94 RADIATION BIOLOGY 



of abscissas in Fig. 1-56 is stretched in proportion to the true range of the elec- 

 trons, i.e., approximately in proportion to the square of the energy T [see Eq. 



(32)]. 



Extrapolation of the curve in Fig. 1-56 at its steepest point serves to 

 identify a depth which may be taken as an index of maximum penetration, 

 i.e., as an effective range. The practical characterization of maximum penetra- 

 tion will be considered again in Sect. 4-2f. 



Little is known about the displacement of the electrons sidewise from the beam 

 direction; one may estimate that the average value of this displacement is com- 

 parable to the average depth of penetration. 



4-2b. Intermediate Energy: Predominance of Energy Loss hy Collision. 

 As mentioned before, the energy dissipation along the track acquires 

 greater and greater importance as compared to the scattering effects for 

 electrons whose speed approaches more and more closely the velocity of 

 light. This relates to the circumstance that the "stopping power," or 

 rate of energy loss, of an electron depends on the electron velocity rather 

 than on its energy [Eq. (17)] and therefore no longer decreases when the 

 energy increases beyond 1 Mev. On the contrary the probability of 

 deflections keeps decreasing as the energy increases, approximately in 

 inverse ratio to the square of the energy. Therefore electrons of increas- 

 ing energy, in the multimillion-volt range, dissipate a greater and greater 

 fraction of their energy before being greatly deflected from their initial 

 direction. 



The rate of energy dissipation of these electrons is, very roughly, 

 independent of the energy and falls within the range of 



1 to 2p Mev/cm (33) 



where p indicates the density of the material in g/cm\ The actual value 

 lies nearer to the lower limit of this range for heavy materials, like lead, 

 and nearer to the upper hmit for Kght materials. This result may also 

 be expressed with reference to the energy dissipation in a layer of material 

 of known mass per unit area, independently of its density. The energy 

 loss falls between 1 and 2 Mev per g/cm- of mass of the layer. 



For electrons of sufficiently high energy only a very small fraction of 

 the initial energy remains after an electron has undergone a substantial 

 deflection. The initial energy required for this depends on the atomic 

 number of the material, since the deflection effects are more important in 

 heavy than in light materials. In light materials the deflection effects 

 are not very important even at low energies, and therefore the energy loss 

 predominates beginning at a few million electron volts. In heavy mate- 

 rials scattering predominates greatly at low energies; accordingly scat- 

 tering becomes unimportant only at much higher energies. In fact, in 

 materials like lead, there remains no energy range in which the energy 

 loss by collision constitutes the main obstacle to penetration, because 



