A brief description is given of the mechanism of Prof. E. T. Whittaker which compels all exchanges between the kinetic energy of electrons and radiant energy to conform to the quantum condition. A modified form of the mechanism is suggested, consisting of two magnetons, or two ring electrons, placed near together with their planes parallel. It is pointed out that the quantum mechanism gives the law of force postulated by Langmuir in his model of a static atom, which leads to results identical with those obtained from the circular orbits of Bohr's theory.
A brief description is given of the mechanism of Prof. E. T. Whittaker which compels all exchanges between the kinetic energy of electrons and radiant energy to conform to the quantum condition. A modified form of the mechanism is suggested, consisting of two magnetons, or two ring electrons, placed near together with their planes parallel. It is pointed out that the quantum mechanism gives the law of force postulated by Langmuir in his model of a static atom, which leads to results identical with those obtained from the circular orbits of Bohr's theory.
In Professor Whittaker's highly interesting and suggestive application of my model the postulated structure is a system of magnets rigidly connected like the spokes of a wheel, having poles of the same name at the circumference, the corresponding poles of contrary name being all at the centre. He shows that when a bombarding electron, moving in the direction of the axis, approaches such a wheel it sets the wheel turning, the rotation of the poles constituting what he calls a “magnetic current.” If the initial velocity of the bombarding electron falls short of a certain limiting value, the encounter is perfectly elastic, and the electron is reflected back without loss of energy; the point at which its direction of motion becomes reversed may be on either side of the plane of the wheel, depending on the electron's initial velocity of approach. If the initial velocity exceeds the stated limit, the electron passes clear through the system and escapes, but with a definite reduction of velocity, corresponding to a quantum of energy which it has given up to the wheel. When the encounter is elastic, the angular velocity which the wheel acquires during the approach of the electron is lost during the return of the electron. When the encounter is not elastic, and the electron has passed clear through, the wheel is left with an angular velocity ω; and the energy which that represents is the source of the consequent radiation.
Abstract The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of “duplexity ” phenomena, the observed number of stationary states for an electron in an atom being twice the number given by the theory. To meet the difficulty, Goudsmit and Uhlenbeck have introduced the idea of an electron with a spin angular momentum of half a quantum and a magnetic moment of one Bohr magneton. This model for the electron has been fitted into the new mechanics by Pauli,* and Darwin,† working with an equivalent theory, has shown that it gives results in agreement with experiment for hydrogen-like spectra to the first order of accuracy. The question remains as to why Nature should have chosen this particular model for the electron instead of being satisfied with the point-charge. One would like to find some incompleteness in the previous methods of applying quantum mechanics to the point-charge electron such that, when removed, the whole of the duplexity phenomena follow without arbitrary assumptions. In the present paper it is shown that this is the case, the incompleteness of the previous theories lying in their disagreement with relativity, or, alternatetively, with the general transformation theory of quantum mechanics. It appears that the simplest Hamiltonian for a point-charge electron satisfying the requirements of both relativity and the general transformation theory leads to an explanation of all duplexity phenomena without further assumption. All the same there is a great deal of truth in the spinning electron model, at least as a first approximation. The most important failure of the model seems to be that the magnitude of the resultant orbital angular momentum of an electron moving in an orbit in a central field of force is not a constant, as the model leads one to expect.
In his doctoral thesis in 1911, Bohr reached the conclusion that at thermal equilibrium metal atom has no magnetic effect. Therefore, when establishing the hydrogen atom model in 1913, he did not consider the Lorentz force, but only the Coulomb force. The radius of the hydrogen atom he obtained is half smaller, and the orbital rotation frequency is twice larger. It must be multiplied by 1/2 to be consistent with the value of the Rydberg experiment. He proposed to calculate the photon frequency by using the average value of the zero frequency of infinite quantum number and the basic frequency, but it is not applicable to the energy levels for the ordinary quantum numbers, and later he called it the correspondence principle. In our modified Bohr model, we eliminate and solve Bohr's half frequency problem; The photon energy is equal to the difference between the two energy levels, and the photon frequency is equal to the difference between the two rotation frequencies of the electron; All excited states of hydrogen atom are elliptical orbits, and the nucleus is located in the center of the ellipse; The microscopic model of photonic structure is established, and the microscopic mechanism of atomic luminescence and quantum entanglement is given.
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.
Bohr’s quantum condition is an indispensable assumption for classical quantum theory. However, strictly speaking, Bohr's quantum condition does not hold when deriving the energy of an electron forming a hydrogen atom from the perspective of the theory of relativity. In this paper, it is thought that the relationship enfolded in Bohr's quantum condition, i.e., is suitable as a new quantum condition to replace Bohr’s quantum condition. Also, in quantum mechanics, the energy of an electron is derived based on the theory of relativity, as exemplified in the theory of Sommerfeld. However, this paper points out that the previous energy formula based on the theory of relativity is mistaken. It also proposes a previously unknown formula for the kinetic energy of an electron.
Abstract We review the Bohr atomic model, where certain conditions (quantum conditions) were used to select certain “allowed” circular orbits for the electrons in an atom. Sommerfeld realized that a more generalized condition, applied to the action variables, would be consistent with the Bohr condition and also allow elliptical orbits. This condition amounted to the quantization of the phase space occupied by an orbit. This had independently been suggested by Planck. We also discuss the similarities between classical mechanics and the geometric optics limit of a wave theory.