Matter wave-particle duality

If they were to account for the spectrum of atomic hydrogen and then atoms of the other elements, scientists of the early twentieth century had to revise the nineteenth-century description of matter to take into account wave-particle duality. One of the first people to formulate a successful theory (in 1927) was the Austrian scientist Erwin Schrodinger (Fig. 1.23), who introduced a central concept of quantum theory. 

Erwin Schrodinger (1887-1961 Nobel Prize for physics 1932) transferred the concept of wave-particle duality of matter developed by L. V. de Broglie for electrons to the whole atom and thus developed wave mechanics. The Schrodinger equation allows a description of orbitals as the probability of the location of the electrons. Wave mechanics represented a significant development, but were subsequently shown to be insufficient. 

Wave-particle duality The description of matter as a wave or a particle is possible and neither is preferred. Particle-type questions get particle-type answers and wave-type questions get wave-type answers. 

The electron, discovered by J. J. Thomson in 1895, was first considered as a corpuscule, a piece of matter with a mass and a charge. Nowadays things are viewed differently. We rather speak of a wave-particle duality whereby electrons exhibit a wavelike behavior. But, in Levine s own words [45], quanmm mechanics does not say that an electron is distributed over a large region of space as a wave is distributed it is the probability patterns (wavefunctions) used to describe the electron s motion that behave like waves and satisfy a wave equation. 

Electron diffraction In 1924, de Broglie postulated his principle of wave-particle duality. Just as radiation displays particle-like characteristics, so matter should display wave-Uke characteristics. It followed, therefore, from eqs (22) and (2.7) that a particle with energy, E, and momentum, p, has associated with it an angular frequency, , and wave vector, k, which are given by... 

Einstein s idea started a truly revolutionary development in physics quantum mechanics, It opened up wide new horizons and clarified many outstanding problems in our view of the structure of matter, Quantum mechanics is based on the idea of wave-particle duality. Einstein first applied this idea to the nature of light, but it was... 

Twentieth-century scientists had to rebuild their description of matter to take into account wave-particle duality. One of the first people to succeed was the Austrian scientist Erwin Schrodinger, and we shall concentrate on his approach. 

Up to now, we have summarized quite a number of seemingly bizarre results. However, all of these results can be understood by accepting the idea of wave-particle duality, which may not be predicted from classical physics, but is not intrinsically inconsistent with it. It could be argued that now we simply know more about the nature of matter and light thus the concepts of waves and particles, previously thought to be so different, simply have to be extended to a middle ground. 

The fact that atoms, electrons, nuclei, and other forms of matter have some properties that lead us to describe them as particles and other properties that we associate with waves is referred to as the wave-particle duality of matter. This wave-particle duality is hard to understand but it is a fact—a part of the world in which we live. 

This wave-particle duality applies also to matter. Electrons, protons, neutrons, and other material panicles have been found to have properties which we usually correlate with wave motion. For example, a beam of electrons can be diffracted in the same way as a beam of X-rays. The wavelength associated with an electron depends upon the speed with which it is traveling. For electrons which have been accelerated by a potential drop of 40,000 volts, the wavelength is 0.06 A. 

The series of Radioactive disintegrations the uranium-radium series, the uranium-actinium series, the thorium series, and the neptunium series. The age of the earth. The fundamental particles electron, proton, positron, neutron, positive, negative, and neutral mesons, neutrino. The photon (light quantum) the energy of a photon, hv. Planck s constant. The wave-particle duality of light and of matter. The wavelengths of electrons. 

By 1930, these paradoxes had been resolved by quantum mechanics, which superseded Newtonian mechanics. The classical wave description of light is adequate to explain phenomena such as interference and diffraction, but the emission of light from matter and the absorption of light by matter are described by the particlelike photon picture. A hallmark of quantum, as opposed to classical, thinking is not to ask What is light but instead How does light behave under particular experimental conditions Thus, wave-particle duality is not a contradiction, but rather part of the fundamental nature of light and also of matter. 

The key new ideas of qnantnm mechanics include the quantization of energy, a probabilistic description of particle motion, wave-particle duality, and indeterminacy. These ideas appear foreign to ns because they are inconsistent with our experience of the macroscopic world. We have accepted them because they have provided the most comprehensive account of the behavior of matter and radiation and because the agreement between theory and the results of all experiments conducted to date has been astonishingly accurate. 

In the absence of any catalytic influence, this reaction is exceedingly slow (Hoffmann and Boyce, 1983 Hoffmann and Jacob, 1984 Boyce et al., 1983). However, in the presence of light with X < 285 nm this reaction is accelerated manyfold thus in a liberal definition of catalysis, wherein we consider the wave particle duality of light and matter (Hawking, 1988), this reaction is catalyzed nominally by light. The autoxidation of S(IV) (Eq. 20) is also sensitive to trace... 

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