2170 - Notes, Syllabus Section III, lecture 16 (2/21/96)
(Here is the previous lecture )
How could we ever observe the wave like behavior of particles?
Look for phenomena associated only with waves! E.g., look for diffraction
around an edge, or through a slit, or interference. The first such result was
in 1925, by Davisson and Germer, at Bell labs. They were busy studying
crystal surfaces by electron beam reflection, and were seeing the classical
behavior - electrons scatter in all directions, with a very slight dependence
on scattering angle, and an even weaker dependence on electron energy. Then
their apparatus broke, exposing the nickel target to air. To get rid of the
oxide, they baked the nickel, and in the process re crystallized the nickel
into one large uniform crystal. The result - their electron scattering now
behaved very differently! The electrons showed strong reflection only at
particular angles, and had a clear energy dependence. The (simplistic)
explanation goes like this:
Electrons are behaving like an incoming wave, with wavelength
.
The path length difference is D sin(theta). So, if D sin(theta) is an integer
number of wavelengths, then one gets constructive interference (bright spots)
They plotted intensity in a funny way (polar graphs, on left),
Plots are shown for 54 eV of electron energy, and for this case,
D=2.15 A (the inter atomic spacing, measured with X-rays), and the wavelength =
2.15 sin(50) = 1.65 Angstroms.
The momentum is
.
(For these small voltages, you can check that the electrons are very much
non-relativistic. )
For V=54 Volts, h/p=1.66 A, de Broglie is right on the money!
Davisson and Germer systematically checked, varying electron energy (and later,
crystal spacing), and it continued to agree perfectly.
Here is the
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