0(-(3) = -0(P) (8a) 



0(oo) = 1/2 . (8b) 



It may be noted that for |xl< a , |yl< b , |z|<h , Eq. (6) gives C. = C . 



at t = in view of (8a , b) ; while for |xi>a or |yl>b or lzl> h , C. = 



at t = as desired. 



For simplicity we will consider the special case where a = b = h and hence 



3 

 the volume of the source is 4a . At the point x = y = z = in the source , 



Eq. (6) then reduces to 



C 



liA)] 



C^ = 8 I 0/,=^) 1 . (9) 



Thus the relative concentration Cs / C . at the center of the source is a function 

 of Kt/a^ only. For sufficiently large t(t>a^/K)^ 





C /- ^ \3/2 



at the center of the source ; while at t = , C. = C . . A plot of the general 

 relation (9) for the decay of concentration at the center of the instantaneous box 



source is shown in Fig. 3. The specific time scale at the top of this graph is 



2 3 



based upon K = 1 cm /sec and a = 36 cm (corresponding to a volume of 0. 186m 



or about 50 gal ) . The value of C is of course given by 



oi 



Mi 



r • (11) 



Ol 



4a 



137 

 Thus if M^ = 0.01 curie for isotope C in one package source, then 



3 

 C . = 54 m c/m or 54 [ic/kg , which would decay to a concentration of 



0.06 |jLc/kg in about 10 hours even without any mean current to aid the dispersal. 



