Examples of degeneracy in the following topics:
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- 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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- 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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- In an octahedral complex, this degeneracy is lifted.
- Discuss the degeneracy of the d orbitals in an octahedral metal complex.
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- Here we have included the possibility that the lower state has a $g_f$-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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- In thermal equilibrium the number of atoms in a particular state is proportional to $ge^{-\beta E}$ where $\beta=1/kT$ and $g$ is the statistical weight or degeneracy of the state (for $L-S-$ coupling $g=2(2J+1)$), so we find that
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- 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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- Discuss the d-orbital degeneracy of square planar and tetrahedral metal complexes.
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- 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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- This is called degeneracy.