Page 65
|
9/28/09 |
Particles Like Waves
|
The fact that electrons behaved like particles was well established by the early twentieth century. But the discovery that light waves had particle-like properties suggested to Count Louis de Broglie that particles might have wave-like properties. Therefore, he made the bold assumption in his doctorial dissertation that the wavelength l associated with a particle was related to its momentum p through the relationship l = h/p.
This assumption shed considerable light on Bohr’s hypothesis
that the angular momentum of an electron in a Bohr orbit was an integral multiple
of 
. By assuming that the electron in orbit had a de Broglie wavelength and that that
wave circled back on itself and interfered with
itself, then only those orbits that had an integral number of wavelengths were
stable. All other orbits would destructively interfere with themselves to
cancel themselves out. The requirement that the electron’s wavelength constructively
interfere with itself was mathematically equivalent to the requirement that the
electron’s angular momentum be an integral multiple of 
.
But the de Broglie hypothesis was based solely upon the assumption of symmetry in the universe and the only evidence that it was true was the theoretical explanation of a theoretical model of the atom that was already known to be incomplete. There simply was no experimental evidence to suggest that particles really had wavelengths. That evidence was eventually supplied by Clinton J. Davidson and Lester H. Germer through an experiment performed in 1927. The Davidson-Germer experiment diffracted electrons off of a crystal the same way that the Bragg experiment scatted x-rays off of a crystal. In both cases, the crystalline lattice acted like a microscopic diffraction grading to produce constructive interference at specific angles. Knowing the spacing of the lattice and measuring the angle of scattering, Davidson and Germer were able to determine the wavelength of the electron. Comparing that wavelength with the de Broglie wavelength confirmed de Broglie’s hypothesis. Electrons really did interfere with themselves like waves.
|