### Introduction

^{222}Rn, is an alpha-emitting radioactive substance which belongs to the decay chain starting from

^{238}U and has a half-life of 3.8 days. Since radon is a noble gas in nature and the half-life of radon is longer than that of isotopes

^{220}Rn (55 seconds) and

^{223}Rn (3.96 seconds), it can escape and diffuse from the earthly rock and soil to the air by diffusion and pressure difference. It is considered to be the second reason of death caused by lung cancer [1] because inhaled radon and its daughter product can irradiate the lung [2]. Radiations are carcinogenic. For human being, naturally-occurring

^{222}Rn is a common source of radiation exposure from inhaled and tissue-deposited radionuclides, and the

^{232}Th exposure which occurs in soil, is less common. Cancers associated with exposure to particular nuclides, usually in an occupational context, include lung cancer, bone sarcomas, liver cancer, leukemia and thyroid cancer [3].

### Materials and Methods

### 1. Soil Exhalation Rate Measurement

Choosing and locating the measuring point.

Recording the location of the measuring point.

Preparing the surface to be investigated if necessary by removing for example, rock, roots, and grass.

Installing the soil surface emission chamber on the surface of the soil under investigation.

Setting the RAD7 in place.

Purging the accumulation container with radon-free air.

Making air tightness between the container and the surface under investigation.

Performing the accumulation of radon in the container.

Monitoring the variations of the radon activity concentration measured by the RAD7 for a period of measuring time.

Recording the date and time of the accumulation process.

Reading the data (radon activity concentration) recorded during the accumulation process.

Calculating the surface exhalation rate.

^{−1}. Inside the RAD7 the key alpha spectrometer is a passive implanted planner silicon (PIPS) detector and in normal mode the RAD7 achieves better precision by counting

^{218}Po and

^{214}Po alpha peaks. In sniff mode only, the peaks from

^{218}Po are counted. As shown in Table 1 the total volume of the closed system was about 1.93 L and the area of surface chamber was about 366 cm

^{2}.

### 2. Balance Equation

^{−2}· s

^{−1}), from the soil surface is assumed constant, the changes in C (t), the radon concentration of the system in Bq · m

^{−3}, can be expressed with the radon influx term and the decay term as given in Equation 1. The radon exhalation rate is also expressed as E

_{A}(atom · m

^{−2}· s

^{−1}) in terms of the atom. In real cases, one should consider two more terms which account for leakage effect and back-diffusion in Equation 2. Two constants of leakage effect and back diffusion, λ

_{l}and λ

_{b}, have the same dimension (s

^{−1}) as physical decay constant λ. For leakage effect, we may assume that the outside radon concentration C

_{out}is zero because it will remain very small (near to zero) when compared with detecting system radon or soil radon concentrations. With this assumption (C

_{out}=0) and an initial zero condition, Equation 3 is the solution to the differential equation and well describes the radon concentration of detecting system as a function of time during measurement. And V (m

^{3}) is certain volume of detector chamber and soil surface area of chamber is used as S (m

^{2}).

##### (1)

$$\frac{\text{dC}}{\text{dt}}=\frac{\mathrm{\lambda}\xb7{\text{E}}_{\text{A}}\xb7\text{S}}{\text{V}}-\mathrm{\lambda}\xb7\text{C}=\frac{\text{E}\xb7\text{S}}{\text{V}}-\mathrm{\lambda}\xb7\text{C}$$##### (2)

$$\frac{\text{dC}}{\text{dt}}=\frac{\text{E}\xb7\text{S}}{\text{V}}-\mathrm{\lambda}\xb7\text{C}-{\mathrm{\lambda}}_{\text{l}}\xb7(\text{C}-{\text{C}}_{\text{out}})-{\mathrm{\lambda}}_{\text{b}}\xb7\text{C}$$##### (3)

$$\text{C}(\text{t})=\frac{\text{E}\xb7\text{S}}{\text{V}\xb7(\mathrm{\lambda}+{\mathrm{\lambda}}_{\text{l}}+{\mathrm{\lambda}}_{\text{b}})}\left(1-{\text{e}}^{-(\mathrm{\lambda}+{\mathrm{\lambda}}_{\text{l}}+{\mathrm{\lambda}}_{\text{b}})\xb7\text{t}}\right)$$### 3. Exhalation Rate Acquisition from Fitting

