58 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 



tion to beta particles emitted from radioisotopes for which the energy dis- 

 tribution is continuous from zero to a well-defined maximum value. The 

 observed absorption curve for beta particles from these sources is sometimes 

 roughly logarithmic and often can be represented by an exponential function 

 over the greater part of its range. Unlike similar curves for gamma rays, 

 however, it has a finite and definite termination. The exponential character 

 of the absorption can be interpreted only as a fortuitous effect due to a com- 

 bination of the Fermi energy distribution of the emitted particles, scattering, 

 and absorption by radiative and ionization energy loss. When the absorp- 

 tion curve does appear as a straight line when plotted on semilogarithmic 

 graph paper, the beta intensity / (e.g., counts per minute) at a depth x in an 

 absorber is given by 



/ = I e-» x 



where I = initial intensity (or counts) with no absorber 



fj. = absorption coefficient, cm 



x = depth of absorber, cm 

 A form sometimes more convenient is found in terms of the mass-absorption 

 coefficient a = p/p, where p is the absorber density in grams per cubic 

 centimeter. The absorber thickness x is then measured in grams per square 

 centimeter and a expressed in square centimeters per gram. This coefficient 

 is relatively insensitive to the atomic number Z of the absorber since the 

 number of electrons per unit mass decreases slowly with increasing atomic 

 weight and for light elements is therefore essentially constant. An empirical 

 relation for the mass-absorption coefficient, valid for the light elements and 

 with a probable error in energy of 0.2 mev, is [4] 



22 

 a 



171.33 



J -'m 



where E m = maximum energy, mev 



and in terms of the half-value thickness d (where I = 0.5I o ) the relation is 



d = 0.693a = 0.032£i; 33 



These expressions are valid only when a considerable portion of the absorption 

 curve appears, within the experimental error, as a straight line when plotted 

 on semilogarithmic graph paper. 



More often, when plotted on semilogarithmic graph paper with the absorber 

 thickness as the linear abscissas, the absorption curve is found to be concave 

 toward the origin or otherwise distorted and cannot be represented by a 

 simple exponential function. The shape of the curve depends on the initial 

 energy distribution of the beta particles and is also strongly influenced by the 

 geometry of the counting arrangement. For this reason an absorption 



