The Wave Nature

Light has wave nature. It has electric and magnetic fields which are perpendicular to each other, and can travel through space. No medium is required. Because of its wave character, we can define light in terms of fi-equency and wave length. The distance between two adjacent crests or troughs, or any two adjacent identical points on a wave is called wave length (X). Frequency (f) is 

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The Schrodinger equation cannot be subjected to firm proof but was put forward as a postulate, based on the analogy between the wave nature of light and of the electron. The equation was justified by the remarkable successes of its applications. 

Since the recognition in 1936 of the wave nature of neutrons and the subsequent demonstration of the diffraction of neutrons by a crystalline material, the development of neutron diffraction as a useful analytical tool has been inevitable. The initial growth period of this field was slow due to the unavailability of neutron sources (nuclear reactors) and the low neutron flux available at existing reactors. Within the last decade, however, increases in the number and type of neutron sources, increased flux, and improved detection schemes have placed this technique firmly in the mainstream of materials analysis. 

When Davisson and Germer reported in 1927 that the elastic scattering of low-energy electrons from well ordered surfaces leads to diffraction spots similar to those observed in X-ray diffraction [2.238-2.240], this was the first experimental proof of the wave nature of electrons. A few years before, in 1923, De Broglie had postulated that electrons have a wavelength, given in A, of ... 

L. V. de Broglie (Paris) discovery of the wave nature of electrons. 

There was no experimental evidence for the wave nature of matter until 1927, when evidence was provided by two independent experiments. Davisson found that a diffraction pattern was obtained if electrons were scattered from a nickel surface, and Thomson found that when a beam of electrons is passed through a thin gold foil, the diffraction pattern obtained is very similar to that produced by a beam of X-rays when it passes through a metal foil. 

In classical mechanics both the position of a particle and its velocity at any given instant can be determined with as much accuracy as the experimental procedure allows. However, in 1927 Heisenberg introduced the idea that the wave nature of matter sets limits to the accuracy with which these properties can be measured simultaneously for a very small particle such as an electron. He showed that Ax, the product of the uncertainty in the measurement of the position x, and Ap, the uncertainty in the measurement of the momentum p, can never be smaller than M2tt ... 

The famous experiment proposed by Aharonov and Bohm [53,54] is schematically represented in Fig. 6. In such an experiment, a source emits an electron beam directed toward a wall in which two slits, located on each side of the beam axis, are located. A photographic plate (film) placed behind the slits records impacting electrons. After the emission of a large number of electrons by the source, the aforementioned film exhibits neat, clear, and dark fringes that are parallel to the slits. This result is interpreted as a manifestation of the wave nature of electrons. 

Two main ideas are related to the development of this technique. The first one is the wave nature of the matter. As postulated by Louis de Broglie in 1924, a free electron with mass m, moving with speed v, has a wavelength % related to its momentum (p = mv) in exactly the same way as for a photon, that is,... 

The second idea related to the LEED technique is, as its name indicates, the diffraction phenomenon. With the wave nature of the electrons established, information on the interaction of a beam of light with matter can be extrapolated to understand the interaction of a beam of electrons with a crystal. In this sense, the corresponding relationship is that of a monochromatic beam of light—that with a single frequency and single wavelength—with that of a beam of electrons of fixed energy. 

Figure 6.17 shows a schematic of the LEED system. The sample is bombarded through the left by a beam of electrons. Only radiation or electrons (remember the wave nature of matter ) with the same energy as the incident beam are detected. These electrons are called elastic backscattered electrons. The detection system is a fluorescent screen placed in front of the sample. Holding the screen at a large positive potential accelerates the electrons. Once they reach it, they excite the phosphorus in the screen, marking it with bright spots characteristic of the diffraction pattern. Finally, a camera in front of the screen records the diffraction pattern. 

Was this your answer Moving According tode Broglie, particles of matte1 behave like waves by virtue of their motion.The wave nature of electrons in atoms is pronounced because electrons move at speeds of about 2 million meters per second. 

If you think the wave nature ofthe electron is bizarre, explore this site for information on and references to the potentially revolutionary theory that particles, forces, space,... 

The dimensions of the car and the nature of the materials of the car dictate that there will be certain frequencies that reinforce themselves upon vibration. When the vibration of the tires matches the car s natural frequency the result is a resonance, which is selfreinforcing waves. The wave nature of the car, however, is simply due... 

ELECTRON MICROSCOPE. The concepts that eventually led to the development of electron microscopes came out or the discovery of the wave nature of the electron in 1924. The effective wavelength of the electrons varies with accelerating voltage and is less than 1 A >. = /< 150/ V) A. This short wavelength makes possible far better resolution and higher magnification in the electron microscope as compared with the optical microscope. 

The wave nature of electrons explains so many previously unexplained facts for the following reason. If waves are confined to a finite region of space, iliey form characteristic shapes and patterns that are specific to (lie nature of the confinement. [Figure 8 in the entiy on Chemical Elements shows waves in space confined to the neighborhood of a central point.] Only those and no other patterns can develop in this sort of confinement. But this is just the confinement that electrons suffer when they are confined around the atomic nucleus by electric attraction. The electron waves in atoms must assume some of these patterns. The simple patterns are lower than the more complex ones they are lower in energy. Indeed, the electrons in an atom assume the lowest possible patterns. 

Wavefunctions of electrons in atoms are called atomic orbitals. The name was chosen to suggest something less definite than an orbit of an electron around a nucleus and to take into account the wave nature of the electron. The mathematical expressions for atomic orbitals—which are obtained as solutions of the Schrodinger equation—are more complicated than the sine functions for the particle in a box, but their essential features are quite simple. Moreover, we must never lose sight of their interpretation, that the square of a wavefunction tells us the probability density of an electron at each point. To visualize this probability density, we can think of a cloud centered on the nucleus. The density of the cloud at each point represents the probability of finding an electron there. Denser regions of the cloud therefore represent locations where the electron is more likely to be found. 

This section reviews the evidence for the wave nature of light and of X-rays, and then puts these two forms of radiation into the context of electromagnetic radiation in general. 

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