#### 1) Linear Fitting

##### (8)

$$\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}=\sqrt{{\left(\frac{{\mathrm{\sigma}}_{\text{A}}}{\text{A}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{V}}}{\text{V}}\right)}^{2}+\left(\frac{{\mathrm{\sigma}}_{\text{S}}}{\text{S}}\right)}$$##### (9)

$${\left(\frac{{\mathrm{\sigma}}_{\text{A}}}{\text{A}}/\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{V}}}{\text{V}}\hspace{0.17em}\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{S}}}{\text{S}}\hspace{0.17em}\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}=1$$#### 2) Exponential Fitting

##### (11)

$$\begin{array}{c}\text{k}=\mathrm{\lambda}+{\mathrm{\lambda}}_{1}+{\mathrm{\lambda}}_{\text{b}}\\ \text{E}=\frac{\text{B}\xb7\text{k}\xb7\text{V}}{\text{S}}\end{array}$$##### (12)

$$\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}=\sqrt{{\left(\frac{{\mathrm{\sigma}}_{\text{B}}}{\text{B}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{V}}}{\text{V}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{k}}}{\text{k}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{S}}}{\text{S}}\right)}^{2}}$$##### (13)

$${\left(\frac{{\mathrm{\sigma}}_{\text{B}}}{\text{B}}/\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{V}}}{\text{V}}/\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{k}}}{\text{k}}/\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}+{\left(\frac{{\mathrm{\sigma}}_{\text{S}}}{\text{S}}/\frac{{\mathrm{\sigma}}_{\text{E}}}{\text{E}}\right)}^{2}=1$$### Results and Discussion

^{−3}.

### 1. Linear Fitting

^{−2}· s

^{−1}and the range of E

_{A}was 2.139–2.316 atom · cm

^{−2}· s

^{−1}.

### 2. Exponential Fitting

^{−2}· s

^{−1}and E

_{A}was ranged of 2.27–3.48 atom · cm

^{−2}· s

^{−1}, unlike that of linear fitting, it does not change greatly depending on the measurement interval or time. However, the relative measurement uncertainty decreases with the measurement time increase, 17.65% for 2 hours, 11.00% for 3 hours, and 9.05% for 4 hours. For relative uncertainty level below 15%, 3 hour measurement was chosen that had E range of 51.6–69.2 mBq · m

^{−2}· s

^{−1}and E

_{A}2.46–3.30 atom · cm

^{−2}· s

^{−1}. For better result of measurement, below 10% relative uncertainty, 4 hours and more measurement time is needed or about 51.3–68.2 mBq · m

^{−2}· s

^{−1}and E

_{A}2.45–3.25 atom · cm

^{−2}· s

^{−1}. Exponential fitting had four parameters which were B, V, k and S. The most contributor to uncertainty of E is k that charged the average of 75.1% and the uncertainty contributions were 13.4%, 8.7%, and 2.9% for B, V, and S, respectively.

### 3. Continuously Soil Radon Exhalation Rate Measurement procedure

### Conclusion

^{−2}· s

^{−1}and E

_{A}was ranged of 2.139–2.316 atom · cm

^{−2}· s

^{−1}for 30 minutes measurement in linear fitting method. One hour measurement may result in a lower uncertainty, but bending down may already occur and the E value may be underestimated. It is suggested 1 hour measurement that had relative uncertainty below 10% for measurement time. In this method, three parameters which are fitting parameter (A), volume of the system (V) and area of surface chamber (S) were involved in calculating the exhalation rate and uncertainty. On average contribution, A contributes 59.75%, V is 30.13%, and S is 10.13%.

^{−2}· s

^{−1}and E

_{A}was 2.46–3.30 atom · cm

^{−2}using 3 hours measurement. Exponential fitting with 4 hours measurement time case resulted in reduced 10% relative uncertainty. In this fitting, two fitting parameters (fitting parameter [B] and total decay constant [k]) were parted of four exhalation rate parameters that two others are V and S. Among them, k which is the major uncertainty contributor was charged the average of 75.1%, B had 13.4%, V had 8.7%, and S had 2.9% in average relative uncertainty.

^{−2}· s

^{−1}or 2.139–2.316 atom · cm

^{−2}· s

^{−1}for 30 minutes measurement in linear fitting method and 51.6–69.2 mBq · m

^{−2}· s

^{−1}or 2.46–3.30 atom · cm

^{−2}for exponential fitting using 3 hours measurement.