**1. Introduction**

Radon (222Rn) and thoron (220Rn) are naturally occurring radioactive gases generated from the 238U- and 232Th-series. It is well known that radon and thoron are the biggest contributors to human radiation exposure from natural sources [1]. The World Health Organization (WHO) has recognized them as the second largest cause of lung cancer after smoking [2]. Indoor and outdoor radon and thoron concentrations vary widely from place to place depending on geological features and meteorological condition of an area (see, e.g., [3]). In general, indoor radon concentration is continuously supplied by a portion of outdoor radon, an infiltration rate of 10 Bq m−<sup>3</sup> h−<sup>1</sup> was reported [1]. In addition to the health effect assessment due to its inhalation, outdoor radon monitoring is useful in several scientific disciplines as a radioactive tracer. Its half-life of T1/2 = 3.82 days is comparable to the air masses' transit time across the major continents. Outdoor radon monitoring serves also on earthquake forecasting, geological faults identifications or ore

Y.; Suzuki, T.; Yamada, R.; Zhuo, W.; Kranrod, C.; Iwaoka, K.; Akata, N.; Hosoda, M.; Tokonami, S. Long-Term Measurements of Radon and Thoron Exhalation Rates from the Ground Using the Vertical Distributions of Their Activity Concentrations. *IJERPH* **2021**, *18*, 1489. https://doi.org/10.3390/ ijerph18041489

**Citation:** Modibo, O.B.; Tamakuma,

Academic Editor: Paul B. Tchounwou Received: 24 December 2020 Accepted: 30 January 2021 Published: 4 February 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

exploration, and environmental reprocessing in mining [4–7]. Some researchers have reported a positive correlation between outdoor radon concentration and radon exhalation rate from the ground [8–10]. Therefore, the exhalation rates of radon and thoron, which are often called flux or flux density, are useful parameters to understand human health risk due to radon and thoron inhalation, and many researchers have reported data obtained by field and experimental studies [11–14]. Generally, a common technique for exhalation rate measurement is based on placing an accumulation chamber on the ground surface to accumulate radon gas exhaling from the ground and using radon monitor to measure radon concentration and deduce radon exhalation rate, the technique has been applied for short- and long-term radon exhalation rate measurements [15]. However, it is difficult to evaluate both radon and thoron exhalation rates simultaneously using this method due to short half-life of thoron (T1/2 = 55.6 s). Alternatively, Zhuo et al. [10] reported on the long-term measurement technique of radon exhalation rate using a passive type radon and thoron discriminative monitor and a ventilated type accumulation chamber. However, their report did not evaluate thoron exhalation rate. It was reported that thoron activity concentrations from a source such as the materials of building walls and the ground have a unique distribution [16–19]. In the present study, long-term radon and thoron exhalation rates from the ground were simultaneously measured for a period of four years by applying the previously reported technique of ventilated type accumulation chamber [9]. From the results obtained, the seasonal variations of radon and thoron exhalation rates from the ground were discussed.

#### **2. Materials and Methods**

#### *2.1. Ventilated-Type Accumulation Chamber System for Measuring Radon-Thoron Exhalation Rates from the Ground*

A naturally ventilated accumulation chamber (0.8 × 0.8 × 1.0 m3) which is a stainlesssteel box with an open bottom was embedded 15 cm into the ground on the campus of the National Institute of Fusion Science (NIFS) located in Gifu Prefecture, Japan (N35.325◦, E137.168◦), as shown in Figure 1. Two rectangle openings (20 × 10 cm2) were perforated at the upper right and lower left walls of the stainless-steel box to get air ventilation, and each opening was covered on the inside side by a fiber filter (Whatman® No. 41) and the outside side by a rain/wind shelter. Thus, the change of particles (dust) outside cannot interfere with the inside environment of the stainless-steel box as the two openings are covered with filters. According to the report by Zhuo et al. [10], wind speed inside and outside of the ventilated accumulation chamber was monitored, and it was found that the inside wind speed could hardly be affected by the change of outside winds. Additionally, the air and soil conditions (pressure, temperature, relative humidity, and water potential) monitored simultaneously inside and outside of the stainless-steel box showed that except for the air humidity both the soil and air conditions inside and outside were nearly the same throughout the year, and it showed that the passive radon-thoron monitor used here is not affected by air humidity [10]. The vertical distributions of radon and thoron concentrations inside the accumulation chamber were obtained using a passive type radon-thoron discriminative monitor (RADUET, Radosys Ltd., Budapest, Hungary) [20]. The Raduets are composed of two different diffusion chambers of the same inner volume of about 30 cm3. The chambers are made of electroconductive plastic with a cylindrical form. The radon–thoron discrimination principle is based on the diffusion characteristics of each chamber. Radon in the air with its longer diffusion length is able to diffuse through an invisible air gap of one of the chambers located between its lid and bottom. Thoron can scarcely diffuse into that chamber with such a small pathway due to its very short half-life and lower diffusion length compared to that of radon. The second chamber has 6 holes of 6 mm of diameter opened at the side of the chamber which allow the diffusion of thoron as well as radon, the 6 holes are recovered by an electroconductive sponge to block the passage of charges particulate in the diffusion chamber [20]. The detection limits for the typical measurement period (3 months) were estimated to be 3 and 14 Bq m−<sup>3</sup> for radon and thoron, respectively [21]. The RADUETs were placed at heights of 1, 3,

