Radon in the environment


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Theory
 


 
 

 

Radon-222 decay chain

 

Radon (Rn) is an inert, radioactive gas which has several isotopes. The most important isotope in this experiment is 222Rn, and belongs to the radioactive decay series starting with 238U and ending 206Pb, a stable lead isotope (see fig. 2.1). The other two isotopes that can be measured in this experiment, 220Rn and 219Rn, belong to different decay chains. Unlike the other members of these decay series, radon is a gas and is therefore capable of escaping from a material in which it is formed into the surrounding air. The mining industry is an important radon producer. When mining waste is stored close to the earth surface, large amounts of radon can easily escape into the environment and cause a high radon concentration locally. A more widespread problem is the accumulation of radon in dwellings. Uranium traces are present in soil and, as a result, in almost all building materials. If radon makes its way into a (badly ventilated) home, it can build up to high concentrations and may become a health hazard. Although our skin is thick enough to protect us from the alpha-particles emitted by the three polonium isotopes from the decay series of 222Rn, it are especially these isotopes that are most harmful when they disintegrate inside our lungs. After smoking, which is responsible for 87% of the lung cancer cases, radon is estimated to be the second leading cause (12%) of lung cancer in the USA today [5]. In order to offer an indication of the risks of radiation, the International Commission of Radiological Protection (ICRP) has given norms ([1], p.181), indicating the maximum dose of radiation that should be acceptable for human health.
In this experiment, the decay products of the exhaled radon gas from a sample are collected in a "Radon exhalation meter". The radioactivity of these radon daughters is measured by detecting the outcoming alpha particles. The most abundant radon isotope is 222Rn, which itself is a member of the decay chain of 238U. The decay chain of 222Rn is shown is figure 2.1. The half-life for each radioactive member of the chain is indicated, as is the alpha-particle energy (in keV).

Figure 2.1: Decay chain of  238U. The part from  222Rn to  206Pb is relevant for the experiment.

 

Apart from 222Rn, there are two other radon isotopes originating from naturally occurring radioactive isotopes: 220Rn, which is a daughter of 232Th, and 219Rn, which is a daughter of 235U (click on these isotopes to view the decay chains and additional information). Under certain experimental circumstances the decay products of these radon isotopes will be found.

 

Radon concentration growth

 

Radioactive decay is governed by the rule ([1], p.173):

 

(2.1)

In which t is the elapsed time (in seconds), N(t) is the number of radioactive nuclides at time t, N0 is the number of radioactive nuclides at t=0 and λ is the decay constant (in s-1), which is characteristic for a certain radioactive isotope. One can easily calculate that this decay constant is related to the half-life τ1/2 (time that half of the nuclides have disintegrated) in the following manner:
 

(2.2)

The activity of a radioactive sample is expressed in becquerel (Bq), the number of disintegrations per second. Equation 2.1 is the solution of the first-order differential equation:
 

(2.3)

Equations 2.1 and 2.3 describe the behavior of one radioactive isotope decaying to its daughter. If a radioactive isotope is a member of a decay chain, a growth term enters the differential equation (eq. 2.3) as a result of the decay of its mother. If Ni is the number of atoms of the ith member in a decay chain, the differential equation becomes:
  .

(2.4)

This set of coupled first order differential equations can be solved analytically. Some specific solutions of these differential equations can be shown in the applet on this page. In this applet, the differential equations are solved under the conditions that at Ni(t=0)=0 for all isotopes and that the number of radon atoms N0(t) grows as will be derived in the next section (see eq. 3.5).
In the experiment, the activity of the daughters from the gas radon, which is exhaled by some sample, is measured (see fig. 2.2). The driving force behind the flow of radon gas from the pores within a material into the enclosure is determined by a concentration gradient (diffusive flow) and a pressure gradient (pressure driven flow). In absence of a pressure gradient, radon gas flow is fully governed by diffusion, which can be described by Fick's first law:
 

(2.5)

In this equation J is the net transport rate of the gas per cross sectional area of the bulk material (Bq·m-2·s-1), C is the activity concentration of radon in the pore volume (Bq·m-3) and e is the porosity (volume fraction pores). The diffusion coefficient D (m2·s-1) is a measure of the ease with which radon can migrate through the material. Fick's law may be used to relate the absolute value of the radon concentration gradient at the surface to the exhalation rate E (Bq·m-2·s-1). For simplicity, radon flow through the material as a result of a pressure gradient is neglected, here.
 

(2.6)

Figure 2.2: Schematic picture of the setup. The radon concentration in the can increases due to contributions indicated with green arrows, while decreasing terms are indicated with red arrows. The increase of radon as a result of radium decay can be neglected since the radium concentration in the can will be very low while its half-life is very long (1603 year).

In fig. 2.2 the different contributions to the radon concentration Ccan in a can, placed on an exhaling surface, are depicted. In formula form, this concentration Ccan can be described by:
 

(2.7)

where leakage of radon is assumed to be proportional to the radon concentration in the can. The symbols A and Vcan refer to the surface of the exhaling material covered by the can (m2) and the volume of the can (m3), respectively. A better description is obtained when the effect of the radon concentration growth on the diffusion is taken into account. This is accomplished by introducing a linear decrease term of the exhalation rate with increasing concentration in the can:
 

(2.8)

When equations (2.7) and (2.8) are combined, a differential equation is obtained which has the following solution:
 

(2.9)

in which the effective time constant λeff = λback + λRn + λleak. In the System Design and Measurement Procedure section, we will show how this expression for the concentration in the can Ccan can be related to the activity that is actually measured.



In the applet below, growth curves of the daughters of radon-222 can be simulated. From the decay series 222Rn until 206Pb, the number of atoms and the number of decays from each isotope can be plotted. Note that in the applet the can volume Vcan, the exhaling surface A, the geometric factor δ, and the collection efficiencies ε1, ε2, εtot are all set to unity.


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