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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Atomic Nuclei: Nuclear Spin State Overview01:03

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

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Related Experiment Video

Updated: Jun 29, 2026

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
10:52

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

Published on: July 27, 2022

Solving the two-center nuclear shell-model problem with arbitrarily oriented deformed potentials.

Alexis Diaz-Torres1

  • 1Department of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia.

Physical Review Letters
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

A new method solves the two-center problem for deformed potentials. Calculations for carbon-12 plus carbon-12 reactions show nonaxial symmetry is key to understanding molecular resonances.

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Last Updated: Jun 29, 2026

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
10:52

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Nuclear Physics
  • Quantum Mechanics
  • Computational Chemistry

Background:

  • The two-center problem is fundamental in nuclear and molecular physics.
  • Realistic, deformed potentials require advanced computational techniques.
  • Understanding molecular resonances is crucial for reaction dynamics.

Purpose of the Study:

  • To present a novel, general technique for solving the two-center problem.
  • To apply this method to realistic, deformed nuclear potentials.
  • To investigate the role of nonaxial symmetry in molecular resonances.

Main Methods:

  • Potential separable expansion method.
  • Calculation of molecular single-particle spectra.
  • Application to deformed Woods-Saxon potentials for (12)C+(12)C system.

Main Results:

  • Demonstration of a general technique for the two-center problem.
  • Accurate calculation of molecular single-particle spectra for (12)C+(12)C.
  • Identification of the critical role of nonaxial symmetric configurations.

Conclusions:

  • The potential separable expansion method offers a powerful approach to the two-center problem.
  • Nonaxial symmetry significantly influences molecular resonances in low-energy reactions.
  • This technique provides insights into nuclear reaction dynamics.