IONIZATION AND BIOLCXilCAL EFFECTS 95 



In general, most of the energy is carried by waves in the neighborhood of 

 double this wave-length. 



In the case of soft X-rays, produced, for instance, at 50,000 volts, the 

 minimum wave-length is 0.247 A, and reciprocally the energy of the 

 secondary electrons liberated by such radiation, by either the photo- 

 electric or Compton effect, cannot exceed 50,000 ev. Indeed, a negligible 

 number would even approach this energy Umit. Fifty thousand volt 

 electrons will travel a distance of about 5 cm. in atmospheric air, which 

 corresponds to approximately 0.06 mm. in living tissues. This is the 

 theoretical maximum range, but actually most of the ionization loci are 

 much shorter, perhaps less than 0.01 or 0.02 mm. In this short distance 

 several hundred ion pairs are liberated. As the voltage at which X-rays 

 are produced increases, the path of the fastest secondary electrons 

 increases also. Hence, some relatively long ionization loci are now 

 present which were entirely absent in the case of softer X-rays. Further- 

 more, the average locus is also longer. 



If the number of ion pairs produced per centimeter were the same 

 throughout the path, the total distance traveled by the secondary 

 electron would be proportional to the voltage required to give it its initial 

 speed, because it takes the same amount of energy to produce a pair of 

 ions at every point in the path, m a given material. This is approxi- 

 mately true in the first part of the trajectory of high voltage — high-speed 

 — electrons. But as the speed reaches a certain relatively low^ value, the 

 rate of ionization increases rapidly and a large number of ions are pro- 

 duced in a short distance. The number of ions per centimeter set free by 

 high-speed beta particles, therefore, is approximately constant (actually 

 it increases somewhat) along most of its trajectory, and then becomes 

 several times larger near the end of its path. A two miUion volt electron, 

 such as some of the beta particles of radium, can liberate in living tissue 

 a total of 60,000 ion pairs, at the rate of about 3000 to 4000 per millimeter 

 throughout most of its trajectory. In the last part of its path, amounting 

 to a small fraction of a millimeter, the ionization rate is several times 

 higher. The total distance traveled through tissue by such a beta 

 particle is considerably longer than 1 cm., but on account of the tortuous 

 path which the electron follows the actual range is generally shorter than 

 1 cm. For lower-voltage beta particles the range is correspondingly 

 shorter (approximately). 



Remembering that in an organic material the abstraction of energy 

 from hard radiation takes place largely by the Compton effect and that 

 through this process electrons of low as well as high speed are produced, it 

 follows that even in the case of gamma rays a large proportion of the 

 secondary electrons do not travel very far in living tissue. The ionization 



^ It is nevertheless a very high speed. 



