De Broglie’s hypothesis

The first consistent attempt to unify quantum theory and relativity came after Schrddinger s and Heisenberg s work in 1925 and 1926 produced the rules for the quantum mechanical description of nonrelativistic systems of point particles. Mention should be made of the fact that in these developments de Broglie s hypothesis attributing wave-corpuscular properties to all matter played an important role. Central to this hypothesis are the relations between particle and wave properties E — hv and p = Ilk, which de Broglie advanced on the basis of relativistic dynamics. 

De Broglie s hypothesis of matter waves received experimental support in 1927. Researchers observed that streams of moving electrons produced diffraction patterns similar to those that are produced hy waves of electromagnetic radiation. Since diffraction involves the transmission of waves through a material, the observation seemed to support the idea that electrons had wave-like properties. 

How does de Broglie s hypothesis account for the fact that the energies of the electron in a hydrogen atom... 

Planck s revolutionary idea about energy provided the basis for Einstein s explanation of the photoelectric effect in 1906 and for the Danish physicist Niels Bohr s atomic model of the hydrogen atom in 1913. Their success, in turn, lent support to Planck s theories, for which he received the Nobel Prize in physics in 1918. In the mid-1920s the combination of Planck s ideas about the particle-like nature of electromagnetic radiation and Erench physicist Louis de Broglie s hypothesis of the wavelike nature of electrons led to the formulation of quantum mechanics, which is still the accepted theory for the behavior of matter at atomic and subatomic levels. 

Experimental confirmation of de Broglie s hypothesis was soon obtained in 1927 hy the observation that electron beams can be diffracted in much the same way... 

In 1927, Davisson and Germer experimentally confirmed de Broglie s hypothesis by reflecting electron from metals and observing diffraction effects. In 1932, Stem observed the same effects with helium atoms and hydrogen molecules, thus verifying that the wave effects are not peculiar to electrons, but result from some general law of motion for microscopic particles. 

Because de Broglie s hypothesis is applicable to all matter, any object of mass m and velocity v would give rise to a characteristic matter wave. However, Equation 6.8 indicates that the wavelength associated with an object of ordinary size, such as a golf ball, is so tiny as to be completely unobservable. This is not so for an electron because its mass is so small, as we see in Sample Exercise 6.5. 

De Broglie s hypothesis and Heisenberg s uncertainty principle set the stage for a new and more broadly applicable theory of atomic structure. In this approach, any attempt to define precisely the instantaneous location and momentum of the electron is abandoned. The wave nature of the electron is recognized, and its behavior is described in terms appropriate to waves. The result is a model that precisely describes the energy of the electron while describing its location not precisely but rather in terms of probabilities. 

In 1927 the German physicist Heisenberg stated the Uncertainty Principle, which is the consequence of the dual behaviour of matter and radiation (de Broglie s hypothesis). It states that it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron (or any sub-atomic... 

CONTEXT This is the fundamental application of de Broglie s hypothesis to chemistry. At the bulk scale, where we carry our compounds in beakers and measure volumes by eye, classical mechanics is perfectly accurate. However, when we deal with the structure within individual atoms and molecules, the relevant masses and distances are too small for classical mechanics to accurately describe the system. 

De Broglie s hypothesis can be used to justify two of Bohr s major assumptions, advancing the atomic model toward the picture we hold of the atom today. Bohr s assumption (II), that the electron does not radiate, is supported... 

In this chapter, we ve examined a semi-classical version of the simplest atoms that predicts how the energy in these microscopic systems comes to be a quantized parameter. Now we need to develop a more rigorous and more general approach, starting from de Broglie s hypothesis but with fewer preconceptions about the nature of the particles that make up the atom. 

We can understand de Broglie s hypothesis by equating the expression for energy from special relativity and from quantum theory ... 

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