Degeneracy

Course Home

Short Topical Videos

• Statistical Degeneracy (Aaron Parsons)

Reference Material

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

Related Topics

• Black-Body Radiation
• Boltzmann distribution
• Maxwellian velocity distribution

Boltzmann Distribution

1 Definition

Degeneracy, often denoted $g_{i}$, 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:

$g_{n}=\sum _{l=0}^{n-1}(2l+1)=n^{2}\,\!$

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

$g_{n}=4n^{2}.\,\!$

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:

Ratios of hydrogen excited states to the ground state as a function of temperature