Abstract
A modified uncertainty principle coupling the intervals of energy and time can lead to the shortest distance attained in course of the excitation process, as well as the shortest possible time interval for that process. These lower bounds are much similar to the interval limits deduced on both the experimental and theoretical footing in the era when the Heisenberg uncertainty principle has been developed. In effect of the bounds existence, a maximal nuclear charge Ze acceptable for the Bohr atomic ion could be calculated. In the next step the velocity of electron transitions between the Bohr orbits is found to be close to the speed of light. This result provides us with the energy spectrum of transitions similar to that obtained in the Bohr’s model. A momentary force acting on the electrons in course of their transitions is estimated to be by many orders larger than a steady electrostatic force existent between the atomic electron and the nucleus.
Highlights
The Bohr model of the hydrogen atom [1] assumed circular trajectories for electrons circulating about the atomic nucleus and the motion along these trajectories has been quantized
We see that the Formulae (25)-(27) for the upper bounds of the intervals of momentum and energy approach the relations which are well known from the classical relativistic mechanics
When applied to the hydrogen-like atom, the lower bounds of the intervals for the position interval and interval of time lead to an upper bound for the atomic number Z equal to 137
Summary
The Bohr model of the hydrogen atom [1] assumed circular trajectories for electrons circulating about the atomic nucleus and the motion along these trajectories has been quantized. The present paper tends to meet this question in case when an approach to the energy spectrum is done on the basis of the uncertainty principle, the essence of which are the energy differences ∆E applied together with the time intervals. Heisenberg [5] has coupled the observables which are the intervals of the position coordinate and that of momentum in the uncertainty relations similar to that given in (7) for the energy and time. Required to transform the kinetic energy of a particle motion into the energy of the electromagnetic radiation [18]
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