10, 30, and 80 cm from the ground surface inside the accumulation chamber. For laboratory analysis, the RADUETs were exchanged every three months: spring, March–May; summer, June–August; autumn, September–November; winter, December–February. The solid-state track detectors (CR-39; BARYOTRAK, Nagase Landauer, Ltd., Tsukuba, Japan), which were installed in the RADUETs, were taken out and chemically etched for 24 h in a 6M NaOH solution at 60 ◦C [21]. The number of alpha tracks was counted using an optical microscope and image analysis software (ImageJ, National Institutes of Health, Bethesda, Maryland, USA). Radon and thoron concentrations were calculated according to the International Organization for Standardization (ISO) 16641 [22]. The conversion factors from track densities of CR-39s to radon and thoron concentrations had been already evaluated using the radon-thoron calibration chamber in Hirosaki University [23]. Environmental parameters of temperature, relative humidity and atmospheric pressure inside the accumulation chamber were measured continuously using a portable type meteorological monitor (TR-73U, T&D Corp., Matsumoto, Japan).

**Figure 1.** Photo and schematic drawing of the ventilation-type accumulation chamber system for measuring radon and thoron exhalation rates from the ground.

#### *2.2. Evaluation of Radon and Thoron Exhalation Rates Using the Ventilated Type Accumulation Chamber*

According to Zhuo et al. [10], the radon exhalation rate *E*Rn (mBq m−<sup>2</sup> s−1) obtained using the ventilated type accumulation chamber can be calculated by Equation (1).

$$E\_{\rm Rn} = 1000 \times C\_{\rm Rn} \times Z\_{\rm max} \times \frac{Q + \lambda\_{\rm Rn}}{3600} \tag{1}$$

Here, *C*Rn is the average radon concentration at each height (Bq m−3), *Z*max is the height of the chamber from the ground surface (=0.85 m), *Q* is air exchange rate in the accumulation chamber, and *<sup>λ</sup>*Rn is the decay constant of radon (7.6 × <sup>10</sup>−<sup>3</sup> <sup>h</sup><sup>−</sup>1). Air exchange rate in the chamber was evaluated using carbon dioxide (CO2) gas and a CO2 monitor (TR-76Ui, T&D Corporation). Generally, the air exchange rate is much larger than the decay constant of radon. Therefore, the decay constant of radon can be neglected (*Q* >> *λ*Rn,Q+ *λ*Rn ≈ *Q*).

According to the one-dimensional diffusion equation reported by Katase et al. [24], the thoron concentration *C*Tn(*z*) at a height *z* (m) above the ground is given by Equation (2).

$$C\_{\rm Tn}(Z) = \frac{E\_{\rm Tn}}{\sqrt{(Q + \lambda\_{\rm Tn})D\_{\rm e}}} \cdot \exp\left(-\sqrt{\frac{Q + \lambda\_{\rm Tn}}{D\_{\rm e}}} Z\right) \tag{2}$$

Here, *E*Tn is the thoron exhalation rate from the ground (Bq m−<sup>2</sup> s<sup>−</sup>1), *λ*Tn is the decay constant of thoron (44.9 h−1), and *D*<sup>e</sup> is the effective diffusion coefficient in free air (1.2 × <sup>10</sup>−<sup>5</sup> <sup>m</sup><sup>2</sup> <sup>s</sup>−1) [25]. In this study, the following exponential regression formula was applied to the vertical distribution of thoron concentration in each season for the simplified estimation of thoron concentration at 0 m.

$$C\_{\rm Tn}(Z) = \ a \cdot \exp(-bz) \tag{3}$$

Thoron concentration at the ground surface (*z* = 0 m) was estimated by Equation (3). Then, thoron exhalation rate *E*Tn (mBq m−<sup>2</sup> s−1) was evaluated by Equation (4) obtained by substituting *z* = 0 into Equation (2).

$$E\_{\rm Tn} = 1000 \times C\_{\rm Tn,0} \times \sqrt{D \cdot \frac{(Q + \lambda\_{\rm Tn})}{3600}}\tag{4}$$

Here, *C*Tn,0 is the thoron activity concentration at 0 m (Bq m<sup>−</sup>3).
