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The method of thoron progenies evaluation

1. Introduction

The Radon Daughter Monitor (RDM) measures also the Potential Alpha Energy Concen­tration (PAEC) of thoron (Rn-220) decay products. It uses continuous sampling and alpha spectroscopy. This method does not need any calibration chamber. It is similar to methods controlling such a chamber.
The evaluation of thoron PAEC uses the 8.8 MeV alpha radiation of Po-212. There is no influence of the thoron reading by Rn-222 progenies (maximum alpha energy of 7.7 MeV).
Because of the used technique the separation of different thoron decay products is not possible. That is, the instrument does not give individual results for Pb-212 and Bi-212. Additionally it cannot estimate the Rn-220 gas concentration as it does for Rn-222.

2. Evaluation algorithm

The activity of the nuclides at the surface of the sampling filter increases during sampling. Therefore also the calibration factor of the instrument changes continuously. The is taken into account by the evaluation software. During a measurement the RDM simulates collection and decay of the radioactivity on the sampling filter of the instrument. That is, it solves the differ­ential equations describing this process in real time using the actual, measured air flow rates. The simulation calculates an alpha count for a predefined fixed PAEC. The registered alpha counts of the Po-212 activity at the filter is compared with the simulated alpha counts. The actual PEAC is calculated from both counts and the predefined PAEC.
The tables in the appendix show the calculated filter activities and alpha counts. The tables are created by exactly the same algorithm as used in the RDM.

3. Assumptions

The calibration factor of the RDM is the ratio of alpha counts and the Potential Alpha Energy Concentration in the air. It is influenced by the sampling time, the air flow rate, and the mix­ture of thoron decay products. There exist two main decay products in the environmental air: Pb-212 and Bi-212. The concentration ratio R = [Bi-212]/[Pb-212] depends on the age of the air and their wall deposition rates. That is, in living rooms the ratio depends on the ventilation rate and the plate out at the walls and the furniture.
The concentration ratio is in the order of R = 0.5. The radioactive equilibrium (R = 1) is unrealistic for buildings.
For relative short sampling times (up to 6 h) the concentration ratio influences the reading of the RDM significantly. For longer sampling times the reading is independent from the mix­ture ratio.
The standard software of the RDM assumes a ratio R = 0. Therefore it overestimates the PAEC for short sampling times. This is done for radiation protection purposes. The instru­ment displays never less than the real PAEC. On request the RDM uses any other ratio. The most realistic results are given for R = 0.5.
Table 1 shows the expected and the maximum systematic deviations. The expected deviation is the reading at R = 0 compared with R = 0.5. The maximum deviation is the reading at R = 0 compared with R = 1. The data are taken from the tables in the appendix.

Table 1
Expected and maximum errors of the RDM for counting intervals of 2 h
Counting interval	Expected deviation	Maximum deviation
0 h - 2 h	1.9	2.8
4 h - 6 h	1.2	1.3
10 h - 12 h	1.05	1.1
22 h - 24 h	1.01	1.03
46 h - 48 h	1.00	1.01

4. Lower detection limit

The tables of the appendix include also information about the lower detection limit for thoron progeny. The tables are calculated for typical operating conditions of the RDM.
The lower detection limit depends on the user-selected counting time interval and the time of counting after the start of a measurement. The examples in table 2 are calculated for 10 registered alpha counts during the counting time interval. This corresponds with a mean error (standard devia­tion) of ± 33%.

Table 2
Lower detection limit of the RDM for thoron progeny
Counting interval	Working level	MeV / l
0 h - 2 h	0.001	150
0 h - 4 h	0.0002	25
4 h - 6 h	0.0001	15
10 h - 12 h	0.00006	7
22 h - 24 h	0.00003	4
46 h - 48 h	0.00003	4

5. Time resolution

Sometimes the concentrations of radon (Rn-222) and thoron (Rn-220) in buildings vary dra­matically from one day to the next. Therefore a minimum measuring time of several days is recommended. For such a long period the RDM suits best.
The half life time of Pb-212 is 10.6 h. Therefore the time resolution for thoron progeny is somewhere between 10 h and 20 h. Short pulses of PEAC are not directly recognized by the instrument. But they are taken into account precisely in the long-term mean values.
Also much shorter measuring times than 10 h are possible because the evaluation software adjusts its calibration factor dynamically. All actual calibration factors of the instrument are outputted on request.