364 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 



accuracy of the method [14] by at least a factor of 10. Among the radio- 

 active isotopes that have been standardized by this method are Co 60 , Na 24 , 

 Au 198 , I 128 , I 131 , and Fe 59 . Other isotopes can be used later when their level 

 schemes are better known. 



When the beta- and gamma-counter efficiencies obtained by this method are 

 plotted as a function of the energy of the beta particles or gamma rays, curves 

 such as those shown in Fig. 101 are obtained. In this diagram the strong 

 dependence of counting efficiency on energy may be clearly seen. If one 

 wishes now to standardize other radioactive isotopes that have no convenient 

 level scheme for coincidence measurement, it is possible to interpolate on the 

 beta- and gamma-counter efficiency curve and obtain the efficiency for any 

 other energy, provided that the geometry is not changed. In this way 

 counter efficiencies for pure beta emitters, such as P 32 , C 14 , and S 35 , may be 

 determined [42]. The efficiency curve for counters may be predicted by some 

 semiempirical considerations. Although it seems to be entirely permissible 

 to extrapolate on the gamma-counter efficiency curve for energy regions 

 where selective K or L absorption in the counter is unimportant, this is not 

 quite so with the beta-counter efficiency curves because the energy distribu- 

 tions of beta particles from different radioactive isotopes do not follow the 

 same law. The shape of the beta spectrum depends on whether or not the 

 spectrum is allowed or forbidden and there is not sufficient experimental and 

 theoretical evidence to make very accurate predictions of the shape of the 

 spectrum. In spite of this, however, no great error is incurred in most cases 

 when the extrapolation technique is used. Similar difficulties arise when 

 positron emitters are to be standardized. Here the shape of the low-energy 

 end of the positron spectrum is very uncertain and the best method appears 

 to be the use of the annihilation radiation (0.51-mev gamma rays). The 

 efficiency for counting annihilation gamma rays may be easily determined 

 from the gamma-counter efficiency curve. 



13.6. Long-life Beta Standards. It is useful to compare the results of 

 disintegration-rate determinations by the coincidence method with other 

 independent methods. Chronologically, the first such method was one using 

 gravimetrically prepared samples. In addition to primary standards, the 

 use of long-life secondary beta-particle and gamma-ray standards is very 

 important in routine measurements because their periodic measurement 

 informs one of the changes of sensitivity of counting and ionization measuring 

 instruments. 



a. Uranium Standard. Fermi was one of the first to use radiations from 

 UX2 as beta-particle standards. The usual practice is to prepare a pure 

 sample of U 238 and then wait long enough for radioactive equilibrium to be 

 reached between UI, UXi, UX 2 , and UZ. As is well known in a case of 

 radioactive equilibrium, the rate of disintegration of the parent isotope is 



