of a photon, p = h/Ȝ, could also be applied to matter. A particle’s wavelength, sometimes called the de Broglie wavelength, is related to its
momentum by Ȝ = h/p, as shown in Equation 1.
De Broglie’s insight provided a crucial step in the understanding of the atom. He and other physicists used the idea to write down equations for
the standing waves corresponding to any particle confined to a small space. The form of the matter waves (also known as the wavefunction of
the particle) leads to predictions about the behavior of the particle. This is the principle behind quantum mechanics, also called wave
mechanics.
37.3 - Observing matter waves
When light is shone through a pair of small slits, an interference pattern results. We
show a light interference pattern in Concept 1.
If electrons can act like waves, they should also display interference patterns, and they
do. The slits used should be of a width comparable to the wavelengths of the electrons
in the experiment, which are moving at a speed such that their wavelength is on the
order of 10í^10 meters. You see the interference pattern caused by sending electrons
through slits in Concept 2.
At the time that de Broglie proposed his theory of matter waves, it was not possible to
make slits small enough to demonstrate electron diffraction. However, in 1927 two
physicists named Clinton Davisson and Lester Germer inadvertently produced electron
diffraction using a crystal of nickel. The spacing between atoms in the crystal happened
to be on the order of the electron wavelength, causing the electrons’ matter waves to
interfere.
After witnessing this and the diffraction of other particles such as neutrons and whole
hydrogen atoms, scientists began to take the wave-like nature of particles for granted,
or perhaps better put, to marvel at it as a fact of nature. They called it the wave-particle
duality.
Once they finished marveling, they also concluded that they could take advantage of
the wave properties of matter. Wave diffraction imposes a limit on how small of an
object can be resolved when it is probed with radiation of a certain wavelength. For
example, an ordinary microscope uses visible light and glass lenses, and cannot
resolve objects much smaller than 10í^6 m, which is on the order of the wavelength of
visible light.
To gain increased resolution, a transmission electron microscope (TEM) employs
electrons instead of light. The wavelengths of those electrons are about ten thousand
times smaller than that of light, which allows the TEM to resolve objects down to a size
of about 10í^10 m. Just as the light in an ordinary microscope passes through a sample
that is fixed on a glass slide, the electron beam (think of it as a wave) passes through
the thin sample on the way to a detector. An ordinary microscope uses a glass lens to
focus light rays; the TEM uses magnetic fields to focus the charged electron beam.
In Concept 3 is an artificially-colored image captured by a transmission electron
microscope. It shows a salivary gland of a mosquito infected by the Eastern equine
encephalitis virus (red dots). The individual viruses are about 60 nanometers in
diameter, and even smaller details than this are visible in the image. In comparison, the
best optical microscopes can only resolve details as small as 200 nanometers.
Finding the wave in light
Light’s wave-like properties visible in
interference patterns
Matter waves
Electron interference pattern
Pattern also created by projecting
electrons at crystal
Transmission electron
microscope
Takes advantage of small wavelengths
of electrons
Resolves details at a scale of 10í^10
meters