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Related Concept Videos

Noble Gases02:54

Noble Gases

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The elements in group 18 are noble gases (helium, neon, argon, krypton, xenon, and radon). They earned the name “noble” because they were assumed to be nonreactive since they have filled valence shells. In 1962, Dr. Neil Bartlett at the University of British Columbia proved this assumption to be false.
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Nuclear Binding Energy

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The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons...
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The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature. At standard temperature and pressure, or STP (273.15 K and 1 atm), one mole of an ideal gas (regardless of its identity) has a volume of about 22.4 L — this is referred to as the standard molar volume.
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The Pauli Exclusion Principle03:06

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Equilibrium Conditions for a Particle01:23

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Reduced Mass Coordinates: Isolated Two-body Problem01:12

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In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
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Fabrication of Uniform Nanoscale Cavities via Silicon Direct Wafer Bonding
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Confined helium on Lagrange meshes.

D Baye1, J Dohet-Eraly2

  • 1Physique Quantique, and Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles (ULB), B-1050 Brussels, Belgium. dbaye@ulb.ac.be.

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Summary

The Lagrange-mesh method accurately calculates confined helium atom properties, achieving high precision for energies and pressures with minimal computation. This method offers a balance of computational simplicity and variational accuracy.

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Area of Science:

  • Atomic Physics
  • Computational Chemistry
  • Quantum Mechanics

Background:

  • The Lagrange-mesh method combines computational efficiency with high accuracy.
  • Studying confined atoms is crucial for understanding matter under extreme conditions.

Purpose of the Study:

  • To apply the Lagrange-mesh method to a confined helium atom.
  • To investigate both soft (potential-based) and hard (spherical cavity) confinement effects.
  • To calculate atomic properties like energies and inter-particle distances.

Main Methods:

  • Utilized the Lagrange-mesh method for calculations.
  • Employed perimetric coordinates for soft confinement.
  • Used rescaled perimetric coordinates ([0,1]) for hard confinement in spherical cavities.

Main Results:

  • Achieved high accuracy (11-15 significant figures) for energies and distances with short computation times.
  • Calculated pressures on the confined helium atom.
  • Demonstrated high relative accuracy for pressures (better than 10^-10 for radii < 1), surpassing existing literature values.

Conclusions:

  • The Lagrange-mesh method is highly effective for studying confined atomic systems.
  • The method provides accurate results for energies, distances, and pressures under various confinement scenarios.
  • This approach offers a significant improvement over previous computational methods for confined atoms.