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When carrying out the double slit experiment using electrons or buckyball molecules, do the particles have to be traveling at near light speed velocities to produce an interference pattern?

double split

Results of a double-slit-experiment performed by Dr. Tonomura showing the build-up of an interference pattern of single electrons. Numbers of electrons are 11 (a), 200 (b), 6000 (c), 40000 (d), 140000 (e).

One of the most amazing things about quantum mechanics, in my opinion, is that we're beginning to see that it applies, not just to microscopic particles moving near light speed, but also to larger objects moving more slowly. Being able to perform the famous double slit experiment with buckyballs is indicative of the power of quantum mechanics as a scientific theory.

To get a little technical, there's really one equation which dictates how a double slit experiment should be performed, and it's this:

doublesplit  formula1

This equation relates three things: p is the momentum of a particle, which depends on the particle's speed and mass, h is a constant (called Planck's Constant, with a horrendous value of 6.63 x 10-34 Joule-seconds!), and λ is what's known as the de Broglie wavelength. Louis de Broglie was a French physicist who, in his PhD thesis in 1924, argued what we now know to be true - that both light and particles can behave like waves. The connection between particles and waves that he came up with is the equation I've just mentioned. That's why λ is called the de Broglie wavelength (when you discover something, you get to have it named after you!). The de Broglie wavelength describes the effective wavelength that a particle would have when it was behaving as a wave.

So it's obvious that, in order for the double slit experiment to work, the particles in question (be they photons, electrons, buckyballs or airplanes) have to be behaving like waves, and that's determined by the de Broglie wavelength. Step two of setting up our experiment has to do with the dimensions of the double slit experiment. The interference pattern is dictated by the distance from one bright line (coherence) to the next:

doublesplit formula2

where D is the distance from the slit to the screen (or detector), little d is the spacing between the slits, and λ is going to be our de Broglie wavelength.

Let's assume we want to use electrons for our experiment. We build a setup with the screen placed 1 meter from the slits, and the two slits 1 millimeter apart (maybe we found this equipment in a storage closet in the physics department...). This setup will make the distance between the bright spots on our screen 1000 times what the de Broglie wavelength of our incoming electron is. We want to be able to actually see the interference pattern in our detectors, so perhaps we should request that the spacing of the bright spots be about 1 millimeter (this would depend on the detectors, of course). This means the de Broglie wavelength of our electron has to be about one meter. Now we go back to the equation for de Broglie wavelength, and see that we know h and we now know λ, so we can calculate what p should be. Since we know the mass of the electron, calculating the momentum is essentially the same as calculating the speed; for our experiment, we find the electron needs to be going about 0.0007 m/s! That's a tiny speed... about 2 inches a minute (kind of like pouring ketchup)!

Such a "tabletop" experiment perhaps isn't a good setup to measure electrons (they actually do it using diffraction gratings instead of slits, with spacing much smaller than 1 mm), but the basic point is that the de Broglie wavelength gets smaller with increasing speed, and that makes a double slit experiment harder and harder to do, because you have to adjust your setup to match the changing wavelength. For the buckyball experiment (see http://physicsworld.com/cws/article/news/2952), the researchers used slits about 100 nanometers apart (a nanometer is one millionth of a millimeter), and shot the buckyballs through the slits at about 200 meters per second (roughly 500 mph), much slower than the speed of light. The de Broglie wavelength is what dictates whether a particle is behaving like a wave - and thus whether or not you see an interference pattern.

Answered by:

Kelly Chipps (AKA nuclear.kelly)
Postdoctoral Fellow
Department of Physics
Colorado School of Mines

Submitted by:

Mog from Rainford, UK