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29.6 The Wave Nature of Matter
It is reasonable to ask if there is a particle-wave duality for matter as well since we have seen connections between matter and photons.
The answer is yes.
The consequences will be shown in the next section.
When waves spread out and interfere as they pass through a double slit, they are detected on a screen as tiny dots.
The waves and the patterns produced on the screen can be explored using quantum detectors.
A radical proposal was made by a French physics graduate student in 1923.
Nature would be symmetric if matter had both particle and wave properties.
If we think of a wave as a particle, then what we think of as a particle may also be a wave.
The suggestion was so radical that it was greeted with skepticism.
Einstein said that the thesis was probably correct and that it might be of fundamental importance.
Einstein and a few other physicists supported de Broglie in his quest for a doctorate.
interference is the hallmark of a wave.
If matter is a wave, it must be constructive and destructive.
In order to see interference effects, a wave must interact with an object about the same size as its wavelength.
Since is very small, it is also small.
To see its wave characteristics, the bowling ball would have to interact with something much smaller than anything known.
When waves interact with objects larger than their wavelength, they show no interference effects and move in straight lines.
To get easily observed interference effects from particles of matter, the longest wavelength and smallest mass is needed.
The effect was first observed with electrons.
Clinton J. Davisson and G. P. Thomson were both physicists.
The patterns are similar to light interacting with a grating and are consistent with interference of electrons.
All particles have wave properties.
All particles have a relationship between wavelength and momentum.
The wave nature of particles was treated with wave equations in four papers published by the Austrian physicist.
Many others began important work at the same time.
Heisenberg formulated a mathematical treatment of the wave nature of matter that used matrices rather than wave equations.
The development of quantum mechanics was a result of de Broglie's work.
Davisson and G. P. were both awarded the prize for their vision in 1929.
The pattern was obtained by diffracted electrons.
There are bright and dark regions.
If you want to interact with crystal lattice structures that are about this size, you should calculate the electron's velocity.
The classical formula can be used to find the electron's energy and convert it to eV.
The low energy means that the electrons could be accelerated through a 54.0-V potential.
The results confirm the assumption that the electrons are nonrelativistic since their speed is just over 1% of the light's speed and the energy of the electron is about the same as the speed of light.
We would have had to use more involved calculations if the electrons had turned out to be relativistic.
The wave nature of matter can be seen in the electron microscope.
There is a limit to the detail that can be observed with any probe having a wavelength.
observable detail is limited to one wavelength.
It is easy to get electrons with smaller wavelength than visible light with a potential of 54 V. An electron microscope can detect much smaller details than an optical microscope.
There are two types of electron microscopes.
electrons that are emitted from a hot filament are accelerated by the transmission electron microscope The sample is passed through the broadened beam.
A magnetic lens focuses the beam image onto a fluorescent screen, a photographic plate, or a light sensitive camera from which it is transferred to a computer.
The TEM requires a thin sample to be examined in a vacuum.
magnifications of 100 million times the size of the original object can be provided by it.
The TEM allows us to see individual atoms.
The beam is focused onto the sample by using magnets.
The beam is moved around to look at the sample in the x and y directions.
The data for each electron position is processed by a CCD detector, which produces images like the one at the beginning of the chapter.
The advantage of theSEM is that it doesn't require a thin sample or 3-D view.
Its resolution is ten times less than a TEM.
A scanning electron microscope is used to observe small details, such as the tooth of a Himipristis, a type of shark.
When they interact with objects similar to their wavelength, protons, helium nuclei, and many others have been observed to exhibit interference.
All particles have the same wave nature.
The implications of the de Broglie wavelength include the quantization of energy in atoms and the change of our basic view of nature on the small scale.
The next section shows that there are limits to the precision with which we can make predictions.
There are limits to the degree to which we can measure an object's location.
The wave nature of matter allows it to have many characteristics of other waves.
Diffraction gratings produce patterns for light based on the spacing and wavelength of the light.
This effect is most pronounced when the wave interacts with objects with the same wavelength.
The bottom part of the spacing between the planes in a crystal is like the openings in a grating.
The paths of electrons scattering from successive planes differ by one wavelength at certain incident angles.
There is partial to total destructive interference at other angles.
Dramatic interference patterns can be produced by this type of scattering from a large crystal.
The father-and-son team first explored and analyzed Bragg reflection.
The path-length differences are shown in the expanded view and are similar to the pattern of x rays reflected from a crystal.
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