degeneracy
Physics
Chemistry
Examples of degeneracy in the following topics:
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Crystal Field Theory
- Crystal field theory states that d or f orbital degeneracy can be broken by the electric field produced by ligands, stabilizing the complex.
- When the ligands approach the central metal ion, the degeneracy of electronic orbital states, usually d or f orbitals, are broken due to the static electric field produced by a surrounding charge distribution.
- Discuss the relationships between ligand binding in a metal complex and the degeneracy of the d orbitals and between the geometry of a metal complex and the splitting of the d orbitals.
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Degeneracy
- This is degeneracy.
- If they are equal then we have a degeneracy, if not, we don't.
- Therefore we have proved that if the ratio of the lengths of the sides of the drum is irrational, then there is no degeneracy.
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Octahedral Complexes
- In an octahedral complex, this degeneracy is lifted.
- Discuss the degeneracy of the d orbitals in an octahedral metal complex.
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Oscillator Strengths
- Here we have included the possibility that the lower state has a -fold degeneracy and we have summed over the degenerate upper states.
- Except for the degeneracy factors for the two states, the Einstein coefficients will be the same, so we can define an oscillator strength for stimulated emission as well,
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Thermal Distributions of Atoms
- In thermal equilibrium the number of atoms in a particular state is proportional to where and is the statistical weight or degeneracy of the state (for coupling ), so we find that
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The Third Law
- Instead of being 0, entropy at absolute zero could be a nonzero constant, due to the fact that a system may have degeneracy (having several ground states at the same energy).
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Tetrahedral and Square Planar Complexes
- Discuss the d-orbital degeneracy of square planar and tetrahedral metal complexes.
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Einstein Coefficients
- You can think of the statistical weight as the number of ways that the atom can be in the particular state, the degeneracy of the state.
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Wave Equation for the Hydrogen Atom
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Another velocity-dependent force: the Zeeman effect
- This is called degeneracy.