510 L. H. G R A Y 



graphs because the separate droplets are not resolved, but the propor- 

 tion of clusters of a given size is believed to be much the same at all 

 linear ion densities and has been estimated by Kara-Michailova and 

 Lea (30) to be as shown in Table II. 



TABLE II 



Size Distribution among Ion Clusters (30) 



It will be seen that on about 45% of occasions an ionizing particle 

 ejects an electron from an atom that it traverses with insufficient 

 energy to produce further ionization so that only a single ion pair is 

 formed. Less frequently clusters of two, three, or more ion pairs are 

 formed and on about 12% of occasions the electron is ejected wdth suf- 

 ficient energy to produce more than four ion pairs. Such an electron 

 may itself be regarded as an ionizing particle having a definite track 

 and is customarily referred to as a 5 ray. The distinction between a 

 cluster and a very short 8 ray is obviously quite arbitrary. 



It is important for the correct interpretation of radiobiological 

 experiments to take these facts into account. For example, suppose 

 it is desired to calculate the chance that a dose of 100,000 r. of jS 

 radiation will ionize an entity having the dimensions of a small plant 

 virus or bacteriophage particle 25 m^ in diameter. Since the virus 

 is about the same size as the individual ion clusters, we have to calcu- 

 late the probability that a cluster and not a single ion pair is formed 

 within the virus. Now, although single ion pairs are the most com- 

 mon form of cluster the weighted mean size of all clusters having the 

 size distribution shown in Table II is three ion pairs. For all radia- 

 tions, therefore, the mean number of clusters per unit volume is 

 equal to one-third of the mean number of ions per unit volume. 

 Since 1 r. of jS radiation produces 1.7 ions per 10"^^ gram of virus 

 protein the number of clusters formed is 0.6 X 10^^ per gram per 

 roentgen. Assuming the density of virus protein to be 1.35 gram per 

 cubic centimeter, the average number of clusters formed within the 

 virus particle by 10^ r. is therefore: 



10^ X 0.6 X 10^2 X^sTT (12.5)3 X lO'^i X 1.35 = 0.66 



The clusters will be distributed among the particles in accordance 



