If B^ designates the arc within which diffusion is constrained by 

 the boundaries, then, letting 



360° 



(4) 



w^e have in general 



(5^ s(r,t) - „ exp 



2itD(Pt)2 



Pt 



where s(r, t) is here concentration per unit volume, since the factor 

 1/D has been entered into the right side of the equation. 



The maximum concentration occurs at the center of the diffusing 

 volume, and is given by 



nM 

 (6) S (t) 



27i;D(Pt)2 



At the center the concentration decreases continually with time. 



At any distance r_ from the center, the concentration first rises 

 to a ma:ximum value, and thereafter decreases with time. Thus, as- 

 suming that the introduction is truly a point source (i. e. , neglecting 

 initial mechanical dilution), there will be, for any finite amount of 

 radioactive wastes introduced, an area within which the concentration 

 exceeds, for a time, the ppc values for the environment. This area will 

 at first increase in size to a maximum value, and thereafter v/ill de- 

 crease in size until a time is reached at which the concentration is 

 everywhere less than ppc values. This time can be obtained from 

 equation 6 by setting SQ(t) equal to the ppc value for the particular iso- 

 tope in question. Thus 



(7) t 



ppc 



where tppc is the time after which the concentration everywhere is 

 less than the ppc concentration, which is here designated by s . 



Equation 5 can be solved for the distance, at any time _t, at which 

 the concentration has just reached ppc values, by setting s(r, t) equal 

 to Spp^ . Thus 



nM 



(8) r = Ptin 



2TiD(Pt)2s 



ppc 



33 



