KINETICS OF KADlOCAUliUX I.NCUltl'UliATlON 



395 



i^gs ' *' i 



l^rg 



fJ'ig 



M; 



^gs 



ksT + fco — m 



^JLig 



The constants may be evaluated by solution oUhe simultaneous equa- 

 tions involving ao, /3,), and 70, where ao = Go - G, etc. It may be shown 



2.0 



3.0 



time 



Fig. 3. The accretion of radioactivity within each of the three compartments, 

 assuming unit values for all parameters. The dotted curve denotes the loss of radio- 

 activity from compartment G on sudden removal of radioactivity from incoming 

 carbon dioxide. 



that the roots of the cubic ecjuation, ?n,, may be either real and dis- 

 tinct, or one real and two complex. If one chooses parameters of 

 unity, i.e., Co = 1, and ki = ko = krg = ksr = 1 (so that kgs = k\ + 

 krg = 2), then the m's contain complex roots. Under these conditions 

 the solutions of the ecjuations for G, S, and R are: 



G = 1 - 0.740f"°-^"" + 0.305c --^''' sin (1.0288^ + 4.15!)) 



,S' 



1 - O.STHe-^-^'o-" + 0.5G3c-'-=^'''sin(1.0288/ + 3.368) 



R = 1 



1.255e"°=^°" + 0.331fi-2-^-'''sin(1.0288/ + 0.880) 



