178 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



dependent upon many factors, such as (a) relative placement of counter 

 and sample, (6) absorption by counter-tvibe window and air space between 

 tube and source, (c) air scattering of beta particles into the counter, (d) 

 effect of backscattering from source support, (e) scattering from source 

 support structure and wall housing, and (/) mass of source in causing 

 both scattering and absorption. By the use of standard counting condi- 

 tions, all the above factors except the last can be easily maintained 

 constant and therefore need not be further considered. However, it is 

 necessary to consider in some detail the effects of self-absorption on the 

 counting rate. 



The self-absorption effect can, of course, be approximated from the 

 beta energy of the particular isotope (Chap. 6) for the preliminary plan- 

 ning of sample preparation. However, it is necessary to obtain quantita- 

 tive data for the actual application of correction factors. The most 

 widely used method for evaluation of the observed activity is to convert 

 this value to the activity that would have been observed at some specified 

 thickness. 



The most commonly used thicknesses for reference are zero thickness 

 or infinite thickness (maximum observed activity for increasing amounts 

 of a sample of constant specific activity). In the preparation of a set of 

 standards of constant specific activity, the determination of the infinite- 

 thickness value is difficult because the observed activity increases in the 

 following manner: 



^ = 1 - e--' (5-2) 



where N = observed activity 



A'' 00 = activity at infinite thickness 

 Tc = sample thickness, mg/cm' 

 IJL = self-absorption coefficient, cm-/mg 



Figure 5-7 shows such a constant-specific-activity curve for S^^. The 

 slope at thickness equal to zero, which is represented by the broken line 

 No, represents the relationship between activity and weight of sample if 

 no self-absorption has occurred. Uncertainties in the determination of 

 this slope are due to self-scattering of the beta particles by the thin sam- 

 ples and to the difficulties in obtaining a uniform spread of the thin sam- 

 ples. Uncertainties in determination of activity at infinite thickness .V« 

 are due to the nature of the curve as it approaches zero slope, which may 

 be complicated by the fact that the surface gets closer to the window as 

 the sample thickness is increased. 



The equation for self-absorption, where A^'o is the true activity of the 

 sample and T represents the sample thickness, in milligrams per square 

 centimeter, there being a constant amount of sample activity, is 



