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.