Light wave-particle duality

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

Quantum description of light the wave/particle duality... 

We are used to thinking of electrons as particles. As it turns out, electrons display both particle properties and wave properties. The French physicist Louis de Broglie first suggested that electrons display wave-particle duality like that exhibited by photons. De Broglie reasoned from nature s tendency toward symmetry If things that behave like waves (light) have particle characteristics, then things that behave like particles (electrons) should also have wave characteristics. 

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... 

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. 

If one considers the wave nature of light, one may think that the photon size is roughly equal to its wavelength (say 500 nm) however, when the photon is absorbed by an atom, it "disappears" within a body of radius 0.5 nm this is a manifestation of the intricacies of the wave-particle duality, which are discussed in Section 3.39. 

Planck, M. 1858-1947 Quantum theory of light and radiation wave/particle duality Mason (1961)... 

Due to the wave-particle duality of neutrons, they can be reflected and refracted in a manner similar to light. Reflected neutron beams can interfere with each other to produce a reflected beam intensity that is characteristic of the reflecting material (Lekner, 1987). Detailed analysis of the reflectivity is able to able to provide information on the structural organization normal to the surface on which the beam is incident. Neutron reflectometry is particularly useful (vis a vis x-ray reflectometry), since selective isotopic labeling can be used to highlight particular regions of interest in a surface structure. This is especially valuable for monolayers on surfaces. 

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. 

A paradox which stimulated the early development of the quantum theory concerned the indeterminate nature of light. Light usually behaves as a wave phenomenon but occasionally it betrays a particle-like aspect, a schizoid tendency known as the wave-particle duality. We consider first the wave aspect of light. 

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. 

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... 

The wave theory of light reached its climax with Hertz s contributions around 1888. Physics was now in a state of turmoil, tom apart by the wave-particle duality caused by the quantum theory. As a result, research in photo- and opto-related areas was divided into two streams quantum electrodynamics and molecular spectroscopy. 

X-Rays, like light, exhibit a wave-particle duality. Certain properties of x-rays are better understood when a beam of x-rays is regarded as a stream of photons. Whereas a wave is characterized by wavelength X and frequency v, a photon is characterized by its energy E and momentum p, which are related to X and v by... 

One of the w atershed events in the development of physics and chemistry was the appearance of Einstein s landmark paper explaining the photoelectric effect, establishing the corpuscular nature of light, and leading to the modern view of the wave-particle duality of the microscopic realm. 

The answers to the above questions, not all of which need he presented here, were formulated between 1925 and 1926, in the revolution of modern quantum theory, which shook the foundations of physics and philosophy. Remarkably, the central theme of quantum theory was the nature of light, and what came to be called the wave-particle duality. But other broader implications of the new theory existed, and the first inkling of this was given in 1924 by Louis de Broglie (Fig. 3.26) in his doctoral dissertation. He postulated that particles may also possess wavelike properties and that these wavelike properties would manifest themselves only in phenomena occurring on an atomic scale, as dictated by Planck s constant. He also postulated that the wavelength of these matter waves, for a given particle such as an electron or proton, would be inversely proportional to the particle s momentum p, which is a product of its mass m and speed... 

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