92 



RADIATION BIOLOGY 



To indicate the progress of the average deflection as the electrons dis- 

 sipate their energy, we may consider the progressive decrease of the cosine 

 of the angle 6 between the momentary direction of each electron and its 

 initial direction. The mean value of cos d for a population of electrons 

 decreases approximately in proportion to the 0.3Z power of their kinetic 

 energy, where Z is the atomic number of the material penetrated (Blan- 

 chard and Fano, 1951). For a heavy material this means that (cos 6) 

 drops to 3^2 by the time the electrons have dissipated only a fraction, 



avg 



2.3/Z 



(31) 



of their initial energy. Even for a light material like tissue, (cos 0)avg 

 becomes quite small by the time most of the energy has been dissipated. 



<^ 



o 

 < 

 m 



0.8 



0.6 



0.4 



0.2 



"O 20 40 60 80 0.2 0.4 06 0.8 10 



ATOMIC NUMBER FRACTION OF INITIAL ENERGY 



(a) (^) 



Fig. 1-55. (a) Fraction of electrons from different sources back scattered by materials 

 of different atomic numbers. {Data from various authors; courtesy H. Seliger, 1950.) 

 (b) Energy distribution of the electrons backscattered by different materials. (Bothe, 

 1949.) 



Since the electrons entering a "heavy" material turn around rather 

 soon, on the average, those electrons which are actually backscattered are 

 likely to emerge from the material with a high residual energy. "Light " 

 materials yield low-energy backscattered electrons (Fig. l-55b). 



Since the penetration of electrons follows a capricious path the concept 

 of "range" of penetration is not so unique for electrons as it is for heavy 

 particles. The total length of the track of an electron in an unbounded 

 material is called the "true range." This length can be calculated from 

 the stopping power of the material, like the range of heavy particles. 



The dependence of the mean "stopping number" B in Eq. (17) upon 

 the energy of an electron may be disregarded over a wide range of electron 

 energies. When this is done the true range R is found to be proportional 

 to the square of the initial kinetic energy T of an electron. Making use of 

 the rules for the estimation of the stopping power indicated in Sect. 4-1 

 and assuming a value of the stopping number B of approximately 10, the 

 following expression is obtained: 



