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College Physics

Notes on the Bohr's theory of hydrogen atom

Zhu Hong

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

The expressions for Bohr radius and Rydberg constant are derived directly from Bohr's two fundamental postulates,Rydberg's formula; and some classical mechanics conclusions concerning the central forces.Furthermore,it is shown that the Bohr's theory is a phenomenological theory and implies the wave nature of matter.

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Turning back to Niels Bohr's model of the hydrogen atom, the paper is trying to resolve one of the issues associated with the model.While N. Bohr in the framework of his model did not find any relation between electron's motion in the atom and radiation emitted, there is a reason to believe that the relation is bound to exist.Furthermore, it is already given by Rydberg's formula that expresses the frequency of radiation as a difference of two other frequencies associated in some manner with electron's rotation.Based on this approach a new value for the radius of the ground stationary orbit is calculated.It appears to be more than Bohr's radius by a factor of 1.588.The question why both values for the radius of the ground stationary orbit (Bohr's radius and a new one) are compatible with Rydberg's formula is considered.Finally, what exactly Niels Bohr overlooked in his model of the hydrogen atom, is discussed.It is established that Rydberg's formula can be derived from the more general parameterized postulates, when Niels Bohr used, regardless of the value of the parameter.
The world should have waited until 1913, when a Danish physicist N. Bohr proposed an entirely new theory for a description and partial explanation of the spectral properties of the hydrogen atom. His theory was based on two postulates, the so-called Bohr postulates, and both of them were impossible to be understood from the point of view of classical physics. Being based on these postulates and employing classical physics, N. Bohr was able to derive explicit expressions for the energy levels of the hydrogen atom and the wavelengths of possible transitions. The hydrogen-like atom has only one electron, and all others have been removed by various ways of ionization. An essential feature of these systems is the presence of one electron only. The Coulomb interaction between this electron and the nucleus is spherically symmetrical. Later, we shall see that the situation becomes considerably more complicated in the case of multielectron atoms.
Rutherford thought to explore the structure of matter by bombarding thin sheets of metals with alpha particles. According to Bohr, the mechanism of emission of e.m. wave is represented by the downward vertical lines connecting states at different n. The two main successes are: explanation of Rydberg formula and expression of Rydberg empirical constant in terms of fundamental constants and the calculation of the size of the atom in agreement with measurements. The remarkable fact that de Broglie hypothesis of pilot waves, when applied to the hydrogen atom, gives excellent agreement with Bohr's theory seems to give foundation that the matter-wave duality is a characteristic of elementary particles like the electrons. Shortly after de Broglie suggestion an experimental verification of de Broglie ideas was successfully attempted. Davisson and Germer needed to choose a crystal whose spacing was such that, under a reasonable acceleration voltage of the electrons, the de Broglie wavelength would be of the order of the lattice spacing.
Consideration of the Rydberg Series leads to a model for the hydrogen atom in which the variable of quantisation is the Lorentz factor, Gamma, and not angular momentum as postulated by Niels Bohr and integral to current theories. This is consistent with an atom in which the electron is seen as an objectively real particle having deterministic position and velocity. The electron is seen to orbit at a constant radius irrespective of the energy state of the atom and so there is no change in potential energy between energy states. All of the energy changes are therefore kinetic in nature. The model also provides a simple physical explanation of the hitherto mysterious Fine Structure Constant.
In this paper, the classical Bohr’s model of the hydrogen atom has been revisited. Two values of fundamental physical properties of an electron in the hydrogen atom has been identified. These physical properties ( & ) are constant in nature. The aim for the review was to contribute to the solution of disagreement between the Bohr’s wavelength ( ) and the Balmer’s experimental observation ( ) for the emission spectrum of hydrogen atom. There are two other constants and that were identified in the Bohr’s equation of the hydrogen atom. The four fundamental physical constants are intrinsic properties of an electron and can be applied to multi-electron system. They can also be obtained from Schrodinger’s equation for hydrogen atom at steady state. These constants may be subjected to scrutiny for their determination for better understanding. Also, since Bohr’s model of hydrogen atom is based on classical mechanics, this paper has provided an alternate method of solving simple problems in atomic physics under Bohr’s model to aid good mental picture of hydrogen atom to scientists.