Degeneracy
Definition and meaning of Degeneracy in chemistry.
Degeneracy is the condition in which two or more distinct quantum states of a system share exactly the same energy level. The number of such states at a given energy is called the degree of degeneracy, usually denoted g.
In more detail
Degeneracy typically arises from symmetry: states related by a symmetry operation of the system (rotation, reflection) must have identical energies. For example, the three 2p orbitals point along different axes but are equal in energy in an isolated atom because space is isotropic. Degeneracy can be lifted, or "split," when the symmetry is broken by an external perturbation, such as a magnetic field, an electric field, or an asymmetric chemical environment like a ligand field around a metal ion. The degeneracy factor also appears explicitly in the Boltzmann distribution and the partition function, since it weights how many microstates contribute at each energy, directly affecting entropy and level populations.
Key facts
| Field | Physical Chemistry |
|---|---|
| Symbol | g (degeneracy factor) |
| p subshell degeneracy | g = 3 |
| d subshell degeneracy | g = 5 |
The five 3d orbitals of a free transition-metal ion are all degenerate, but when the ion sits in an octahedral ligand field, that degeneracy splits into a lower-energy, triply degenerate t2g set and a higher-energy, doubly degenerate eg set.
Frequently asked questions
What does the "degree of degeneracy" mean?
It is the count of independent quantum states sharing one energy level; for instance, g = 3 for a p subshell and g = 5 for a d subshell in a free atom.
How is degeneracy removed?
By breaking the symmetry that caused it, for example applying a magnetic field (Zeeman splitting) or placing an ion in an asymmetric ligand field (crystal field or ligand field splitting).