Radon in the environment
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	System design and measurement procedure
	System Design  Setup  Deducing exhalation rates from measured growth curves  Procedure

System Design
In this section the instrument, with which the radon-222 concentration growth is measured, is discussed. The method relies on the detection of alpha-particles originating from the decay of its short-living daughters 218Po and 214Po. As a consequence of the short range of alpha-particles in air, the detector will only be sensitive to alpha-decay very close to it. When alpha-decay takes place, a number of electrons is stripped off the residual atom by the leaving alpha-particle, resulting in a positively charged ion. By creating an electrostatic field, the (charged) radon daughters can be collected on a thin (3 μm) aluminized mylar foil close to the detector, which enhances the detection efficiency. The fraction of charged decay products that reach the detector will be determined by loss processes. The most important loss processes are: radioactive decay of the ion, deposition on surfaces in the can, and attachment of the ions to particles (water molecules, for instance) in the can. A particle on which an ion attaches will, because of its larger size, have a smaller probability to reach the detector before the ion decays. Furthermore, due to the interaction with the surrounding air, there is an even larger probability for neutralization. Increasing the field strength sufficiently (to about 125 V/cm) will make the measurement relatively independent of these removal processes.
Setup A can, consisting of two concentric stainless steel cylinders, which are closed at one side, is placed on an exhaling surface with its open side. Soft rubber rings provide a seal between the surface and the cylinders. In the volume inside the inner cylinder, which will be referred to as the measuring volume, the decay products of the exhaled radon are collected and their activity is measured. The outer volume serves the purpose of a buffer in order not to let the exhaled radon escape from the inner cylinder. A nitrogen flushing system is used to clear the measuring volume and the buffer volume from radon. Temperature and relative humidity are measured in the measuring volume through use of a Rotronic temperature and humidity transmitter. A differential pressure transducer (Setra, model 264) is used to registrate the pressure differences between the air inside and outside the can. The signals from the pressure transducer and the meteorologic probe are connected to a 16-bit ADC before being read out by a computer. Figure 3.1: Radon exhalation meter used at the Vrije Universiteit in Amsterdam. The upper part of the setup (marked with a dashed box) is fixed with screws and is removed easily when, for instance, the foil needs to be replaced. In the shown configuration, the exhalation meter is placed on a horizontal surface. Instead of a horizontal surface, a vertical wall can be examined by rotating the entire setup by 90 degrees and placing it on the 'foot', which is mounted at one side of the can. To prevent the detector from being contaminated with radioactive radon daughters, an aluminized mylar foil, on which the decay products are deposited, is placed in front of the detector. The electrostatic field, needed to collect the positively charged decay products, is created by installing the detector and the foil at a potential of −2 kV with respect to the walls and the metallic grid near the open end of the can (which are connected to the earth potential). The detector is powered by a battery pack with a voltage of 70 V with respect to the high voltage potential. The detector signal is pre-amplified and subsequently amplified in a shaping spectroscopy amplifier (Canberra 2021). The shaped pulses coming out of the spectroscopy amplifier can be directly fed into a multichannel analyzer. All the data (from the pressure transducer, temperature/humidity meter and the MCA) are transferred to a computer for analysis.
Deducing exhalation rates from measured growth curves
The solid-state detector detects the α-particles originating from the decay of 218Po and 214Po deposited on the foil. The geometry of the setup (see fig. 3.2) and the finite efficiency of the detector cause the count rate of the detector to differ from the sum of the activities from these two decay products. The count rate (s-1) of the detector may be expressed as:
		(3.1)
in which IX is the activity of isotope X and δ is the ratio between the area of the foil and the area of the detector. The factor 2 is a result of the 2π geometry of the detector (only alpha-particles moving from the foil towards the detector are measured). Figure 3.2: Geometry of the detector and the foil. The number of alpha-particles emitted on the foil that reach the detector is determined by the geometry of the foil and the detector. When the distance d between the foil and the detector is much smaller than their dimensions, only the alpha-particles coming from the part of the foil adjacent to the detector and moving into the 2π of solid angle directed towards the detector reach the detector. With an exhalation meter the average count rate of the detector is measured during successive counting periods with a length of ΔT. The average count rate in period i is:
		(3.2)
Here, n(t) denotes the the count rate of the detector at time t since the start of the measurement. This count rate may be expressed in terms of activities of the decay products 218Po en 214Po with the use of equation (2.8). In order to express the average count rate in some period as a function of the radon concentration in the can, we first introduce the collection efficiencies for the two polonium isotopes:
	and	(3.3)
If we subsequently define εtot as the average collection efficiency (εtot=(ε1+ε2)/2) and note that the activity concentration C (Bq·m-3) is obtained by dividing the activity I (Bq) by the can volume V (m3), equations (3.1)-(3.3) may be combined to:
		(3.4)
Note that, although the collection efficiencies are determined in the steady-state situation, they are assumed to have the same value over the entire growth curve. By inserting eq. (2.9) into eq. (3.4) and working out the integral, the following expression for Ni is found (provided that λeffΔT<<1):
		(3.5)
in which the constant C1 is defined by:
		(3.6)
Equation 3.5 may be used to fit to a measured growth curve in order to determine the free exhalation rate. Sometimes only a small part of the growth curve is measured. The exponential function in eq. 3.5 can then be replaced by its series expansion and the free exhalation rate is determined by fitting the first part of the growth curve to the linear term of the expansion. The equation to which the first part of the growth curve should be fitted in that case becomes:
		(3.7)
When a measured growth curve is fitted to eq. 3.5 or eq. 3.7, the fit parameters C1 and λeff can be used in eq. 3.6 to calculate a value for the free exhalation rate Efree. If the alpha-particles emitted by the different polonium isotopes are measured separately through the use of energy-selection, εtot should be replaced by (ε1/2) or (ε2/2) in eq. 3.6.
Procedure
The procedure for the measurement of the exhalation rate of some material is given by the following steps; Identify relevant parameters with their uncertainties Flush the measuring volume with nitrogen Perform a series of many measurements with long periods and continue until a steady-state situation has been reached Calculate the relevant variables on basis of these data Perform an error analysis Graph or tabulate the relevant data and their respective uncertainties Draw conclusions
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