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Nuclear Stability03:18

Nuclear Stability

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Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
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The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Other Nuclides: 31P, 19F, 15N NMR01:16

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Many organic, inorganic, and biological molecules contain spin-half nuclei such as nitrogen-15, fluorine-19, and phosphorus-31. As a result, NMR studies of these nuclei have found extensive applications in chemical and biological research.
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Electron Configuration of Multielectron Atoms03:26

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The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...
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Critical nucleus composition in a multicomponent system.

T Philippe1, D Blavette1, P W Voorhees2

  • 1Groupe de Physique des Matériaux (GPM), Normandie Université, UMR CNRS 6634 BP 12, Avenue de l'Université, 76801 Saint Etienne du Rouvray, France.

The Journal of Chemical Physics
|October 3, 2014
PubMed
Summary
This summary is machine-generated.

Classical nucleation theory explains critical nucleus properties and composition deviations. For low supersaturation, deviations from equilibrium tie-lines are linked to Gibbs energy differences, suggesting significant changes near the spinodal line.

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Area of Science:

  • Thermodynamics
  • Physical Chemistry
  • Materials Science

Background:

  • Classical nucleation theory describes phase transitions.
  • Understanding critical nucleus properties is crucial for predicting phase stability and transformation kinetics.
  • Previous models often simplified multicomponent system behavior.

Purpose of the Study:

  • To derive the properties of a critical nucleus using capillarity theory.
  • To provide an analytical solution for critical nucleus composition under low supersaturation.
  • To investigate the factors causing deviations from equilibrium tie-lines in multicomponent systems.

Main Methods:

  • Application of capillarity theory within the classical nucleation framework.
  • Derivation of analytical solutions for critical nucleus composition.
  • Analysis of Gibbs free energy landscapes for multicomponent systems.

Main Results:

  • An analytical solution for critical nucleus composition was obtained for low supersaturation.
  • Deviation from equilibrium tie-lines is primarily driven by differences in the Hessian of the Gibbs energy of the phases.
  • The magnitude of compositional deviation is proportional to the supersaturation level.

Conclusions:

  • The derived theory is applicable to any multicomponent system.
  • Significant deviations in nucleus composition from equilibrium are expected near the spinodal line, even though the analysis is strictly for low supersaturation.