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.

Correlation Between Energy Transfer Rate and Atomization Energy of Some Trinitro Aromatic Explosive Molecules

An assumptive theoretical relationship is suggested to describe the property of molecular atomization energy and energy transfer rate in the initiation of explosions. To investigate the relationship between atomization energy and energy transfer rate, the number of doorway modes of explosives is estimated by the theory of Dlott and Fayer in which the rate is proportional to the number of normal mode vibrations. It was evaluated frequencies of normal mode vibrations of eight molecules by means of density functional theory （DFT） at the b3p86/6-31G（d,p） level. It is found that the number of doorway modes shows a linear correlation to the atomization energies of the molecules, which were also calculated by means of the same method. A mechanism of this correlation is discussed. It is also noted that in those explosives with similar molecular structure and molecular weight, the correlation between the atomization energy and the number of doorway modes is higher.

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.

Possible Evolutionary Models in the Initially Hydride Earth Theory

A modern view of the properties of chemical elements has confirmed the theory of the hot origin of the Earth. The next step in developing this theory was the hypothesis of the initial hydride Earth. In this work, we attempted to find additional evidence for this hypothesis and show additional effects that flow from it. The effect of the physical properties of atoms and ions on their behavior during the formation of the Earth was studied. The maximum contribution to the distribution of elements was made by those elements whose content in the original protoplanets of the disk was the maximum. Correlation dependence is obtained, which allows one to calculate the distribution of elements in the protoplanetary disk. It was shown that hydrogen was the main element in the proto substance located in the zone of the Earth’s formation. In this case, various chemical compounds formed, most represented by hydrogen compounds—hydrides. Since the pressure inside the Earth is 375 GPa, this factor forces the chemical compounds to adopt stoichiometry and structure that would not be available in atmospheric conditions. It is shown that many chemical elements at high pressure in a hydrogen medium form simple hydrides and super hydrides—polyhydrides with high hydrogen content. Pressure leads to a higher density of matter inside the planet. Given the possibility of forming polyhydrides, there is the possibility of binding the initially available hydrogen in an amount that can reach 49.3 mole%. Young Earth could contain about 10.7 mass% of hydrogen in hydrides, polyhydrides, and adsorbed form is almost twice higher than previous estimates. This fact additionally confirms the theory of the original hydride Earth. In hydrides, the occurrence of the phenomenon of superconductivity was discovered. Polyhydrides were shown as potential superconductors with a high critical temperature above 200 K. We, based on these data, hypothesized the presence of superconducting properties in the Earth’s core, which explains the presence of a magnetic field in the Earth, as well as the unevenness and instability of this field and the possibility of migration of the Earth’s poles. The fact that the Earth has a hydroid core causes its change in time due to the instability of hydrides. Arranged several possible models of the destruction of the Earth’s core. The calculations showed that both models give close results. These results give predictions that can be measured. The proposed models also made it possible to estimate the initial size of the Earth. Possible ways of further testing the hypothesis of the initial hydride Earth is shown.

A novel method for atomization energy prediction based on natural-parameter network

Atomization energy(AE)is an important indicator for measuring material stability and reactivity,which refers to the energy change when a polyatomic molecule decomposes into its constituent atoms.Predicting AE based on the structural information of molecules has been a focus of researchers,but existing methods have limitations such as being time-consuming or requiring complex preprocessing and large amounts of training data.Deep learning(DL),a new branch of machine learning(ML),has shown promise in learning internal rules and hierarchical representations of sample data,making it a potential solution for AE prediction.To address this problem,we propose a natural-parameter network(NPN)approach for AE prediction.This method establishes a clearer statistical interpretation of the relationship between the network’s output and the given data.We use the Coulomb matrix(CM)method to represent each compound as a structural information matrix.Furthermore,we also designed an end-to-end predictive model.Experimental results demonstrate that our method achieves excellent performance on the QM7 and BC2P datasets,and the mean absolute error(MAE)obtained on the QM7 test set ranges from 0.2 kcal/mol to 3 kcal/mol.The optimal result of our method is approximately an order of magnitude higher than the accuracy of 3 kcal/mol in published works.Additionally,our approach significantly accelerates the prediction time.Overall,this study presents a promising approach to accelerate the process of predicting structures using DL,and provides a valuable contribution to the field of chemical energy prediction.

