Degeneracy
Definition and meaning of Degeneracy in chemistry.
Degeneracy is a condition where two or more distinct quantum states share the exact same energy level. The states are different but hold the same amount of energy. The number of these matching states is called the degree of degeneracy.
In more detail
Degeneracy usually comes from the physical symmetry of a chemical system. States that look identical from different angles must have identical energies. For example, isolated atoms have empty space extending evenly in all directions.
Because space is highly symmetric, some atomic orbitals hold the same energy. We can lift or break this degeneracy by removing that perfect symmetry. We might place the atom inside a strong magnetic or electric field.
We could also place it very close to other charged atoms. These outside forces affect the different quantum states in different ways. This causes their energy levels to split apart into entirely separate values.
Many students confuse degenerate states with perfectly identical states. The quantum states are physically distinct and occupy different regions of space. They just happen to sit at the exact same energy level.
Degeneracy plays a massive role in figuring out the entropy of a chemical. It tells us how many different ways a system can arrange itself. More degenerate states mean more options for the tiny particles to exist.
Key facts
| Field | Physical Chemistry |
|---|---|
| Symbol | g (degeneracy factor) |
| Cause | Physical symmetry in a system |
| Result of broken symmetry | Energy levels split apart |
| p subshell degeneracy | g = 3 |
| d subshell degeneracy | g = 5 |
Look at the five 3d orbitals of a single transition metal atom. When the atom is alone, all five orbitals are perfectly degenerate. They all have the exact same energy. Now imagine placing this atom inside a crystal surrounded by six other charged atoms. This setup is called an octahedral ligand field. The outside charges push differently on the different 3d orbitals. This breaks the symmetry and splits the energy levels. Three orbitals drop to a lower energy, and two rise to a higher energy. The original five-fold degeneracy is completely destroyed.
Frequently asked questions
What does the degree of degeneracy mean?
It is the exact count of independent quantum states that share one energy level. For example, a p subshell has a degree of 3.
Are degenerate quantum states exactly the same thing?
No. The states are physically different and might point in different directions. They just happen to possess the exact same amount of energy.
How do you break or remove degeneracy in an atom?
You must break the physical symmetry of the system. You can do this by applying a magnetic field or placing the atom near other charged particles.