This article points out an error in a large number of wellknown textbooks of modern physics, atomic physics and quantum mechanics. We prove that replacing the electron mass by the reduced mass in Bohr's equation for the radius of the electron does not yield Bohr's orbit radius, but rather the electron (orbit particle)-proton (nucleus) separation. Bohr's orbit radius has nothing to do with reduced mass. In energy formula, it is indeed correct to use the reduced mass. The conclusion also refers to exotic atoms.
This article points out an error in a large number of wellknown textbooks of modern physics, atomic physics and quantum mechanics. We prove that replacing the electron mass by the reduced mass in Bohr's equation for the radius of the electron does not yield Bohr's orbit radius, but rather the electron (orbit particle)-proton (nucleus) separation. Bohr's orbit radius has nothing to do with reduced mass. In energy formula, it is indeed correct to use the reduced mass. The conclusion also refers to exotic atoms.
Experimental results: Ionization energy of the electrons at the atom.Bound of the Diatomic Molecules.From Bohr to Schröndiger.Deduction of the radius formula with the analogy of the atom with the blackbody research from Planck and harmonic oscillators.Why the electrons orbit around the nucleus with specific radius for the case of electron as particle.Why the electron doesn´t radiate energy at the stationary levels as a wave and as a particle.Diffraction and Interference for the electron by using the Fourier Approach and Wave Properties
The Bohr model is historically important in the understanding of quantum physics. It gives many important results for the hydrogen atom including atomic size and ionization energy. It is sometimes referred to as a semi-classical calculation, because it includes the physics of angular momentum quantization without the full quantum mechanical description of an electron wave. It is tremendously useful for gaining physical intuition of the quantum nature of the atom. In the Bohr model of the hydrogen atom, an electron has a circular orbit with speed v and radius r about the proton. The Bohr quantization condition is that an integer number of electron (de Broglie) wavelengths must fit to the atomic circumference.
The Bohr radius was derived using the non-relativistic de Broglie approximation, not the relativistic de Broglie equation. In this work, we will derive a relativistic Bohr radius from both the relativistic de Broglie approximation and relativistic kinetic energy. The Bohr model of the hydrogen atom has since been replaced by modern quantum mechanics and the Schrodinger equation. It is well known that the Schrodinger equation confirms the first Bohr radius as the most probable radius, but the Schrodinger equation itself is non-relativistic. The Dirac equation can likely be used, but there seem to be very few publications on the relativistically corrected Bohr radius. This is something we will discuss.
This chapter illustrates Niels Bohr's ideas in some detail. In the formulation of his model, Bohr assumed that the electron in the hydrogen atom moves under the influence of the Coulomb attraction between it and the positively charged nucleus, as assumed in classical mechanics. The Bohr model was very successful in explaining the discrete atomic spectra of one-electron atoms. The Bohr model is, of course, a theoretical model of an atom. Using Bohr's quantization postulate, find the linear velocity of the electron's sphere. To find the radius of the orbit, Bohr postulated that the angular momentum of the electron is quantized, i.e., it can only take values that are integer multiples of ħ. The chapter begins with considering the classical equation of motion for the electron in a circular orbit, which is based on Newton's laws of motion and Coulomb's law of electric force.
Turning back to Niels Bohr's model of the hydrogen atom, the paper is trying to resolve one of the issues associated with the model.While N. Bohr in the framework of his model did not find any relation between electron's motion in the atom and radiation emitted, there is a reason to believe that the relation is bound to exist.Furthermore, it is already given by Rydberg's formula that expresses the frequency of radiation as a difference of two other frequencies associated in some manner with electron's rotation.Based on this approach a new value for the radius of the ground stationary orbit is calculated.It appears to be more than Bohr's radius by a factor of 1.588.The question why both values for the radius of the ground stationary orbit (Bohr's radius and a new one) are compatible with Rydberg's formula is considered.Finally, what exactly Niels Bohr overlooked in his model of the hydrogen atom, is discussed.It is established that Rydberg's formula can be derived from the more general parameterized postulates, when Niels Bohr used, regardless of the value of the parameter.
This study investigated the properties and behavior of orbiting leptons, with a focus on their speed, wavelength, frequency, and energy. The research revealed the dependence of lepton speed on the size of the orbit and the magnitude of the charge of the nucleus. The speeds of electrons and muons were found to be similar, but muons being closer to the nucleus exhibited a greater sensitivity to nuclear charge. The analysis also demonstrated that the wavelengths of leptons increase linearly with the principal quantum number and the charge of the nucleus. Moreover, the comparison between Bohr and de Broglie wavelengths highlighted the influence of mass and speed on the wavelength differences. The research provided valuable insights into the relationship between speed, wavelength, frequency, and energy of orbiting leptons in atomic systems. The observations underscored the impact of relativistic motion on these parameters and highlighted the need to account for these effects in theoretical calculations. By examining computed values of lepton speed and analyzing their implications for different energy states and atoms, researchers gained a deeper understanding of lepton properties and the nature of orbital motion. The study incorporated the relativistic motion of leptons, leading to higher energies than those calculated by Niels Bohr. While the differences were small, they underscored the importance of considering relativistic corrections in energy level calculations. The findings emphasized the significance of incorporating these corrections to achieve accurate results, particularly in simple energy level calculations. The impact of the Bohr model extends beyond atomic theory and finds applications in various fields, including atomic physics, chemistry, and materials science. Therefore, this study contributed to our understanding of orbiting leptons, their properties, and their behavior within atomic systems. It highlighted the importance of incorporating relativistic corrections in energy level calculations and provided insights into the relationship between speed, wavelength, frequency, and energy. The investigation also emphasized the significance of the Bohr model in explaining atomic behavior, while acknowledging the advancements and limitations of modern theoretical frameworks like quantum mechanics.