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The Quantum-Mechanical Model of an Atom02:45

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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.
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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...
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The molecular ion peak of a molecule in the mass spectrum provides vital information for molecular identification. However, conventional electron impact ionization can lead to the rapid dissociation of some molecular ions before they reach the detector. A milder ionization method is required to increase the lifetime of such ionized analyte molecules. Chemical ionization (CI) is a gas-phase protonation reaction useful for mass-analyzing analyte molecules that are easily protonated to yield the...
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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws. 
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy (IE1). The first ionization energy for an element, X, is the energy required to form a cation with 1+ charge:
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Erratum: Density effects on electronic configurations in dense plasmas [Phys. Rev. E 97, 023206 (2018)].

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High-Sensitivity Nuclear Magnetic Resonance at Giga-Pascal Pressures: A New Tool for Probing Electronic and Chemical Properties of Condensed Matter under Extreme Conditions
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Carbon ionization from a quantum average-atom model up to gigabar pressures.

Gérald Faussurier1, Christophe Blancard1, Mandy Bethkenhagen2

  • 1CEA, DAM, DIF, F-91297 Arpajon, France and Université Paris-Saclay, CEA, LMCE, F-91680 Bruyères-le-Châtel, France.

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|September 16, 2021
PubMed
Summary

This study calculates carbon ionization under extreme pressures using an average-atom model, finding good agreement with simulations for pressure but noting discrepancies in ionization calculations.

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Area of Science:

  • Plasma physics
  • Computational physics
  • Materials science under extreme conditions

Background:

  • Understanding carbon ionization is crucial for modeling dense plasmas found in astrophysical objects and inertial confinement fusion.
  • Accurate calculation of pressure and ionization states is essential for predicting material properties under extreme conditions.

Purpose of the Study:

  • To calculate carbon ionization and pressure at megabar and gigabar pressures using a nonrelativistic average-atom model.
  • To compare the results with quantum molecular dynamic simulations and the PURGATORIO code.
  • To investigate the accuracy of the average-atom model in predicting these properties.

Main Methods:

  • Utilized a nonrelativistic average-atom model.
  • Calculated pressure via the stress-tensor method.
  • Incorporated electronic electrical conductivity using the Kubo-Greenwood approach.
  • Performed comparisons with quantum molecular dynamic simulations.

Main Results:

  • Achieved good agreement for pressure between the average-atom model and quantum molecular dynamic simulations at gigabar pressures.
  • Observed a discrepancy in average ionization, consistent with previous findings using the PURGATORIO code.
  • Demonstrated excellent agreement for average ionization when compared directly with the PURGATORIO code.

Conclusions:

  • The nonrelativistic average-atom model provides a reliable method for calculating pressure in dense carbon plasmas.
  • Further investigation is needed to resolve discrepancies in average ionization calculations between different simulation methods.
  • The study highlights the importance of cross-validation between theoretical models and simulation codes for accurate plasma property prediction.