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Journal of Modern Physics

Relation between the Intervals ΔE and Δt Obtained in the De-Excitation Process of Electrons in Metals

Stanisław Olszewski

Published Jan 1, 2012• 9 citations
Publisher

Abstract

A relation between the intervals of energy and time, derived in a former paper and associated with the electron transitions on the Fermi surface of a metal, is examined in comparison with the experimental data. These data are obtained from the de-excitation process of electrons in metals. A comparison between theory and experiment demonstrated that the new relation between energy and time is fitted much better for the experimental results than the well-known relation due to the Heisenberg theory.

DOI
10.4236/jmp.2012.33030

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A relation between the intervals of energy and time, derived in a former paper and associated with the electron transitions on the Fermi surface of a metal, is examined in comparison with the experimental data. These data are obtained from the de-excitation process of electrons in metals. A comparison between theory and experiment demonstrated that the new relation between energy and time is fitted much better for the experimental results than the well-known relation due to the Heisenberg theory.
The motion of electron wave packets of a metal is examined classically in the presence of the magnetic field with the aim to calculate the time intervals between two states lying on the same Fermi surface. A lower limiting value of the transition time equal to about 10–18 sec is estimated as an average for the case when the states are lying on the Fermi surface having a spherical shape. Simultaneously, an upper limit for the electron circular frequency in a metal has been also derived. A formal reference of the classical transition time to the time interval entering the energy-time uncertainty relations known in quantum mechanics is obtained.
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.
Quantum aspects of the Joule-Lenz law for the dissipation energy have been studied. In the first step, in an analysis of the energy-time principle of uncertainty, this gives a lower limit of the time interval and an upper limit of the energy interval which can be admitted in a quantum transition process. Moreover, for the low energy excitations, the transition time between the levels is found to be close to the oscillation time periods characteristic for these levels. A reference obtained among the transition time Δt, transition energy ΔE and the Planck constant h indicates that Δt should approach approximately the time period of the electromagnetic wave produced in course of the transition.
The paper presents a non-probabilistic approach to the time interval associated with the energy emission produced by the electron transition in a quantum system. The calculations were performed for the hydrogen atom and the electron particle in a one-dimensional potential box. In both cases, the rule of conservation of the electron momentum has been applied. The results, limited to the time intervals of transitions between two neighbouring quantum energy levels, occur to be much similar to those obtained earlier with the aid of the Joule-Lenz energy emission theory.
A transformation of the electron states—say those enclosed in a potential box—into the de Broglie waves done in the paper, enabled us to calculate the energy change between two quantum levels as a function of the specific heat and difference of the temperature between the states. In consequence, the energy difference and that of entropy between the levels could be examined in terms of the appropriate classical parameters. In the next step, the time interval necessary for the electron transition between the levels could be associated with the classical electrodynamical parameters like the electric resistance and capacitance connected with the temporary formation of the electric cell in course of the transition. The parameters characterizing the mechanical inertia of the electron were next used as a check of the electrodynamical formulae referring to transition.