12 



suddenly dispersed from a common origin simultaneously, and M. = 100 curies 

 for the total activity of C ^^^ , then C^ would be about .0004 jxc/kg at 1 km . 

 This is only twice that given in Table I based upon a continuous supply at the 

 rate of 100 curies per year . 



B. Continuous Source at Uniform Leaching Rate 



In the preceding analysis it was considered that the total material in the 



package soxrrce was released instantaneously. Consider now that the walls of 



the container are permeable and of thickness proportional to the size a . We 



will make the following hypothesis : the amount of radioactivity diffusing throu^ 



the permeable walls per unit time is directly proportional to the surface area of 



the container , directly proportional to the difference in concentrations inside 



and immediately outside the container and inversely proportional to the thickness 



of the walls. Thus if Q. is the rate of leaching for a given isotope then it is 



presumed that 



Q. = k-. A A Ci ^jg^ 



a 



where A C^ is the concentration inside the container minus that at the outer 

 walls, A is the exposed surface area and k. is a constant for the isotope 



considered . 



2 

 For a box of dimensions 2a x 2a x a resting on the bottom , A = 12a 



while the volume is 4a . In the initial stage tlie concentration outside the box 



will be very small compared with that inside and we can take as the upper limit 



of AC. simply M./ 4a (the initial concentration in the box). Thus 



