The de Broglie Hypothesis

The relationship between the circumference of an allowed orbit (2nr) and the wavelength (X) of the electron is given by 

Louis Victor Pierre Raymond Due de Broglie (1892-1977). French physicist. A member of an old and nohle family in France, he held the title of a prince. In his doctoral dissertation, he proposed that matter and radiation have the properties of both wave and particle. For this work, de Broglie was awarded the Nohel Prize in Physics in 1929. 

De Broglie s reasoning led to the conclusion that waves can behave like particles and particles can exhibit wavelike properties. De Broglie deduced that the particle and wave properties are related by the following expression  

Sample Problem 6.5 illustrates how de Broglie s theory and Eqiration 6.9 can be applied. 

Strategy Use Equation 6.9 to calculate the de Broglie wavelengths. Remember that the mass in Equation 6.9 must be expressed in kilograms for the units to cancel properly. 

must be expressed in kilograms for units to cancel properly in Equation 6.9. 

---

The Wave-Particle Duality of Matter—The de Broglie Hypothesis... 

De Brc lie proposed that matter should show wave-like properties. The de Broglie hypothesis was supported by Davisson and Germer s studies of electron diffraction. Every object has a wavelength that depends on its momentum (the product of its mass and velocity). 

Thereby, the de Broglie hypothesis has been widely accepted as a scientific law. To reiterate, particle-wave dualism is one of the cornerstones of quantum mechanics. 

The realization that electrons have wave properties leads at once to an interpretation of Bohr s hypothesis of stationary orbits. Figure LI shows the de Broglie wave associated with an electron in a Bohr orbit of radius r. If the circumference Inr is equal to an integer n multiplied by the wavelength X, the wave will fit into the orbit an integral number of times, and constructive interference will occur Figure. Xa). 

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. 

By the early 1920s, it was standard knowledge that energy had matter-like properties. In 1924, a young physics student named Louis de Broglie stated a hypothesis that followed from this idea. What if, de Broglie wondered, matter has wave-like properties ... 

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. 

Confirmation of this hypothesis is obtained by the X-ray examination of soaps and fatty esters by Shearer, Piper, Grindley and Muller (J.O.S. cxxiil. 2043, 1923) (see also Friedrich, Physikal. Zeit. xiv. 317, 1913, De Broglie, G.R. olxxvi 738,1923, Becker and Jahnke, Z. Phys. Ohem. xcix. 242, 1923), who have shown that two types of chain formation occur in carbon compounds in accordance with our preconceived views on the tetrahedral orientation of the valencies of the carbon atom. The spacing of the planes in these two types is indicated in the following diagram ... 

In 1924, considering the nature of the light and matter, Lois de Broglie proposed that small particles sometimes show wave-like properties. In 1927, his hypothesis was proved by the deviation of electron beams like X-rays by a crystal. 

Quantum mechanics began with a daring hypothesis by Louis de Broglie (he was a student at the time) if light has a dualistic wave/particle nature, why not matter His reasoning led to the prediction that a particle of mass m and velocity V would exhibit wavelike properties with wavelength... 

It was only in 1927 from the experiments of Davisson and Germer and slightly later from those of G. P. Thomson that it was found that these electron beams exhibit exactly the same diffraction phenomena as those which Von Laue, Friedrich and Knipping had observed with X-rays in 1912. For X-rays this result was in agreement with the prevailing conception of the nature of these rays. With electrons, however, this wave character appeared to be completely in conflict with the ideas which had been supported for more than 50 years, nevertheless only three years before De Broglie had published his fundamental hypothesis on the wave nature of electrons in his thesis (1924). 

From his relation (4 ) De Broglie was able immediately to draw a very important conclusion regarding the stationary states of a hydrogen atom. His result agreed with that of Bohr. Whereas however in Bohr s theory the stationary states were introduced completely ad hoc to explain the spectra, they follow with De Broglie logically and obviously from the basic hypothesis. 

This was a revolutionary and quite nebulous suggestion, not easily accepted at the time. If it was not for the intervention of Einstein, excited with the proposal, Louis de Broglie would most likely have failed his doctoral examination. Louis de Broglie found support for his hypothesis and attempted to clarify the wave characteristics of a moving electron by... 

We shall therefore briefly review the experimental efforts in this field throughout the last century. Soon after Louis de Broglie proposed his wave hypothesis for material particles matter wave phenomena were experimentally verified for electrons [Davisson 1927], atoms and dimers [Estermann 1930], and neutrons [Halban 1936 Gahler 1991]. A replica of Young s double-slit experiment with matter waves was demonstrated by Jonsson for electrons [Jonsson 1974], by Zeilinger et al. for neutrons [Zeilinger 1988], by Carnal and Mlynek for atoms [Carnal 1991] and by Schollkopf and Toennies for small molecules and noble gas clusters [Schollkopf 1994 Schollkopf 1996 Bruch 2002],... 

Quite independently of the line of thought just explained, the problem of atomic structure has been attacked with the lielp of the ideas developed in the preceding chapter. According to the hypothesis of de Broglie (p. 79), to every corpuscle thenj corresponds a wave, the wave-length of which, in the case of rectilinear motion of the corpuscle, is connected with the momentum by the relation... 

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. 

It is commonly accepted that the old quantum theory era spans from the birth of Planck s quantum hypothesis to the formulation of Schrodinger s equation. This section describes the old quantum theory in three parts the failure of classical mechanics, the birth of the quantum theory, and the completion of wave mechanics.5 8) This century obviously began with the birth of quantum theory. Many researchers appeared on the scene of quantum theory at the time, but we remember mostly the contributions of four researchers Max Planck (1901), Albert Einstein (1905), Niels Bohr (1913), and de Broglie (1923). Then Schrodinger proposed the new wave equation to conclude the age of the old quantum theory. Heisenberg established matrix mechanics and formulated the uncertainty principle. 

---