Exchange energy of electrons in degenerate orbitals

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SUMMARY

The discussion centers on the concept of exchange energy in degenerate orbitals and its role in the stability of half-filled and fully filled orbitals. Participants clarify that the high exchange energy contributes to stability due to the mathematical overlap of orbitals rather than a physical desire of electrons to exchange positions. Key points include the nature of electron transitions, the significance of quantum numbers, and the representation of electron states through wave functions and eigenstates.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly electron behavior in orbitals.
  • Familiarity with the concept of exchange energy in atomic physics.
  • Knowledge of quantum numbers and their role in electron transitions.
  • Basic comprehension of wave functions and probability distribution functions.
NEXT STEPS
  • Research the mathematical formulation of exchange energy in quantum mechanics.
  • Study the implications of electron transitions between orbitals using quantum numbers.
  • Explore the concept of eigenstates and their significance in quantum mechanics.
  • Investigate the role of orbital overlap in determining exchange energy and stability.
USEFUL FOR

Students and professionals in quantum physics, atomic physics researchers, and educators seeking to deepen their understanding of electron behavior and stability in atomic orbitals.

hav0c
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We are taught that a reason for the stability of half filled or fully filled orbitals is due to the high exchange energy.
Now i get why the exchange energy would be higher compared to other configurations but i don't understand why electrons present in degenerate orbitals would want to exchange their positions..
 
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some different topics:
1)
http://en.wikipedia.org/wiki/Atomic_electron_transition
2)
An electron jumps between orbitals in the same way as it moves around within a single orbital; "nature's law". The difference is that to change orbitals, some of the quantum numbers of the electrons have to changes.
3)
An electron does not have a position but occupies all space. Observations of the electron position are given in the wave function. Also related to the probability distribution function.
4)
The orbitals are eigen states of energy operator. Electron can exist in any state, but this state is representable by superposition of eigenstates.
 
janhaa said:
some different topics:
1)
http://en.wikipedia.org/wiki/Atomic_electron_transition
2)
An electron jumps between orbitals in the same way as it moves around within a single orbital; "nature's law". The difference is that to change orbitals, some of the quantum numbers of the electrons have to changes.
3)
An electron does not have a position but occupies all space. Observations of the electron position are given in the wave function. Also related to the probability distribution function.
4)
The orbitals are eigen states of energy operator. Electron can exist in any state, but this state is representable by superposition of eigenstates.
Alright but i still haven't got my answer
 
hav0c said:
We are taught that a reason for the stability of half filled or fully filled orbitals is due to the high exchange energy.
Now i get why the exchange energy would be higher compared to other configurations but i don't understand why electrons present in degenerate orbitals would want to exchange their positions..

I'm not sure I understand your question. I don't think it's about "electrons wanting to exchange their positions", I think it's a mathematical factor that depends on the overlap of different orbitals.
 
Einstein Mcfly said:
I think it's a mathematical factor that depends on the overlap of different orbitals.

can you please elaborate?
my actual question is -how is exchange energy a relevant factor to stability and what is it actually.
 

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