Abstract
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.
Highlights
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 aim of the paper was to get an insight into the time interval connected with the electron transition between two neighbouring quantum energy levels in the hydrogen atom
In the first step, the paper demonstrates that when the size of the velocity vL entering the Lorentz transformation amounts the size vn of the electron speed along some orbit n in the hydrogen atom, the effect of transformation reduces the electric field En by the term −En making the electric field between the electron and nucleus equal to zero
Summary
In an application of the Bohr model to the energy spectrum of the atomic hydrogen, the electric field—acting between the electron and nucleus—plays a do-. The magnetic field—due to circulation of the electron along its orbit—though it does not enter the spectral calculations, can be important for the Lorentz transformations of different kind applied to the vector fields active in the atom. In effect of that interaction the spectrum of the energy levels identical to that known from the Bohr atom can be calculated Another application of Bn in (1)—taken into account together with the quanta En of the electric field acting between the nucleus and electron—concerns the calculation of the drift velocity of electron possessed in the hydrogen atom; see [2] [3].
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