Physics · Advanced university
Excited-state population with degeneracy
The probability refers to the whole excited level, including all its degenerate states.
Method and conditions
The probability refers to the whole excited level, including all its degenerate states.
Pexc = g e^(−Δ/kBT) / Z
Worked examples
For a two-level canonical model with ground degeneracy 1, excited degeneracy 7 and Δ/(kBT)=1.7, find the total probability of being in the excited level. Round the final result to 4 decimal places if needed.
Normalize the excited weight 7e^(−1.7) by 1+7e^(−1.7).
0.5612
For a two-level canonical model with ground degeneracy 1, excited degeneracy 6 and Δ/(kBT)=1.1, find the total probability of being in the excited level. Round the final result to 4 decimal places if needed.
Normalize the excited weight 6e^(−1.1) by 1+6e^(−1.1).
0.6664
Try it
For a two-level canonical model with ground degeneracy 1, excited degeneracy 3 and Δ/(kBT)=1.1, find the total probability of being in the excited level. Round the final result to 4 decimal places if needed.
For a two-level canonical model with ground degeneracy 1, excited degeneracy 5 and Δ/(kBT)=2.3, find the total probability of being in the excited level. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0.4997
Normalize the excited weight 3e^(−1.1) by 1+3e^(−1.1).
- 0.3339
Normalize the excited weight 5e^(−2.3) by 1+5e^(−2.3).
Further reading and review references
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