Bohr's Quantum Theory Research Articles

The historical role of the Adiabatic Principle in Bohr's quantum theory

It is widely known that both the Correspondence Principle and the Adiabatic Principle were the two pillars of Bohr's quantum theory. However, the Correspondence Principle usually gets much more attention in historical accounts. A closer look at Bohr's quantum theory shows that, although the fate of the Adiabatic Principle was closely tied up with the validity of mechanics, it also played a significant role in the old quantum theory. In the early 1920s, when dealing with multielectron atoms, Bohr was forced to reshape the theory and thus to reconsider the relative relevance of the two principles. It is precisely the late preponderance of the Correspondence Principle which has, in perspective, biased the historical weight attributed to each of them.

Centenary of the Franck‐Hertz experiments

In 1925 the Nobel Prize in Physicswas awarded jointly to James Franck(1882–1964) and Gustav L. Hertz(1887–1975) “for their discovery ofthe laws governing the impact of anelectron upon an atom” [1]. Theyconducted an ingenious set of exper-iments in 1913 and 1914 in whichthey measured the ionization po-tential of different gases [2]; stud-ied collisions between gas moleculesand slow electrons [3]; developed atheory of ionization by collision [4];determined the ionization potentialof mercury vapor with the methodof electron collision [5]; and car-ried out spectroscopic experimentswith mercury vapor which yieldedthe spectral line 253.6

Computer Simulations of Quantum Theory of Hydrogen Atom for Natural Science Education Students in a Virtual Lab

The present article is primarily targeted for the advanced college/university undergraduate students of chemistry/physics education, computational physics/chemistry, and computer science. The most recent software system such as MS Visual Studio .NET version 2010 is employed to perform computer simulations for modeling Bohr's quantum theory of hydrogen (H) atom in class-setting of a virtual laboratory. The necessary computer algorithm is developed to compute discrete values of the orbit radius, and stationary energy levels of Bohr's H-atom. More than 2000 computer simulations are performed to investigate the quantum model behavior starting from the ground state of H-atom until we reached the energy continuum. One of the natural consequences of Bohr's model is that it could provide a perfect corroboration of the experimentally observed spectrum of H-atom with that empirically obtained from formulas derived by famous scientists of 19th and 20th centuries. Using old theory of classical electrodynamics, it was not possible to explain the observed line spectrum of H-atom. Bohr's quantum model of H-atom set the stage for the development of a modern branch of physics and chemistry in microscopic world, the so called quantum mechanics and very recently of a new computing technique known as quantum computing.

From Propagation to Structure: The Experimental Technique of Bombardment as a Contributing Factor to the Emerging Quantum Physics

I observe that quantum physics emerged at the turn of the last century when physics had shifted its concern from propagation phenomena to questions of structure. This transition materialized with the development of a new experimental technique, the bombardment method. The transition is well exemplified by the move from the experimental studies of Heinrich Hertz to those of Ernest Rutherford, and from those of Heinrich Hertz and Philipp Lenard to those of James Franck and Gustav Hertz. I trace the history of Rutherford's experimental bombardment method as it emerged from nineteenth-century propagation studies. I then demonstrate the use of the bombardment method in another experimental context, namely, in the celebrated experiment of Franck and Hertz. I locate the root of this experiment in Lenard's experimental studies and analyze Franck and Hertz's flawed interpretation of it. I conclude by underlining the crucial role that Bohr's quantum theory of the atom played in helping to establish these bombardment experiments as milestones of modern physics.

