556 BELL SYSTEM TECHNICAL JOURNAL 



where c represents the velocity of light. Writing this into the de Brog- 

 lie formula and evaluating constants for the electron one obtains as a 

 close approximation. 



/ 1S0\ ^/2 

 X= {—-) [1 -4.9X10-^P^] 



for V in volts. Thus the theoretical wave-length of 150-volt electrons 

 is one Angstrom unit or 10~^ cm., and the wave-length of the 53 kv. 

 electrons employed in this experiment is 0.0546 Angstroms which is in 

 good agreement with the value found experimentally. 



These results which are from previously unpublished data by Davis- 

 son and Germer constitute perhaps the simplest demonstration of the 

 wave aspect of electrons and verification of the de Broglie relation — 

 the simplest, at any rate, in which use is made of crystal diffraction. 



E. Rupp has demonstrated the diffraction of electrons by an ordin- 

 ary ruled optical grating and has obtained thereby values of electron 

 wave-lengths which agree with the theoretical values within the rather 

 wide limits of error of this border line experiment. This is, in fact, 

 an experiment more immediately intelligible than any involving the 

 use of crystals. But Rupp's photographic plates exhibiting these 

 results are not very impressive, and, therefore, I have not arranged 

 for their reproduction in this report. 



The Bragg reflection, though the easiest to interpret among the types 

 of crystal diffraction, is not the most easily demonstrated, nor the 

 most striking, nor yet the type which yields most information concern- 

 ing the diftVacting crystal and the atoms composing it. It is the Hull- 

 Debye-Scherrer type of diffraction which is in these respects preemin- 

 ent, and the type which has been most thoroughly investigated. A 

 mass of finely divided crystals of random orientation is placed in the 

 path of a beam of monochromatic radiation; a photographic plate set 

 at right angles to the incident beam receives and records the radiation 

 from the diffracting material. It is evident perhaps that the pattern 

 produced by an aggregate of a very great number of crystals oriented 

 at random will be the same as that generated by a single crystal turned 

 into equally many random positions. Thus, if the material is iron, the 

 single crystal in a particular orientation gives rise to the first order 

 diffraction spot of Fig. 2; rotate the crystal about the primary beam 

 and this spot generates a circle or ring — so also for the second and 

 higher spots, each of them generates a ring. 



But the atoms comprising the crystal may be regarded as arranged 

 in many different sets of planes — there are, in fact, an infinite number 

 of such arrangements. Of these, one is unique in having a greater 



