Unattached fraction

Unattached Fraction—That fraction of the radon daughters, usually 218Po and 214Po, which has not yet attached to a dust particle or to water vapor. As a free atom, it has a high probability of being exhaled and not retained within the lung. It is the attached fraction which is primarily retained. 

This inverse relationship between equilibrium factor and "unattached" fraction and their relationship to the resulting dose is important in considering how to most efficiently and effectively monitor for exposure. This inverse relationship suggests that it is sufficient to determine the radon concentration. However, it is not clear how precisely this relationship holds and if the dose models are sufficiently accurate to fully support the use of only radon measurements to estimate population exposure and dose. 

Bandi, F., A. Khan, and C.R. Phillips, Effects of Aerosol Poly-dispersity on Theoretical Calculation of Unattached Fractions of Radon Progeny, this volume (1987). 

Effects of Aerosol Folydispersity on Theoretical Calculations of Unattached Fractions of Radon Progeny... 

Theoretical calculations of unattached fractions of radon progeny require prediction of an attachment coefficient. Average attachment coefficients for aerosols of various count median diameters, CMD, and geometric standard deviations, ag, are calculated using four different theories. These theories are ... 

Theoretical calculations of unattached fractions of radon or thoron progeny involve four important parameters, namely, 1) the count median diameter of the aerosol, 2) the geometric standard deviation of the particle size distribution, 3) the aerosol concentration, and 4) the age of the air. All of these parameters have a significant effect on the theoretical calculation of the unattached fraction and should be reported with theoretical or experimental values of the unattached fraction. 

In order to calculate the theoretical unattached fraction of radon progeny the appropriate differential equations must be developed to describe the net formation of unattached radon progeny. The system may be visualized schematically for RaA as illustrated in Fig. 2. It is assumed that there is no flow into or out of the system or removal by electric fields. The equations which describe the system presented in Fig. 2 are ... 

The unattached fraction of RaA is independent of the radon concentration since the factor XjNi cancels out. 

Theoretical unattached fractions of RaA using average aerosol concentrations and count median diameters as found in track and trackless Canadian uranium mine are presented in Table III. The reported uranium mine aerosol properties are N 120,000 particles/cm3 and CMD = 0.069 ym for a trackless mine and N =... 

Figure 5 shows the variation of the hybrid theory with CMD for various Og. It is obvious that assuming an aerosol to be mono-disperse when it is in fact polydisperse leads to an underestimation of the attachment coefficient, leading in turn to large errors in calculation of theoretical unattached fraction. 

Unattached fractions of RaA (at t = °°) for two mine aerosols and for a typical room aerosol are shown in Table III. It is usually assumed that the attachment of radon progeny to aerosols of CMD < 0.1 ym follows the kinetic theory. In Table III it is apparent that the hybrid and kinetic theories predict similar unattached fractions for monodisperse aerosols. However, for more polydisperse aerosols, the kinetic theory predicts lower unattached fractions than the diffusion theory and thus the diffusion theory is the more appropriate theory to use. It is also evident that the kinetic-diffusion approximation predicts unattached fractions similar to those predicted by the hybrid theory in all cases. 

Calculation of the attachment coefficient is required for theoretical prediction of the unattached fraction of radon progeny. The hybrid theory, which is a form of Fuchs theory with certain justifiable assumptions, can be used to describe attachment to aerosols under all conditions of Og and CMD. 

Although unattached fractions predicted using the kinetic and diffusion theory for high aerosol concentrations, such as mine atmospheres, are comparable, the same cannot be said for unattached fractions predicted at low aerosol concentrations, such as indoor air. For low aerosol concentrations, neither the kinetic nor the diffusion theory predicts unattached fractions close to those predicted by the hybrid theory. Exclusive use of either of these two theories results in large errors. 

Although the hybrid theory is the most correct theory to use in the prediction of unattached fractions, the error in using the kinetic-diffusion theory in place of the hybrid is small. The kinetic-diffusion theory has the advantage that the solution is in analytical form and thus is more convenient to use than the hybrid theory, which must be solved numerically. 

Finally, whenever theoretical or experimental unattached fractions are reported, the aerosol characteristics Og, CMD and N must also be reported to allow proper interpretation of the results. 

Let us consider an atmosphere where the (activity) concentrations of radon, 222Rn, and its three short-lived daughters, 218Po, 21ifPb and 21I+Bi, are CQ, Ci, C2 and C3, the decay constants and unattached fractions of the daughter products, X, X2, X3, fi, f2 and f3 respectively, and E and E" the energies of the alpha particles from 2 8Po and 21I+Po (the fourth short(est)-lived radon daughter). 

The concentration of radon and its short-lived daughters were measured as well as the unattached fractions of the daughter products and the aerosol concentration. 

The reduction in PAEC is considerably higher than can be accounted for by filtration directly (Jonassen, 1984a, Jonassen and McLaughlin, 1984), because the filtration as suggested, not only removes radioactive material, but also through removal of aerosol particles increases the unattached fractions and thus enhances the plate out- removal of airborne radioactivity. On the other hand the filtration-induced increase in unattached fractions will increase the average radiological dose per unit of PAEC and this is responsible... 

Bigu, J., Radon Daughter and Thoron Daughter Deposition Velocity and Unattached Fraction Under Laboratory-Controlled Conditions and in Underground Uranium Mines, Aerosol Sci., 16 157-165 (1985). 

Then the unattached fraction was calculated in each measurement and was found to be between. 05 and. 15 without aerosol sources in the room and below. 05 in the presence of aerosol sources. The effective dose equivalent was computed with the Jacobi-Eisfeld model and with the James-Birchall model and was more related to the radon concentration than to the equilibrium equivalent radon concentration. On the basis of our analysis a constant conversion factor per unit radon concentration of 5.6 (nSv/h)/(Bq/m ) or 50 (ySv/y)/(Bq/m3) was estimated. 

The working level concept evaluates the unattached fraction and the activity median diameter in an indirect way, through the dose conversion factor. This paper will show that in the domestic environment this is mostly inaccurate to estimate the dose. 

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