190 



RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



relatively accurate. In cases of this sort, B (the activity which is reduced 

 most by the second measurement) must usually be equal to or greater 

 than A if reliable results are to be expected. In general, the greater 

 the difference in the decay rates or absorption, the more successful the 

 method. 



Table 5-5. Illustration of Errors as a Function of Composition of 

 Isotope Mixture in a Subtractive Procedure 



Calculated counts at zero time 



2(5000 + 71) = 10,000 + 142 



(10,200 ± 100) - (10,000 ± 142) = 200 



2(100 ± 10) = 200 + 20 



(10,200 + 100) - (200 + 20) = 10,000 



The general formulas apply to all three cases, but the specific symbolic 

 notation will be given for purposes of clarity. 



Differential Decay. In this method the two isotopes have different 

 half-lives, and a count is taken before and after the passage of time. The 

 general equations for calculation of the composition from the two counts 

 and the known half-lives are as follows: 



A ^ B = Co 

 B ^ F\ 

 A 



Ct/C, 



Ct/Co — Ft 



(5-4) 

 (5-5) 



where Co = count at zero time 

 Ct = count at time / 

 A = count of isotope A at zero time 

 B = count of isotope B at zero time 

 Fa = fraction of isotope A present at time t • 

 Fb = fraction of isotope B present at time t 

 The use of these equations may be illustrated as follows: Assume that 

 a sample containing S^^ (half-life, 87 days) and P^' (half-hfe, 14.3 days) 

 counts 3000 at some given time and 2085 at 20 days later. Fa and Fb are 

 calculated from decay Eq. (1-17) as 0.853 and 0.379. Substituting in 

 Eq. (5-5), 



B ^ 0.853 - 0.695 

 ,4 0.()95 - 0.379 



0.5 



