Sec. 15.3] 



THEORY OF TRACER METHODS 



397 



curies per sec, but the rate of disappearance from the phase is proportional 

 to the concentration, the specific activity, assuming it is zero initially, is 



* = m <» " **> 



microcuries/gm 



As before, k is the turnover rate or k = r/M, where M is the total constant 

 quantity of substance in the phase and r is the constant rate of disappearance. 

 After a long time compared to 1/k, the specific activity approaches the 

 constant value of p/kM. 



d. Transfer between Two Phases. One of the most common rate problems 

 investigated with tracer techniques is the transfer of a labeled substance or 

 of the labeling agent itself from phase 

 A, into which it is introduced, to one 

 or more phases B, C, D, . . . where 

 the activity is measured. It is 

 assumed as before that the system is 

 in a steady state, the amount M of 

 the substance (labeled plus unlabeled) 

 in each phase is constant, and the 

 rates r, of appearance and disappear- 

 ance of the untagged substances are 

 constant. 



Consider A to be the precursor of 

 several phases B, C, D, . . . which 

 receive material directly from A. 

 If the specific activity in phase A is 



raised initially to X microcuries per gm of labeled substance, its subsequent 

 specific activity is x\ = Xe~ klt , where k\ = ri/Mi is the turnover rate, Mi 

 is the total quantity, and r x is the rate of disappearance from A. The specific 

 activity in any one of the phases B, C, or D, for which the turnover rate is 



M% 



PHASE B 



t mo . TIM E 



Fig. 112. Specific activities in separate 

 phases A and B in a simple two-phase 

 system as a function of time. 



is initially zero but after a time / it is 



X2 



k 2 XMi 



(k 2 - ki)M 2 



(g-*i< _ e -k,t) 



microcuries/gm 



The activity in this phase increases from zero to a maximum in the time 



. 1 T h 



max ~ kx - k 2 g h 



Afterward the concentration of the tagged molecules decreases at a rate equal 



