K . M . Thabayneh and R . J . Shawamreh : Radioprotection 2024 , 59 ( 4 ), 306 – 316 309
1 T e ¼ t � lð1 � e �lt Þ ð3Þ
where l is the decay constant of radon-222 ( l = 7.56 10 �3 h �1 ).
3.3 The radon-222 exhalation rate
The radon-222 exhalation study is important for understanding the relative contribution of the material to the total radon-222 concentration found in the dwellings . The equation used for surface exhalation rate is written as ( Shoeib and Thabayneh , 2014 ; Thabayneh , 2018 ):
E A ¼ Cvl ; ð4Þ
AT ef f
and for mass exhalation rate is written as
E M ¼ cvl ;
MT ef f ð5Þ
Fig
. 2 . Experimental setup for the measurement of radon-222 concentration .
( El-Ghossain and Shammala , 2012 ; Thabayneh , 2015 ; Thabayneh and Gharaybeh , 2023 ):
� C Rn Bqm �3 c 0 t
0 r
¼ ¼ k r
; ð1Þ t t r 0
where c 0 is the activity concentration of 226 Ra ( solid radium source ) equal 800 Bqm �3 ; r 0 is the track density ( number of tracks per cm 2 ) in detectors exposed to 226 Ra ; t 0 is the exposure time ( in days ) of detectors are exposed to 226 Ra , equal 70 days ; k is the calibration factor , equal 24.2 Bq m �3 day tracks �1 cm 2 ; r is track density ( number of tracks / cm 2 ) in detectors exposed to soil samples and t is the exposure time ( in days ) of detectors exposed to soil samples , equal 75 day ( El-Ghossain and Shammala , 2012 ; Thabayneh , 2015 ).
3.2 Determination of radium contents
To calculate the radium concentration ( C Ra ) in soil samples , the following relation can be used ( Yousef et al ., 2016 ; Thabayneh , 2018 ):
C Ra ¼ rhA kT e M ; ð2Þ
where r is the track density ( tracks per cm 2 ); h is the distance between the detector and the top of the sample ; A is the surface area from which radon-222 is exhaled ( m 2 ); M is the mass of the sample ( kg ); and T eff is the effective exposure time in ( hr ), which is related to the actual exposure time t , by the relation : where ; E A ( Bqm �2 h �1 ): is the surface radon-222 exhalation rate , E M ( Bq Kg �1 h �1 ): is the mass radon-222 exhalation rate , C : is the integrated radon-222 exposure in ( Bqm �3 h ), v : is the void volume of the container ( m 3 ), A : is the area of the sample ( m 2 ), M : is the mass of the sample ( kg ) ( Shoeib and Thabayneh , 2014 ).
3.4 The annual effective dose
To calculate the annual effective dose resulting from radon-222 concentrations , it is essential to consider the conversion coefficient from absorbed dose and the indoor occupancy factor . Following the UNSCEAR 2000 recommendation ( UNSCEAR , 2000 ), the annual effective dose for a one-year radon-222 exposure can be estimated using the formula as outlined by Kumar et al . ( 2014 ) and Mashal et al . ( 2021 ):
� AED mSvy �1
¼ CRn F T Q ; ð6Þ
where F ( is the conversion factor ) = 9 nSv ( Bq⋅hm �3 ) �1 ; T is 8760 h of a year ( Assuming an indoor occupancy factor is about 80 % of 8760 h , which equals 7008 h and 20 % for outdoors , which equals1752 hours ); and Q is the equilibrium fraction ( 0.6 ) for outdoors and ( 0.4 ) for indoors ( UNSCEAR , 2000 ).
From equation ( 6 ), we can calculate the annual effective dose for indoors and outdoors according to the following relations ( Challan and Atteyat , 2018 ):
� AEDin mSvy �1
¼ 0 : 02523CRn ; ð7Þ
� AEDout mSvy �1
¼ 0 : 00946CRn ; ð8Þ