Degenerate
Definition and meaning of Degenerate in chemistry.
In chemistry, the word degenerate describes two or more orbitals that share exactly the same energy level. These orbitals remain distinct in their spatial orientation. However, an electron would have the exact same energy sitting in any of them.
In more detail
Degeneracy usually arises from the natural symmetry of atoms. For example, consider an isolated atom floating alone in space. Its three distinct 2p orbitals will have identical energy due to spherical symmetry.
This concept is crucial when determining electron configurations. Hund's rule states that electrons must fill degenerate orbitals singly first. They must also have parallel spins before any pairing occurs.
This behavior minimizes repulsive forces between the negatively charged electrons. Sometimes, this delicate energy balance gets disrupted. We call this removing or lifting the degeneracy.
Degeneracy is lifted whenever the atom's symmetrical environment is broken. Applying an external magnetic field will split the energy levels. This phenomenon is known as the Zeeman effect.
The presence of surrounding chemical groups, called ligands, will also break symmetry. This is widely seen in transition-metal complexes. Students often mistakenly think degenerate orbitals are the exact same orbital.
In reality, they are completely separate regions of space. They just happen to exist at the exact same energetic tier.
Key facts
| Field | Physical Chemistry |
|---|---|
| Governing principle | Hund's rule |
| Orbital filling rule | Fill degenerate orbitals singly before pairing |
| Common example | The three 2p orbitals (px, py, pz) of a free atom |
| Symmetry breaking effect | Lifts or removes degeneracy |
| External influences | Magnetic fields, electric fields, or ligand fields |
An isolated manganese ion (Mn2+) has five completely separate 3d orbitals. Because the ion is isolated in space, all five orbitals are perfectly degenerate. Following Hund's rule, its five valence electrons will occupy these degenerate orbitals singly. However, placing this ion inside an octahedral chemical complex changes everything. The surrounding negatively charged ligands repel the d orbitals unevenly. This interaction permanently breaks the symmetry. It splits the once degenerate set into a lower-energy group of three and a higher-energy group of two.
Frequently asked questions
What does it mean when orbitals are degenerate?
It means the orbitals share the exact same energy level. They are distinct regions of space, but electrons inside them hold equal energy.
How does Hund's rule apply to degenerate orbitals?
Hund's rule requires electrons to fill empty degenerate orbitals one by one. They only begin to pair up after every degenerate orbital has one electron.
How does crystal field theory relate to degeneracy?
Free transition-metal ions have five degenerate d orbitals. Placing the ion near ligands breaks its symmetry. This splits the orbitals into new groups with different energy levels.