ELECTRONS AND QUANTA 221 



possibilities of this theory in explaining the properties of the atom as 

 revealed to us by the data of spectroscopy. At last we have an atom 

 endowed with a constitution rather than a set of by-laws. 



The success of the Schroedinger theory in explaining in a natural 

 way the stationary states of the atom and the various rules governing 

 transitions between these states, not to mention numerous others of 

 its successes, must be taken as very strong evidence in favor of the 

 fundamental idea upon which the theory is based — namely, that the 

 duality of wave and corpuscular properties which characterizes light 

 is characteristic also of electrons. If the evidence supplied by these 

 data lacks something in the matter of directness, this deficiency is 

 made good by the experiments on the scattering of electrons by 

 crystals about which I am supposed to be speaking. 



If I have been a long time in coming to the point, the time has not 

 been wasted, for with the picture before us of the energy and mo- 

 mentum of a beam of light being carried by a stream of quanta for 

 which the waves serve only to supply the laws of motion, a workable 

 theory of the scattering of electrons is at once at hand — to a first 

 approximation we merely read "electrons" for "quanta," and there 

 we are. The observations on electron scattering are consistent with 

 the view that the electrons are being guided by waves in just the way 

 we have imagined quanta to be guided in the phenomena of optical 

 diffraction. The only real difficulty seems to be that in the light 

 phenomena it is not easy to believe in the particles, while in the 

 electron phenomena it is hard to have faith in the waves. 



Before going further I should like to point out that we now have 

 two wave-lengths associated with an electron of given speed: one is 

 the length of the X-ray waves which will be generated if the whole of 

 the kinetic energy of the electron is converted into radiation and the 

 other is the length of this new de Broglie wave, the so-called phase 

 wave. The first of these wave-lengths is inversely proportional to 

 the energy of the electron while the second is inversely proportional 

 to its momentum. In terms of the equivalent voltage V of the 

 kinetic energy of the electron, the lengths of the two waves are given 

 in Angstrom units by the formulae 



12,350 J , /150\i/2 



Ax = — y— and \,, = I -— 



and their ratio is given approximately by 



X, _ 1000 



