Relativistic Reduction of the Electron-Nucleus Force in Bohr’s Hydrogen Atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

Bohr’s Spectrum of Quantum States in the Atomic Hydrogen Deduced from the Uncertainty Principle for Energy and Time

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.

Time of the Energy Emission in the Hydrogen Atom and Its Electrodynamical Background

The time of the energy emission between two neighbouring electron levels in the hydrogen atom has been calculated first on the basis of the quantum aspects of the Joule-Lenz law, next this time is approached with the aid of the electrodynamical parameters characteristic for the electron motion in the atom. Both methods indicate a similar result, namely that the time of emission is close to the time period of the electromagnetic wave produced in course of the emission. As a by-product of calculations, the formula representing the radius of the electron microparticle is obtained from a simple combination of the expressions for the Bohr magnetic moment and a quantum of the magnetic flux.

与氢原子有关的原子光谱跃迁问题

本文以氢原子为例,阐述了玻尔的氢原子理论及引入相对论效应及量子理论后氢原子光谱的精细结构和超精细结构。同时,进一步在理论上深入探讨谱线精细结构、跃迁概率、谱线轮廓、谱线强度对原子光谱跃迁的影响,更深入地理解了原子光谱跃迁问题。

玻尔理论中几个问题的讨论

本文讨论了玻尔原子的能级和原子跃迁的条件，并说明玻尔理论是一种唯象理论。

从玻尔假说到发光原理

光是电磁波,发光即产生电磁波或光辐射,发光物理是发光材料创新设计和应用的理论基础.本文从玻尔假说出发,通过分析真空中和非真空中的孤立原子的能级和各类跃迁阐述发光的基本原理,通过分析非孤立原子激发态的能量传递阐述量子剪裁发光和上转换发光物理机制,通过介绍与发光有关的诺贝尔奖让学生了解该领域的最新进展,实现大学物理教学中从基础到前沿的跨越.