The progress of radioisotope technology and application in China

The inception of radioisotope and its application in China are introduced. The research,development, production, application progress and the future development prospect of radioisotope and its products are described.

Bethe–Weizs?cker semiempirical mass formula coefficients 2019update based on AME2016

In the present work, the classical Bethe–Weizs?cker(BW) mass formula with five energy terms is revisited and updated. We use the least-squares adjustments on the binding energy of 2497 different nuclides from the last update of the atomic mass evaluation,AME2016 published in March 2017, to provide a new set of energy coefficients of the mass formula. The obtained set of formula coefficients allowed us to reproduce most of the experimental values of the binding energies for each nucleus with A ≥50. The comparison between the binding energies provided with updated mass formula and those of AME2016 on the one hand, and those of previous works,on the other hand, yields relative errors that oscillate between less than 0.05% and 1.5%. The revisited BW formula is in very good agreement with the experimental data.

Curvature and Size Effects on Reactivities of Mono-to Octa-vacancies in a(5,5) Single-walled Carbon Nanotube

Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vacancies in a（5,5） tube. An ab initio calculation results showed that E_f decreased with increasing the defect curvature K_（V_s）（s = 1~8）. The structures with removed carbon atoms along zigzag chain or the tubular axis were the most stable in each kind of Vs, because their corresponding K_（V_s） was the largest. In addition, local product structures disturbed the variation rule of E_f as K_（V_s）. There was an odd-even oscillation rule in the smallest E_f among each kind of Vs as the s value and vacancies V2, V4 and V6 were more stable. The stabilities of the related vacancy structures were confirmed by two dissociation processes.

Principle for the Working of the Lithium-Ion Battery

The technological advances in Lithium-ion batteries have created many new applications, including electric vehicles. In this short note, we shall explain in simple terms the basic physics why and how it is possible to have high energy capacity in Lithium-ion batteries. However, heating has been a common problem and without appropriate design, they might give fire and explosion as reported.

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

Two Problems of Time Entering Respectively the Relativistic Mechanics and Electron Transport in Quantum Theory

In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the quantum theory, we demonstrate that mechanical parameters entering the electron motion in the Bohr hydrogen atom can provide us with a correct size of the time interval entering the Joule-Lenz law for the emission energy between two neighbouring quantum levels of the atom.

Behavior of the relativistic angular and energy distributions of atoms exposed to a strong and low-frequency circularly polarized laser field

In this Letter, we focus on the theoretical analysis of the relativistic energy and angular distributions of the ejected photoelectrons during the relativistic tunnel ionization of atoms by intense, circularly polarized light. We make a small modification of the general analytical expressions for these distributions. The role of the initial momentum, the ponderomotive potential, and the Stark shift are considered. We also present the maximal angle of electron emission.

Interface adhesion properties characterization of sulfide electrode materials by the combination of BOLS and XPS

Although sulfide electrode materials in lithium battery systems have been intensively investigated due to their low-cost, high theoretical specific capacity, and energy density, there are few studies fousing on the adhesion properties, including the physical origin of hetero-coordination resolved interface relaxation, binding energy and the energetic behavior, and even the accurate quantitative information. In this paper, we present an approach for quantifying the interface adhesion properties of sulfide electrode materials resolved by the combination of bond order-length-strength theory(BOLS) and X-ray photoelectron spectroscopy(XPS), which has enabled clarification of the interface adhesion nature. The results show that the Cu 2p, Fe 2p, and S 2p electrons of Cu S and FeS_(2) compounds shift negatively due to the charge polarization of the conduction electrons of the heteroatoms, while Mo 3d, Sn 3d electrons of Mo S2 and Sn S2 and the C 1 s and S 2p electrons of CS compound shift positively due to the quantum trapping. It is noted that the exact interface adhesion energies of Cu S is 3.42 J m^(-2), which is consistent with the calculation result. The approach can not only clarify the origin of the interface adhesion properties of sulfide electrode materials,but also derive their quantification information from atomistic sites.

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.