THE DISCOVERY OF ELECTRON WAVES 477 



note that in achieving this tour de force Bohr made judicious use of the 

 constant which Planck had extracted from the black body spectrum, 

 the constant h. 



It looked at this time — in the year 1913 — as if the authentic key to 

 the spectra had at last been found, as if only time and patience would 

 be needed to resolve their riddles completely. But this hope was never 

 fulfilled. The first brilliant triumphs of the theory were followed by 

 yet others, but soon the going became distressingly difficult, and 

 finally, despite the untiring efforts of countless helpers, the attack came 

 virtually to a standstill. The feeling grew that deeply as Bohr had 

 dived he had not, so to speak, touched bottom. What was wanted, it 

 was felt, was a new approach, a new theory of the atom which would 

 embrace necessarily all the virtues of the Bohr theory and go beyond it 

 — a theory which would contain some vaguely sensed unifying principle 

 which, it was felt, the Bohr theory lacked. 



Such an underlying principle had been sought for almost from the 

 first. By 1924 one or two ideas of promise had been put forward and 

 were being assiduously developed. Then appeared the brilliant idea 

 which was destined to grow into that marvelous synthesis, the present 

 day quantum mechanics. Louis de Broglie put forward in his doctor's 

 thesis the idea that even as light, so matter has a duality of aspects; 

 that matter like light possesses both the properties of waves and the 

 properties of particles. The various "restrictions" of the Bohr 

 theory were viewed as conditions for the formation of standing electron 

 wave patterns within the atom. 



Reasoning by analogy from the situation in optics and aided by the 

 clue that Planck's constant is a necessary ingredient of the Bohr 

 theory, de Broglie assumed that this constant would connect also the 

 particle and wave aspects of electrons, if the latter really existed. 

 De Broglie assumed that, as with light, the correlation of the particle 

 and wave properties of matter would be expressed by the relations: 



(Energy of particle) E — hv (frequency, waves/unit time). 



(Momentum of particle) p = ha (wave number, waves/unit distance). 



The latter may be written in the more familiar form X — h/p where X 

 represents wave-length. 



Perhaps no idea in physics has received so rapid or so intensive 

 development as this one. De Broglie himself was in the van of this 

 development but the chief contributions were made by the older and 

 more experienced Schroedinger. 



In these early days — eleven or twelve years ago — attention was 

 focussed on electron waves in atoms. The wave mechanics had 



