10 



z axis between the planes z = and z = D . Eq. (12) applies for small t 

 while Eq. (13) applies for large t after the upper boundary begins to sig- 

 nificantly effect the dispersion. 



Our main interest lies in the maximum concentrations which occur at 

 different distances from the source. It can be seen from either Eq. (12) or 

 (13) that the exponential term increases as t increases while the term t~ 

 or t ' decreases. Hence there exists a particular time for each position 

 at which C. is a maximum . 



The time of maximum C. from Eq. (12) is readily found to be 



2 



m 6K 

 and that for Eq. (13) is 



(14) 



2 



m 4K 



Substituting these expressions into Eq. (12) and (13) respectively gives for 

 the maximum concentrations of radioactivity at r : 



A-^l±\ = 0.47-5^ /'^^ (17) 



Coi 



for r > D where r is tlie radial distance from the source along the bottom , 

 It is of interest to note that the maximum concentration at any position r is 

 independent of the diffusivity coefficient K- . However , the time at which this 



