Quantization behavior of electron in medium under electromagnetic induction

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Quantization behavior of electron in medium under

electromagnetic induction*

Zhang Tao

Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing Radiation Center, Beijing

100875, China taozhang@bnu.edu.cn

Abstract

The electron cloud in an atom may accept or return the energy offered by electromagnetic induction in a quantization way. Correspondingly, the equivalent induced current on the electron cloud and its energy assume discrete values.

Keywords: electron cloud, Faraday’s Law of induction, Energy quantization, equivalent induced

current, electromagnetic wave

Recently, the electron-cloud-conductor model was presented: the electron cloud of each electron in media can be seen as an conductor, and the Faraday’s Law applies to this conductor; thus the alternating magnetic field of a light existing in the electron cloud will induce a equivalent current i on the electron cloud, so the electron cloud and the light exchange the refractive energy with each other, and the light speed decreases in media[1]. According to this theory, induced current loops should form on the electron clouds in an insulating medium that is in the alternating magnetic field of a coil, and a considerable induced magnetization in the insulating medium should appear. This behavior is similar to that of a piece of metal. Therefore the insulating medium that is near a coil should be repelled strongly by the coil that suddenly carries a current, just like a piece of metal does. Our experiment results indicate, however, that all the insulating media used in the experiment do not show such a behavior. A possible explanation for above experimental results is that the equivalent induced current i on the electron cloud may be quantized. When interacting with the alternating magnetic fields, the electron cloud in an atom accepts or returns the energy offered by the electromagnetic induction in a quantization way. The equivalent induced current i corresponding to the quantized energy assumes discrete values. We call the discrete energy levels corresponding to the discrete i values the energy levels of induced current, which are denoted by Ecurr. The refractive energy exchanged between the electron cloud and the alternating magnetic field (or the electromagnetic wave) must be equal to the differences between these Ecurr levels. The differences between these Ecurr levels should be smaller than those between atomic energy levels (1s, 2s, 2p, etc.). The electrons cannot stay steadily on these Ecurr *

Supported by Beijing Science & Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education, and the Excellent Young Teachers Program of Ministry of Education, P. R. China.

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levels.

The electron cloud cannot accept the energy part that goes beyond an Ecurr level but does not reach the next Ecurr level. When the induced electromotance offered by ∂B/∂t of an electromagnetic wave is not large enough to start the equivalent induced current i with the minimum Ecurr of the electron cloud, there is no equivalent induced current on the electron cloud, or in other words, the electron cloud will not exchange any refractive energy with the electromagnetic wave, and this electron cloud has no contribution to the refractive index. Generally, ∂B/∂t of the light is much larger than that of the coil. The induced electromotance offered by the light may start the equivalent induced current in the electron clouds in the insulating medium, so the electron clouds and the light can exchange the refractive energy. While the induced electromotance offered by ∂B/∂t of the coil cannot start the equivalent induced current with the minimum Ecurr of the electron clouds, so there is no induced magnetization in the insulating medium. This explains why these insulating media used in the experiment are not repelled strongly by the coil that suddenly carries a current.

The Ecurr energy levels can be understood using the well-established theory of oscillator. When limited in its electron cloud space, the electron has certain quantized total energy, and its potential energy and dynamic energy may translate into each other. So each electron in an atom can be seen as an oscillator. When driven by the induced electromotance, the electron changes its energy in quantization manner, correspondingly the equivalent induced current on this electron cloud will assume discrete values. In most circumstances, the force that the induced electromotance exerts on the electron is in two dimensions. So the oscillator model of two dimensions should be used to calculate the energy levels of the electron. The simple case is the harmonic and isotropic oscillation in two dimensions, and the energy levels of the electron in this case are [2]

En=(n+1)hω=Ecurr，n=0,1,2, … (1)

where ω is the intrinsic angular speed of oscillation of the electron in its electron cloud space. Different electrons (1s, 2s, 2p, etc.) in an atom have different ω values, and have different steps of Ecurr levels and minimum Ecurr levels. As the frequency of the electromagnetic wave increases from 0, the induced electromotance offered by the electromagnetic wave will make more and more electron clouds begin to form their equivalent induced currents, and more and more electrons in the atom begin to exchange the refractive energy with the electromagnetic wave and contribute to the refractive index. Hence the refractive index of the medium will get larger and larger in this process. When all electrons in the atom have exchanged the refractive energy with the electromagnetic wave, the refractive index of the medium will not vary obviously as the frequency of the electromagnetic increases, until the electrons are strongly disturbed.

The refractive energy offered by a visible light may be much larger than each step of Ecurr levels. Thus although the exchange of the refractive energy between the electron cloud and the visible light is still in the quantization manner, the quantization effect of the equivalent induced current i (i.e. the quantization effect of the refractive energy) can be neglected. The exchange of the refractive energy can be seen as a continuous process.

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A molecule of helium has two 1s electrons, and no chemical bond forms between helium molecules. So the electrons in helium molecule have the same ability to gain the refractive energy from an electromagnetic wave. Therefore helium is a suitable substance to show this quantization effect. The curve of the refractive index of helium vs the intensity of a laser, or vs the frequency of the electromagnetic wave in certain frequency range, probably shows evident steps, even fluctuations. Some single crystal materials maybe show the same behavior.

In summary, similar to many quantized energy phenomena, the equivalent induced current i on the electron cloud and the energy Ecurr of i only assume some discrete values. The electron cloud in an atom accepts or returns the refractive energy offered by the electromagnetic induction in the quantization manner. The induced electromotance must be large enough in order to start the equivalent induced current i of a certain Ecurr. When the energy of an equivalent induced current i is much larger than each step of Ecurr levels, the quantization effect of i can be neglected, and the exchange of the refractive energy between the electron cloud and the electromagnetic wave can be seen nearly as a continuous process. References

[1] Zhang, T. (2006 August) Propagation and refractive index of light in media. http://www.paper.edu.cn [2] Zeng, J. Y. (2000) Quantum Mechanics. Beijing: Science Press, p348 (in Chinese)

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