MEASUREMENT OF IONIZING RADIATIONS 171 



Table 2-3. Calculated Values of Geometric Factor g for Spheres 



One consequence of Eq. (19a) is that the average dose within spheres, 

 up to radii of one relaxation length, is given very closely by 



5^ (average) = 0.75Z)^(1 - e'") a < I 



and that, in a medium of concentration Ci, for a small spherical organism 

 having a uniform concentration C-2 of the same isotope, the average dose 

 can be calculated as 



5^ (average) = K^[C^ + 0.75(C2 - Ci)(l - e"")] 



Plane geometries are also frequently encountered in radiobiological experi- 

 ments. They have been dealt with in considerable detail by Rossi and 

 Ellis. 



Of general interest is the dose at a distance h from one surface of an 

 infinite slab of thickness t, both expressed in relaxation lengths for the 

 particular /3 radiation under consideration. For t = =o the geometrical 

 factor g^ is 



g? 



anc 



= yile-^ + hE,{-h)\ outside the slab 

 g0 ^ \ — >^[e~'' + hEi( — h)] inside the slab 



where 



E,(-h) = /; 



e T 



dr 



This integral has no algebraic expression but has been tabulated exten- 

 sively (AVPA, 1940). For any other thickness t of the slab, expressed in 



