DEMONSTRATION OF ELECTRON WAVES 555 



glancing angles are proportional (since all of them are quite small) 

 to the distances from the spots formed by the primary beam to the 

 edges of the respective fogged regions; the fogging is produced by gen- 

 eral or random scattering and its sharp cutoff on the left marks the 

 intersection of the plane of the crystal with the photographic plate. 

 If reflections were specular but non-selective, a spot due to the reflected 

 beam would appear on each strip as far to the right of the fogging edge 

 as the fiducial spot is to the left. This is not what is observed ; there 

 is strong specular reflection at a series of equally spaced angles, and at 

 adjacent angles weaker reflection which apparently is not regular. In 

 other ranges of angle, there is no reflection at all. This is exactly the 

 phenomenon observed with X-rays, the apparently non-regular reflec- 

 tion is ascribed in the latter case to regular and selective reflection from 

 parts of the crystal which are displaced somewhat from the mean 

 orientation of the crystal as a whole — ascribed, that is, to imperfections 

 in the crystal. The same explanation applies here. 



Here then is an experiment in which a stream of electrons exhibits 

 the properties of a beam of waves. The mere occurence of specular 

 reflection is, as we have seen, incompatible with the idea that electrons 

 are simple particles, with such properties as are commonly ascribed to 

 particles. The further observation that the reflection is selective in 

 accordance with the Bragg law amounts to a demonstration that we 

 are dealing with trains of waves — or, at least, to a demonstration of the 

 convenience of this conception — for the Bragg law is simply and 

 accurately explained as a consequence of interference among scattered 

 waves expanding from regularly disposed centers, such as the atoms 

 of a crystal. 



The data of the experiment enable us to calculate the length of the 

 waves. From the Bragg law \ = 2d sin^/w; the reflections are from 

 the (100) atom planes of iron for which d = 1.43 X 10"^ cm. or 1.43 

 Angstrom units; the value of sind/n deduced from Fig. 2 and related 

 data is 0.0189, so that X = 2 X 1.43 X 0.0189 = 0.054 Angstrom 

 units. TJiis is the experimentally determined wave-length of 53 kv. 

 electrons. 



We compare this with the theoretical wave-length computed from the 

 de Broglie formula, X = hjp. The momentum ^ of a particle of rest- 

 mass m and charge e which has been accelerated from rest through a 

 potential difference Fin absolute units is given in relativistic mechanics 

 by 



Ve 1 1/2 



= {IVemyiA 



1 +o , 



