550 BELL SYSTEM TECHNICAL JOURNAL 



was well established experimentally that a beam of monochromatic 

 light can impart to individual electrons in matter amounts of energy 

 proportional to its frequency. The factor of proportionality between 

 these quantities— the energy imparted to the electrons and the fre- 

 quency of the light — is the same as that obtained from the black body 

 spectrum for the factor of proportionality between the energy quantum 

 of the Planck oscillator and its frequency. The relation between the 

 energy e imparted to the electron and the frequency v of the light is 

 expressed, that is, by the formula e = hv, where h is the so-called 

 Planck constant. When one tries to visualize the mechanism back of 

 this phenomenon, he is led inevitably to a corpuscular theory of light. 

 No other view appears adequate to explain this central fact of photo- 

 electricity and others related to it. 



On the other hand, the phenomena of interference and diffraction 

 disposed long ago, as is well known, of an earlier corpuscular theory of 

 light in favor of the wave theory. The demands of these phenomena 

 are as insistent today as every they were, so that the situation comes 

 to this, that one class of optical phenomena indicates clearly that light 

 is a corpuscular radiation, and another indicates no less clearly that it 

 is a propagation of waves. It is hopeless to try explaining photoelec- 

 tric phenomena in terms of nothing but waves, and it is equally hope- 

 less trying to devise a purely corpuscular interpretation of interference 

 and diffraction. 



It was de Broglie's brilliant idea that a situation similar to this might 

 exist in regard to electrons, that electron streams like beams of light 

 might possess in different circumstances the properties both of wave 

 trains and of particle streams. If this were true, and if the wave as- 

 pect alone were adequate to explain the behavior of electrons in atoms, 

 then the unhappy state of affairs which existed in regard to the inter- 

 pretation of spectroscopic data might be remedied. 



The formula e = hv expresses, as we have seen, a certain correlation 

 between the corpuscular and the wave properties of light; if the light 

 regarded as a beam of waves is of frequency v, then when it is regarded 

 as a stream of corpuscles, the corpuscles or photons are of energy 

 e = hv. A second correlation follows at once from this one and from the 

 relation which is known to exist between the transfer of energy and of 

 momentum by a beam of light. This second correlation relates the 

 momentum p of the photon to the wave-length X in vacuo of the asso- 

 ciated waves, and is expressed by the formula p = h/\. Or if we 

 write 0- to represent wave number — the number of waves per cm. — 

 then the two correlations are expressed by the symmetrical formulae 



€ = hv, 

 p = ha. 



