Limit of Electron Microscopy 129 



Scattering of electrons by single atoms is considerably different 

 from the dispersion of light by small particles. Figure 45 shows, 

 side by side, the scattering of a parallel light wave by a body, 

 very small in comparison with a wave-length, and the scattering 

 of 10,000 ev electrons by a hydrogen atom. This example has 

 been chosen, because rigorously calculated data are available. 

 (Mott and Massey,^^ p. 120 and 174.) The light intensity 

 scattered at an angle follows Rayleigh's law 



I(^) =Io(l +cos2^) 



which is symmetrical to the plane of the wave, i.e., it is the same 

 forward as backward. Electrons, however, are scattered almost 

 exclusively forward, and practically all within an angle of 5°. 

 The angle of the cone of scattering is inversely proportional to 



VV. The reason for this different behavior is the very much 

 larger momentum of electrons as compared with photons of 

 comparable energy. 



Figure 46 shows the same phenomenon in more detail. The 

 scattering is here divided into elastic and inelastic components. 

 It can be seen that the inelastically scattered electrons are in 

 general deflected by smaller angles. This can be roughly under- 

 stood from the classical picture, as these electrons have collided 

 with the hydrogen electron, while the elastically scattered ones 

 have collided with the nucleus. They are far less numerous. At 

 100,000 ev, for instance, they represent only 5.1 per cent of the 

 total scattering, while the other 94.9 per cent suffer an average 

 loss of 21.7 ev. At 10,000 ev the figure is 6.5 per cent, at 1,000 

 ev 8.7 per cent. 



Figure 46 shows also for comparison scattering by the hydro- 

 gen ion, i.e., by a proton. This is the well-known Rutherford 

 formula 



where Z is the atomic number; in the case of hydrogen, Z ^ 1. 

 This is a law of very different character, as it goes sharply to 



