Fermi-Dirac statistics, finding all electron configurations

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Discussion Overview

The discussion revolves around Fermi-Dirac statistics and the process of finding all possible electron configurations for a system of 20 electrons with equidistant energy levels. Participants explore the methods for determining the number of configurations and the efficiency of these methods.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how it is known that there are only 24 possible configurations and seeks clarification on the method for finding these configurations.
  • Another participant suggests that the process ultimately comes down to counting, proposing a systematic approach based on sorting configurations by energy levels and occupancy.
  • A later reply reiterates the counting method and raises the possibility of misunderstanding the process, questioning whether it is merely a long trial-and-error method.
  • Another participant asserts that finding the 24 states is not a lengthy process, noting that a computer can perform the task very quickly, while also acknowledging that they are unaware of any method faster than counting the states.

Areas of Agreement / Disagreement

Participants express differing views on the complexity and efficiency of finding electron configurations, with some emphasizing the counting method and others questioning the necessity of trial-and-error approaches. No consensus is reached on the best method.

Contextual Notes

The discussion does not clarify the assumptions behind the counting method or the definitions of terms used, leaving some aspects unresolved.

sigint00
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Hello everyone. I'm having trouble understanding this example: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_5.htm#2_5_2

In this system of 20 electrons with equidistant energy levels, how is it known that there are only 24 possible configurations, and how are those configurations found?
 
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By counting. You can set up fancy sums, but ultimately it is just a matter of counting.
If you want a systematic approach, sort them by energy of the highest occupied level for example, then by occupancy of that level, then by energy of the second highest occupied level, ...
Alternatively sort by number of excited electrons.
 
mfb said:
By counting. You can set up fancy sums, but ultimately it is just a matter of counting.
If you want a systematic approach, sort them by energy of the highest occupied level for example, then by occupancy of that level, then by energy of the second highest occupied level, ...
Alternatively sort by number of excited electrons.

So there's no getting around this just being a long process of trial-and-error? or I'm misunderstanding, maybe...
 
24 states, it is not that long, and a computer does it in less than a millisecond.
I'm not aware of a method that is faster than counting the states, but that doesn't mean there can't be such a method.
 

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