100 RADIATION BIOLOGY 



representing the number of electrons transmitted through foils of increasing 

 thickness resemble the curves of Fig. 1-56 except for the lack of an initial rise. 

 In fact, the plot of "number vs. thickness," rather than the plot of "energy vs. 

 depth," serves usually as a basis for the definition and for the experimental 

 determination of the "extrapolated range" of electrons (see Fig. 1-56). 



The minimum thickness of material which lets no electron through 

 is also of practical importance. This thickness may be called the 

 "maximum range." It coincides, in principle, with the "true range" 

 (see Sect. 4-2c) since maximum penetration is achieved by an electron 

 which happens to undergo no deflection and therefore travels in a straight 

 line until its energy is fully spent; in practice, the probability of straight- 

 Hne travel is vanishingly small. The maximum range is considerably 

 larger than the "extrapolated range" for electrons of moderate energy in 

 heavy materials, where scattering is most important. 



"True" range, "extrapolated" range, and "maximum" range are 

 almost synonymous when energy dissipation by collision predominates 

 over the effect of scattering (see Sect. 4-2b). On the other hand, the 

 concept of "range" becomes meaningless when X-ray production pre- 

 dominates and showers are formed. 



4-2g. Data on Electron Penetration. It would be desirable to present 

 sets of data pertaining to the penetration of electrons of various energies 

 into various material and concerning (1) the stopping power, (2) the 

 "true" range, (3) the "extrapolated" range, (4) the dissipation of energy 

 at various depths, including the case of shower formation, and (5) the dis- 

 tribution of electrons and photons generated by shower processes. 



Data of fair accuracy on items (1) and (2) can be derived from the basic 

 theory of stopping power [Eq. (19), Sect. 2-4b], but no extensive tabula- 

 tion is available and experimental data are scarce and often of low precision. 

 Figure 1-61 shows experimental data on the extrapolated range [item (3)] 

 in aluminum ; corresponding data on other materials are scarce. Quanti- 

 tative information on item (4) is still hmited (see Figs. 1-61 and 1-62), 

 even though it would not be difficult to derive it experimentally in many 

 instances. Quantitative information on showers can be derived from 

 theory with fair accuracy, except at lower energies in heavy materials, 

 but tabulations are scarce. The Wilson (1952) sample calculations on 

 showers constitute some of the most instructive data available. 



4-2h. Penetration of Beta Rays through Thick Foils. The rays from 

 any radioactive substance consist of electrons or positrons of different 

 kinetic energies, which range from zero up to a maximum which depends 

 on the substance. As these electrons penetrate through a material, the 

 lower energy ones stop first and then those of higher and higher energies. 

 The plot of the number of electrons transmitted through a foil vs. the 

 thickness of the foil shows, then, an upward concavity, as in Fig. l-63a. 

 The penetration of the few electrons of highest energy tends to extend the 



