78 RADIATION BIOLOGY 



a 1-Mev electron. (Most of the difference stems from the far lower speed 

 of the a particle; a further factor of 4 stems from its double electric 

 charge.) An a particle experiences an inelastic collision, on the average, 

 every 5 to 10 A in most solids or liquids, an electron less than one every 

 micron. 



Whereas the average spacing of the collisions along the track can be 

 controlled by varying the speed and the charge of the particles, the kind of 

 collisions does not vary to a significant extent from one radiation to 

 another (see Sect. 2-4c and Fig. 1-38). 



Activations may occur in atoms lying at a substantial distance from 

 the line of flight of a particle, as explained in Sect. 2-4a, Actually the 

 track of a particle is identified only by the position of the activations 

 which are produced. These activations do not lie exactly on a straight 

 line even where the track is, on the whole, straight. Nevertheless, the 

 track of a particle may be visualized as an ideal line running down the 

 middle of the region in which the activations are distributed. We may 

 then inquire about the average, number of activations at various distances 

 from this line. The numbers are roughly equal in successive coaxial 

 layers whose thickness increases in a geometric progression and which 

 extend, for example, from 5 to 10, 10 to 20, 20 to 40 A, etc. from the hne. 

 The maximum distance of activations depends on the condition that the 

 collision be "fast" (see Sect. 2-4a). 



Since collisions occur at random along the path of a particle, we may 

 inquire about the probability that the actual distance between two suc- 

 cessive collisions departs from the average distance by various amounts. 

 "Random occurrence" of collisions means that the chance for a collision 

 to occur on a certain section of track is wholly unrelated to whether or not 

 the preceding collision has taken place only a short distance before. The 

 law of probability which governs the actual distance between coUisions 

 may be derived from the following argument. 



Suppose that a large number iVo of particles start to travel under identical 

 conditions and that 10 per cent of them have undergone a collision within a dis- 

 tance 5. The remaining 90 per cent travel on, still unaffected. Therefore, 10 

 per cent of these 90 per cent, i.e., another 9 per cent of the initial Nq particles, 

 experience a collision between the distance 5 and 25; then 10 per cent of the 

 remaining 81 per cent experience a collision between 25 and 35; and so on (see 

 Fig. 1-46). This reasoning applied to very small, infinitesimal, intervals of dis- 

 tance leads to the basic law of distribution of collisions. 



Call N the number of particles which have traveled a distance x without experi- 

 encing any collision. The infinitesimal fraction dj of these particles which 

 undergoes a collision in the next infinitesimal distance interval dx is proportional 

 to dx, 



df = V dx 



