# Degeneracy

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### Short Topical Videos

### Reference Material

- Boltzmann Distribution (Wikipedia)
- Maxwell-Boltzmann Statistics (Wikipedia)
- Boltzmann Distribution Derivation (IITM)

### Related Topics

# Boltzmann Distribution

## 1 Definition

Degeneracy, often denoted , is how many distinct configurations of an system map to one statistical "outcome."

## 2 Degeneracies of the hydrogen atom

The energy degeneracies corresponding to each E_n for the hydrogen atom are given by:

Taking the two electron spin states and the two proton spin states of hydrogen into account, our degeneracies then ultimately become

Using this expression for our degeneracies, we can then show the ratios of excited states of hydrogen to the ground state as a function of temperature: