As we’ve known since the days of Newton, a particle’s momentum is directly proportional to its mass. For a massive particle with large momentum, the size of Planck’s constant makes the de Broglie wavelength very small, even when compared to the wavelengths of light. This made it quite challenging to observe any wavelike behavior of matter particles in the laboratory. Remember, in order to observe wavelike behavior, the waves have to interact with structures that are about the same size as the wavelength.
Aware of these difficulties, de Broglie was asked by a thesis examiner to suggest an experiment that could actually demonstrate his bold assertion. His reply—diffraction of an electron beam from a crystal—was logical, since this had been used to prove that light exhibits wavelike properties. Little did he know, however, that this effect had already been observed, if not fully understood, in the laboratory.
As early as 1922, the American physicists Clinton Davisson and Charles Kunsman had been scattering low-energy electron beams off of various substances. These experimental conditions were opportune since a particle’s momentum is the product of its mass and velocity. To get the longest (and therefore most “detectable”) de Broglie wavelength, you would not only use the lightest particle available (the electron), you had to let it move as slowly as possible, while still going fast enough to keep it moving in a straight line.
Following a few preliminary indications of matter waves, which he had disregarded, Davisson observed indisputable evidence for matter waves in a later experiment with his colleague Lester Germer. Interestingly, their experiment was not originally designed to look for evidence of matter waves, but rather to study the surface of nickel using a low-energy electron beam as a probe.
Fortunately for them, someone accidentally dropped a flask onto their experimental apparatus and punctured its vacuum. In the process of cleaning the original polycrystalline nickel target, portions of the nickel organized into single crystals, which then produced clear and indisputable diffraction patterns. In 1927, Davisson and Germer put it all together and concluded without a doubt that electrons had wavelike properties.
While this was not as simple a diffraction demonstration as the two-slit experiment, it was still clear evidence of wave behavior. In fact, it is exactly the same as the Bragg scattering the atoms in evenly spaced crystal planes provided the opportunity for scattered X-rays to interfere constructively and destructively, making a regular pattern of peaks at certain scattering angles.
The schematic on the left illustrates the intensity of scattered electrons from the nickel target as a function of the scattering angle. The full two-dimensional image on the right represents what would be formed on an electron detector placed above the crystal.
Davisson and Germer had managed to make an electron beam with a de Broglie wavelength comparable to the wavelength of X-rays, so with the similar crystal plane spacing they could observe similar diffraction patterns in the scattered electrons. Not only that, but they could vary the momentum of their electrons, and show that the wavelength changed just the way de Broglie had predicted!
QUANTUM LEAP
For their experimental efforts, Davisson was awarded the 1937 Nobel Prize in physics. He happened to share the prize with a British experimentalist, George Thomson, who had observed electron waves using a different technique. Ironically, George Thomson, who earned the Nobel Prize for demonstrating the electron was a wave, was the son of none other than J. J. Thomson, who earned his Nobel Prize for isolating the electron as a particle.
This was an amazing discovery, and was soon followed by similar experiments with heavier particles like protons, neutrons, and even helium atoms, all of which showed the behavior of waves with a de Broglie wavelength. Experiments had confirmed the wild idea of a mere graduate student that few had taken seriously. This didn’t solve all of the mysteries of the atom by any means, but it established a major truth that is essential to understanding modern quantum physics.
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