PLUTONIUM-BEARING PARTICLES FROM FUEL REPROCESSING 131 



The frequency distribution for natural aerosols with particle diameters between 1 

 fxm and D, calculated from this expression, is given in column 7 of Table 8 and plotted in 

 Fig. 7. 



To see how closely the distribution of particle diameters resembles a log-normal 

 distribution, we assumed that the observed diameters represented a sample of a 

 population having a log-normal distribution. The geometric mean diameter, Dg, and 

 geometric standard deviation, Sg, were calculated from these data by using equations 

 similar to those given earlier for the geometric mean enrichment factor and geometric 

 standard deviation. These values are given in Table 9. Values for the upper 68.27% limit 

 for the diameters were calculated from the product of D^ and Sg. The best-fit log-normal 

 probability curves were plotted on the logarithmic probability graph in Fig. 7 by drawing 

 straiglit lines through coordinates for Dg and Dg X Sg on the 50.00 and 84.14* 

 cumulative percent abscissae, respectively. 



TABLE 9 Distribution of Particle Diameters in 

 Systems I and II 



To detennine the degree of asymmetry, we calculated the skewness (SK) of these 

 frequency distributions by using the relationship 



SK 



^ 3 / InDg-lnD^ed ") (g) 



where Dmed is the median diameter. A perfect log-normal distribution has a skewness of 

 zero. If a distribution has a higher tail to the right than to the left, it is positively skewed. 

 Most of the distributions encountered here are negatively skewed, i.e., have higher 

 left-hand tails. Calculated skewness values are given in Table 9. 



Particle Evaluation by Plutonium Content 



Another characteristic studied was the distribution of plutonium among the particles as 

 indicated by the observed number of fission-fragment tracks in the surrounding 

 polycarbonate. 



The track distribution among particles from both systems was evaluated in the same 

 way as the particle diameters. The fraction of the particles with the number of tracks 



*50.00 + ^^ 