The Place of X-ray Crystallography in the Development of Modern Science

VON LAUE'S discovery of the diffraction of X-rays by crystals effectively provided science with a new eye with which to see the ultimate arrangement of the nuclei and electrons of solid matter. It is true that X-ray analysis does not show atoms and electrons to the eye in the way that a microscope does; the process of interpretation is more complicated, but it is essentially analogous. In an ordinary optical instrument the interference of rays from luminous points is used to build up the optical image by means of a lens system. In X-ray analysis the interference pattern is taken and interpreted mathematically instead of optically to give the nature of the object observed, so that it is just one step farther removed from our inherited mechanism for appreciating the external world. Now we have had this new eye only seventeen years, and although it has shown many marvellous things and enabled us to build for the first time a picture of the intimate structure of solid matter, we cannot believe that it has more than begun to be used. Many more important discoveries are bound to follow from it, and it has still to find its place as an essential instrument in every branch of scientific research. The object of this article is to point out what can already be seen of its possibilities and how it is likely to affect science in the near future. The Three Forms of Information from X-ray Diffraction Apart from the knowledge given on the nature of X-rays—which was of such critical importance in the discovery of atomic numbers and in the verification of Bohr's quantum theory of radiation—the diffraction of X-rays by crystals yields information about three grades of fine structure of matter. Ultimately the diffraction of X-rays is due to the interaction of the radiation with the electrons in the atoms of matter, and so the deepest information it can give is on the position of the electrons in the individual atoms, or, more correctly, information as to the average distribution of density of negative electricity. Here it is most closely related to pure physics and leads to the possibility of the complete description of the state of any piece of matter. But without going nearly so deeply, X-rays can show the position of the maxima of electrical density, that is, the position of each kind of atom, in a regular crystalline structure. It is in this field that the chief work of X-ray crystallography has been done. It is faced with the extensive problem of determining all the different possible types of atomic arrangement in solid substances, which has such a clear bearing on chemistry.

The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohr's Quantum Theory

The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohr's Quantum Theory

The Dielectric Constant of Atomic Hydrogen in Undulatory Mechanics

In a recent paper J. H. Van Vleck(1) used the expressions for the energy of a hydrogen atom in an electric field, derived by I. Waller(2) and the writer,(3) for computing the dielectric constant. The interesting method he applies is analogous to that used by J. H. Jones(4) for the same purpose in Bohr's quantum theory, and is outlined in section 1 of the following paper by Evelyn F. Aylesworth.(5)

The series spectrum of ionised carbon (C II)

For the development of the theory of atomic structure there would appear to be a special need for data relating to the series spectra of the lighter elements. It has, therefore, been thought desirable to publish the present account of the series of singly-ionised carbon without waiting for the completion of the investigation of the spectrum at other stages of ionisation. It is an essential feature of Bohr's quantum theory of spectra that while the series constant for neutral atoms is nearly the same as that for hydrogen, the value of this constant will be increased four times when the atom is singly ionised, nine times when it is doubly ionised, 16 times when it is trebly ionised, and so on. Evidence that a system of series represents a particular stage of ionisation is thus to be sought in the value of the series constant for the system in question. Experimental confirmation has been obtained as far as the second ionisation by Paschen in the case of aluminium,* and as far as the third ionisation by the present writer in the case of silicon.

Some Spectrum Lines of Neutral Helium derived theoretically

IT is well known that, owing to the prohibitive nature of the general problem of three (or more) bodies, Bohr's quantum theory has proved so far to be unable to account for any spectrum lines but those forming a series of the simple Balmerian type, i.e. where N is the familiar Rydberg constant given by 2π2me4/ch3, and κ the number of unit charges contained in the nucleus, or the atomic number. Apart from X-ray spectra of the higher atoms, for which κ is replaced empirically by a smaller and not necessarily a whole number (Moseley, Sommerfeld), and where the requirements of precision are not high, this simple type of formula covers, as a matter of fact, only the spectra of atomic hydrogen (κ = 1) and of ionised helium (κ = 2), which, having been deprived of one of its electrons, presents again the same problem of two bodies as the hydrogen atom. Accordingly, the known spectrum series of He+, the ultraviolet Lyman series, the principal or Fowler's series, and the Pickering series, are all of the simple Balmer type, with n= 2, 3, 4 respectively.