied for part of the day, an additional correction may need to be applied.

This is shown in the following information from International Commission on Radiological Protection 65 (ICRP 1993).

Conversion of radon exposure units (equilibrium factor = 0.40)

1 WLM = 3.54 mJ h m^-3

1 megabecquerel hour per cubic meter (MBq h m^-3) = 2.22 mJ h m^-3

1 MBq h m^-3 = 0.628 WLM

Annual exposure from measured radon concentration

(A)   At home: assuming 7,000 hours spent indoors per year

1 Bq m^-3 = 0.0156 mJ h m^-3

1 Bq m^-3 = 0.0044 WLM

1 WLM = 4 millisieverts (mSv)

1 mJ h m^-3 = 1.1 mSv

(B)   At work: assuming 2,000 hours work per year

1 Bq m^-3 = 0.00445 mJ h m^-3

1 mJ h m^-3 = 1.4 mSv

1 WLM = 5 mSv
 

Arthur Scott, PhD

Reference
International Commission on Radiological Protection. Protection against radon at home and at work. Oxford: Pergamon Press; ICRP Publication 65; Ann ICRP 23(2); 1993.