Because electrons behave as waves, they can be used to “illuminate”
objects in a manner similar to light. An electron microscope is an
instrument that takes advantage of this situation. 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 at an object of
interest. The electrons are focused to illuminate the object, and then to
form the image of that object. A schematic diagram is shown in Figure 4-1.
This system can be used to look closely at very small objects.
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.
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 Voyager 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 x 10^7 m/s). Assume that her atoms have a mass of 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
movie? Why or why not?
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