Protons, Potatoes, and Pluto

De Broglie’s relation is general and applies to any particle, large or small. Every moving mass has the potential to display interference and other wave properties. So why didn’t we notice this before 1927? And why don’t we see it all around us now that we know it’s there? Once again, it’s all a question of scale.

Take Pluto, for example. Whether or not we choose to call it a planet, it has a mass of about 10²² kilograms, and it moves with a speed of about 5,000 meters per second (m/s) as it orbits around the sun. If we plug these values into de Broglie’s relation, we find that the de Broglie wavelength of Pluto is a miniscule 10^-59 meters! That is so much smaller than the smallest fraction of the smallest thing we can ever hope to measure, that it is completely irrelevant and impossible to observe.

How about a smaller object, like a baseball or a slow-moving potato? If it were a small potato (having, say, a mass of 100 grams) and traveling at about 1 m/s, then the de Broglie wavelength would be a lot larger than Pluto’s. In fact, it would be about 10^-33 meters. That’s larger, but still a billion billion times smaller than an atomic nucleus. With wavelengths like this, there is still no hope of ever observing interference or other wave effects of small potatoes in the laboratory.

For the proton itself, however, the story is very different. The momentum of a slow-moving proton beam, for example, can give the protons a de Broglie wavelength as large as or larger than the separation between atoms in solid matter. Then it becomes possible to scatter protons off structures with sizes comparable to the proton’s wavelength, and thus observe the telltale wave signatures caused by constructive and destructive interference.