The great success of Einstein's theory for the photoelectric effect stimulate de Broglie to postulate in his Ph.D. thesis at the University of Paris, that particles might exhibit wave-like properties. Starting from Einstein's relation, Ephoton = h f and using the relation given by Maxwell's equations for the momentum of a light wave, Elight = pc (where p is the momentum of the light, and c is the speed of light), de Broglie derived the expression p =h/
,
where is
the wavelength of light; he proposed that this relation could be
taken over to refer to particles, whose "wavelength" (whatever
that means!) would be given by =
h/p.[Note the deliciously schizophrenic appearance of these formulae; on the right hand side there is a "particle" property - energy or momentum, while on the right hand side there is a "wave" property - frequency or wavelength.]
How could these particle wavelengths be observed? Remember that one identifying feature of waves is their ability to interfere, as in the double slit experiment. However, for electrons, for instance, this wavelength turns out to be very small. Now remember that wave effects (i.e. diffraction effects or interference) are difficult to see if we use measuring devices which are much larger than the wavelengths involved. So it was not surprising that the first confirmation of de Broglie's apparently fantastic proposal should find experimental support in the study of the interaction of electrons with metals. For the regular planes of atoms which are found crystals turn out to be just of the correct order of magnitude to allow observation of interference effects of electrons which are being reflected from metal crystal surfaces. In fact such crystal planes had already been used to show the effects of interference for X-rays - which are just very short wavelength electromagnetic waves; the wavelength of X-rays is around a few Angstroms - 1A = 10-10m - so we need a "diffraction grating" which has line spacing between the slits of the same order of magnitude as this wavelength, and crystal planes do the job!
In 1927, three years after de Broglie's proposal, Davisson and Germer, working at Bell Labs in the US, and, independently G.P. Thomson working at Cambridge University, observed interference patterns in the scattering of electrons. The "wavelength" of the electrons, calculated from the observed interference patterns, agreed exactly with de Broglie's formula.
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