Through his experiments, the physicist Niels Bohr improved upon Rutherford's model of the atom and developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of the hydrogen atom. A simple means for extending the conventional non-relativistic Bohr model of the atom to include the wave nature of electrons is presented. As the derivation requires basic knowledge of classical and wave mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics.
Through his experiments, the physicist Niels Bohr improved upon Rutherford's model of the atom and developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of the hydrogen atom. A simple means for extending the conventional non-relativistic Bohr model of the atom to include the wave nature of electrons is presented. As the derivation requires basic knowledge of classical and wave mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics.
Many teachers like to introduce the Bohr atom toward the end of an introductory physics course. This is an excellent idea, given the historic importance of Bohr’s 1913 work, which provided the bridge from Planck’s quantized interaction of matter and radiation (1900) to the full theory of quantum mechanics (1925-28). Unfortunately, the version of the Bohr atom that appears in many textbooks and is no doubt often presented to students is more wrong than right and may leave both teachers and students wondering why, more than a hundred years later, it is still being taught. This “pedagogic” version postulates that an electron in a stationary state moves in a circular orbit with an angular momentum that is an integral multiple of h/2π (L = nh/2π = nħ)—ħ for the lowest-energy state, 2ħ for the next state, and so on. This picture of the hydrogen atom is wrong in two senses. First it doesn’t conform to our present understanding of the hydrogen atom. This, in itself, is not a reason to scrap it, for the historical development of quantum physics is certainly of interest. But second, it doesn’t conform to the essence of what Bohr actually did. That is a reason not to teach about circular orbits and L = nħ.
This chapter illustrates Niels Bohr's ideas in some detail. In the formulation of his model, Bohr assumed that the electron in the hydrogen atom moves under the influence of the Coulomb attraction between it and the positively charged nucleus, as assumed in classical mechanics. The Bohr model was very successful in explaining the discrete atomic spectra of one-electron atoms. The Bohr model is, of course, a theoretical model of an atom. Using Bohr's quantization postulate, find the linear velocity of the electron's sphere. To find the radius of the orbit, Bohr postulated that the angular momentum of the electron is quantized, i.e., it can only take values that are integer multiples of ħ. The chapter begins with considering the classical equation of motion for the electron in a circular orbit, which is based on Newton's laws of motion and Coulomb's law of electric force.
This paper tries to prove that the existence and properties of the electron’s spin can be established not only as a consequence of relativistic quantum mechanics, but also as a consequence of non-relativistic quantum mechanics of the Hydrogen atom or Hydrogenic atoms. It is, in fact, an extended model of the Hydrogen atom or Hydrogenic atoms. This new model starts from the assumption that to the foundation of atomic structure there is not only a potential of electrical nature, but also a potential of magnetic nature, which, together with the Coulomb potential, determine the movement of electrons around the atomic nucleus. As a consequence of this new model is obtained a non-relativistic theory of Hydrogen atom which takes into account the spin of the electron and leads us to a non-relativistic theory of the atom in agreement with the Stern-Gerlach experiment results. As well the model can be used in order to explain the spectrum of Alkali-atoms.
The aim of Niels Bohr’s “great” paper was to try to explain how Ernest Rutherford’s planetary model of the atom could exist. Bohr never used the words “quantum jump” in the paper, but it became very much in vogue shortly after this. Max Planck and even A. Einstein had not yet made the full evolution beyond classical physics, and the purely classical atomic views of Rutherford and H. Nagaoka did not provide the explanation of the absorption and emission spectra of hydrogen. In truth, Bohr’s “theory” consisted of a very few equations, with very great assumptions. As de Broglie’s work became known, he was hailed for his advances and he would join the list of Nobel Prizes for advances in quantum theory. Wolfgang Pauli did not particularly like the wave and particle approach that de Broglie introduced with his pilot waves in 1924, and would forcefully express these objections a few years later at the Solvay conference.
What was Bohr's response to the problem of wave-particle duality? Before considering this question in detail it will be useful to survey briefly Bohr's work in physics between 1911 and 1923. Bohr and the ‘old’ quantum theory In 1911 Bohr completed his doctoral dissertation on the classical electron theory of metals. Developed by Sir J.J. Thomson and Lorentz, the theory explained electrical, magnetic and thermal properties of metals in terms of the motions of free electrons. Although Bohr made no use of the quantum hypothesis in his dissertation, he noted that classical electrodynamics was incapable of explaining Planck's radiation law and entailed the ultraviolet catastrophe. After completing his dissertation Bohr pursued his post-graduate studies under Thomson at Cambridge University. Finding that Thomson was little interested in his work, Bohr went on to Manchester University in March 1912, to work under Ernest Rutherford. Bohr's move to Manchester was very opportune: the quantum hypothesis was just beginning to receive a wider recognition, thanks largely to the first Solvay Conference in 1911, which Rutherford attended; Rutherford's laboratory, moreover, was one of the most active centres in the investigation of radio-activity. In order to explain the results of experiments on the passage of alpha and beta particles through matter Rutherford had revived Hantaro Nagaoka's (1904) planetary model of the atom. On this model an atom consists of a positively charged nucleus which is orbited by negatively charged electrons, the number of which corresponds to the number of charges on the nucleus.
The Bohr model is historically important in the understanding of quantum physics. It gives many important results for the hydrogen atom including atomic size and ionization energy. It is sometimes referred to as a semi-classical calculation, because it includes the physics of angular momentum quantization without the full quantum mechanical description of an electron wave. It is tremendously useful for gaining physical intuition of the quantum nature of the atom. In the Bohr model of the hydrogen atom, an electron has a circular orbit with speed v and radius r about the proton. The Bohr quantization condition is that an integer number of electron (de Broglie) wavelengths must fit to the atomic circumference.