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1-1: Bohr's Quantum Theory and De Broglie Waves

[Bohr's Quantum Theory]
We learned on the page, 4-3: The Bohr Model of Atoms in the preceding Seminar, that the atomic structure of hydrogen that had been difficult to be understood with classical theory was beautifully explained by Bohr's quantum theory. This theory is sometimes called the old quantum theory.
Here let us summarize the main points of the theory. In Bohr's quantum theory, it is considered that an atom can be described by the Rutherford model of the nuclear atom, in which a heavy nucleus is surrounded by light electrons that move obeying the classical theory. Since this atomic model brought about some difficulties discussed on the pages, 2-7: Summary of Part 2 and 4-1: The Difficulty of the Rutherford Model of the Nuclear Atom in the preceding Seminar, Bohr added the following hypotheses; i.e., postulations of stationary state, frequency condition, and quantum condition.
A schematic sketch of the Rutherford model of the nuclear atom is represented in the following figure, in which the central black sphere is the atomic nucleus, and the small points denote the electrons surrounding the nucleus. While the atomic radius is about , the nuclear radius seems to be less than 1/10000 of it.
The Rutherford Model of the Nuclear Atom
A black big ball at the center is the nucleus and small red points moving around the nucleus are electrons.
By Bohr's Quantum theory, the structure, especially the energy, the radius, the stability and the spectra of hydrogen atom, were explained very well.

[De Broglie Waves]
As mentioned previously, it was clarified by the discovery of the photon that light which had so far been considered to be wave (electromagnetic wave) has also a particle nature. Then de Broglie (France, 1892 - 1987) thought that such things as electrons which had so far been considered to be particles might possess wave nature as well (1932). This is the idea of the de Broglie waves or de Broglie's matter waves.
We know that, in the case of light, the frequency , and the wavelength , are connected respectively to the energy E and the momentum p of photon by means of Einstein's relations

De Broglie assumed that these relations (1) might be valid also for the de Broglie waves. The above Einstein's relations are therefore called Einstein - de Broglie's relations as well.

[The Evidences of De Broglie Waves]
C. J. Davisson (USA, 1881 - 1958) and L. H. Germer (USA, 1896 - 1971) observed the interference phenomena resulting from an electron beam reflected from a single crystal of nickel, and they confirmed that the interference was a perfect fit to Einstein-de Broglie's relations. At the same time, G. P. Thomson (UK, 1892 - 1975) also confirmed the wave nature of electrons using a metallic multi-crystal. (See the photograph of a diffraction pattern of electron beams on the page, 4-4: in the preceding Seminar).
Moreover, O. Stern (Germany, 1888 - 1969) observed the interference patterns produced by projecting beams of helium atoms and hydrogen molecules onto crystals, and confirmed that the results exactly fit the Einstein-de Broglie's relations. Thereby de Broglie waves accompanying not only electrons but also general particles were confirmed experimentally.

[Bohr's Quantum Condition and De Broglie Waves]
Let us consider a hydrogen atom with Bohr's quantum theory. In that theory, the quantum condition to determine the stationary states of the atom seems to claim that the circumference of the orbit of the electron revolving about the nucleus should be an integral multiple of the wavelength of the de Broglie wave of the electron. This has already been discussed on the page, 4-4: The Wave Nature of Electrons in the preceding Seminar. This quantum condition says that the de Broglie wave of the electron must be a continuous standing wave around the nucleus. (See the following figure.)

Bohr's quantum condition for a hydrogen atom.
In this figure, the de Broglie wave does not connect smoothly, because the circumference is not an integral multiple of the wave length. Namely, this figure does not show a correct de Broglie wave in a hydrogen atom. The circumference of a true hydrogen atom must be an integral multiple of the de Broglie wavelength.

We can easily understand and explain this quantum condition by considering the smooth continuity of the de Broglie waves. Thus we can realize that the de Broglie waves play an essential role underlying Bohr's quantum theory. They looked forward to construction of a really new theory from which Bohr's quantum theory itself can be derived inevitably. Such a theory is nothing other than Schroedinger's wave mechanics or quantum mechanics.
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