An electron moving with acceleration and action exceeding the minimum value h generates a quantum of electromagnetic radiation only with a certain probability which is significantly smaller 1. The imperative nature of its action peculiar to macro world, at the micro level is transformed to a probable one. This indicates a critical feature of the action of the Maxwell electromagnetic theory at the micro level. Experimental data show that the lifetime of such excited states many times exceeds the orbital period of the electron (see below for a more detailed explanation). For single-electron systems (hydrogen-like atoms) the levels with n > 1 correspond to the excited states of atom. Continuing with this line of reasoning, we reach a conclusion about the existence of a set of orbits of an electron in an atom meeting the general condition A = n * h. In this case the action A = h can transform into electromagnetic radiation, the “residual” action of an electron will be equal to the minimal value, i.e. Reasoning in the same way, we reach a conclusion about the existence of a second orbit of an electron, and movement in such orbit between stationary points satisfies condition A = 2h. In our model, movement happens between stationary points, while the lack of radiation is a direct consequence of its minimal action. The fact that this doesn't occur should certainly be postulated. While continuously moving in circular orbit, an electron gradually produces more and more action, and in excess of the minimum value (h) gains the ability to emit energy in the form of electromagnetic waves. This logical conclusion looks like the Bohr postulate on the existence of special orbits of an electron.
The electron moves in such an orbit with acceleration, nevertheless, it cannot emit radiation, because this would lead to reduction in its energy and speed, and thus reducing its action below minimum values practically possible. Thus, condition A = h sets electron orbit parameters with a minimal distance from the nucleus. So the action of the electron on the trajectory between two stationary points cannot not be less than h. According to Max Planck’s classic quantum theory there exists a minimal value of action, h. Preliminary estimates show that the action, A, made by the electron during movement at atomic distances has the order of a Planck constant, h. This allows taking a new look at the radiation problem during electron’s accelerating movement in the field of nucleus. Within the ambit of the classical Kepler problem, reducing electron’s angular momentum leads to the contraction of elliptic orbit―so at M à 0 the trajectory of the electron will aspire to a straight line.Īt the point of maximum distance from the nucleus, the speed of the electron equals zero. Yet one more option has remained unanalyzed. This postulate looked (and looks) insufficiently substantiated, and it has been rejected alongside the Bohr model, with onset of the era of wave mechanics. Bohr by passed this restriction by postulating the existence of certain special orbits, along which the electron can move without electromagnetic radiation, and introduced the action quantization rule for movement along these orbits. The main contradiction of these models was―that in line with Maxwell theory the electron moving with acceleration in an electrostatic field of nucleus must emit electromagnetic waves, and thus loose energy. Arnold Sommerfeld extended this model to include elliptic orbits. The model gives Bohr formula for the energy of single-electron atom and suitable values of ionization potentials of the atoms of the second period of the Periodic Table.Ī little over one hundred years ago, Niels Bohr introduced the planetary model of the atom―with electrons revolving in circular orbits around a nucleus. Most of the time the electrons are located on the periphery of the atom, periodically they simultaneously rush to the nucleus, the atom rapidly compresses and immediately decompresses, i.e. Their frequency is of the order of 10 16 Hz. Electrons on the same shell perform symmetric synchronous oscillations. This condition sets the allowable values of the electron energy and the radius of their orbit. The action produced by electrons in movement between stationary points is discrete and proportional to a Planck constant. From a mathematical point of view the movement of an electron in such an orbit will be equivalent to the oscillation of an electron. The trajectory of the electron’s motion is an ellipse with a minor semiaxis, tending towards zero. In this work, we reanalyzed the movement of an electron in the electrostatic field of nucleus.