DEMONSTFLATION OF ELECTRON ■ WAVES 553 



Faraday collector as indicated. The results of investigations of this 

 kind, exhibited by polar diagrams in the same figure, show clearly 

 that the incident beam is regularly reflected as if from the crystal 

 facets. 



The difficulty in explaining this result by the simple concept of elec- 

 trons as particles is, that the surface of the crystal is much too coarse 

 grained to serve as a reflector for particles as small as electrons; the 

 diameter of the electron is of the order 10"^* cm., whereas, the diameters 

 of atoms are of the order 10~^ cm. — greater by a factor 10-' — and this 

 also is the order of the distance of least separation of atoms in the crys- 

 tal face. It is hard to imagine how such a surface can appear smooth 

 to the incident electrons. On the older views regarding interactions 

 between electrons and atoms, the fate of an incident electron should 

 be much the same as the fate of a comet plunging into a region densely 

 packed with solar systems; the electron might emerge from the crystal 

 without loss of energy after a fortunate encounter with a single atom, 

 but its direction of departure should be a matter of private treaty 

 between the individual electron and the individual atom — in particu- 

 lar, it should not be influenced by the arrangement of atoms in the 

 crystal. The fact that nearly all of the full speed scattered electrons 

 move away in the direction of regular reflection from the crystal face 

 means that three atoms at least are involved in the action, since this 

 number is required to fix the plane of the reflecting surface. The 

 simple observation described above is thus inexplicable in terms of 

 atoms and electrons and their interactions as previously conceived. 



It is interesting to try to imagine how this phenomenon would have 

 been interpreted, had it been observed ten years ago. With de Brog- 

 lie's speculations before us, we recognize it at once as one of the cir- 

 cumstances in which the electron streams exhibits the properties of a 

 wave train. The only restriction to this interpretation is that the 

 wave-length must be assumed small compared to the linear dimensions 

 of the reflecting surface. If wave-lengths are given correctly by de 

 Broglie's formula they are, as has been mentioned, of the same order 

 as those of X-rays. This explains why reflections such as exhibited in 

 Fig. 1 are obtained from the face of a crystal, but not from a poly- 

 crystalline surface, however highly polished ; the reflected beam is syn- 

 thesized, so to speak from a multitude of scattered waves spreading 

 out from atoms regularly arranged in layers parallel to the surface — 

 lacking this regularity the synthesis does not occur. 



The specular reflection of X-rays from a crystal face is, as we know, 

 selective in the following respect: the intensity of the reflected beam 

 passes through sharp maxima as the glancing angle d passes through 



