Electrons behaving as waves, can be used to "illuminate" objects in the same way light is. In an electron microscope, electrons are given energy by accelerating them in a manner similar to the way a TV tube works. Then, using magnetic fields, they are directed to the object of interest. In this case, though, the electrons are focused by the magnetic fields to illuminate the object, and then to form the image as shown in Figure 1.
The wavelengths of the electrons are related to their kinetic energies. In electron microscopes, wavelengths as much as 100000 times smaller than those of visible light can be achieved. With such small wavelengths, electron microscopes can reveal features that are as small as 0.000000001 meters (1 nm). Below are some electron microscope pictures.
Additional Problem
A situation where matter waves could become important is the Star Trek transporter. We are not sure how a transporter would really work, but for the purposes of this activity, let us suppose that it decomposes a person into his or her component atoms. Then, it sends the atoms to a new location where the person is reconstructed.
Consider transporting Captain Janeway of the USS Enterprise by such a method. She wishes to reach her new location quickly, so her atoms are sent out of the ship at 10% of the speed of light (3 ´ 107 m/s). Assume that her atoms have a mass of 1 ´ 10-26 kg
What is the de Broglie wavelength of each matter wave?
Each atom must be transmitted through the titanium hull of the starship. The titanium can be considered as a large number of slits separated by 1 nm.
Must the designers of the transporter be concerned about diffraction effects as the captain's atoms are beamed through the hull of the Enterprise? Why or why not?
Would this effect make a good premise for a Star Trek move? Why or why not?