Confusion about electron energy levels

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Discussion Overview

The discussion revolves around the energy levels of electrons in atomic orbitals, specifically addressing the order of filling according to the Aufbau principle. Participants explore the implications of quantum numbers and the factors influencing electron energy levels in multi-electron atoms.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the 4s orbital is filled before the 3d orbital despite the principal quantum number indicating energy levels.
  • Another participant argues that energy levels depend on multiple factors beyond just the principal quantum number, including spin, special relativity, and screening effects from inner electrons.
  • A participant requests clarification on the arguments supporting the order of filling orbitals.
  • It is mentioned that the n+l rule can be used to determine the energy of orbitals, where a higher n+l value indicates higher energy, and if n+l values are equal, the orbital with the higher principal quantum number has higher energy.
  • A later reply expresses confusion about the implications of the n+l rule, suggesting it contradicts the idea that electrons farther from the nucleus have more potential energy.

Areas of Agreement / Disagreement

Participants express differing views on the factors that determine the energy levels of orbitals, and the discussion remains unresolved regarding the implications of the n+l rule and its relationship to potential energy.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the simplicity of energy levels and the complexities introduced by multi-electron interactions, which are not fully resolved.

Yashbhatt
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If 4s orbital is in the 4th shell and 3d is in the 3rd shell and if the Principal Quantum Number is the direct indication of the amount of energy in of the electrons in that shell. Then, why according to Aufbau principle is 4s filled before 3d?
 
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Because an atom's energy doesn't depend on one quantum number only. In other words, if you model the electronic configuration of the multi-electron atom/ion as to resemble the hydrogen's, then there are other effects to take into account (spin, special relativity, screening of the nuclear charge by the inner electrons). There's no 100% accurate theoretical description of the Aufbau Principle, but there are rigorous arguments in favor of it.
If all was simple, then 1s < 2s < 2p < 3s < 3p < 3d < 4s < 4p < 4d < 4f < 5s < 5p < 5d < 5f < 5g < 6s ... would be the normal energy diagram (as for the plain simple H-atom/hydrogenic ions in Schrödinger's description), but due to a myriad of effects (symmetry of the spin-spin couplings between electrons, special relativity), we have these inversions: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s ...
 
What are the arguments?
 
For seeing whether that which orbital has higher energy there a formula in which we have to calculate n+l where n is Principal quantum number and l is Azimuthal quantum number.
Orbital having more value of n+l has high energy.
If value of n+l is equal for two orbitals than orbital having higher principal quantum number has higher energy.
 
Murtuza Tipu said:
For seeing whether that which orbital has higher energy there a formula in which we have to calculate n+l where n is Principal quantum number and l is Azimuthal quantum number.
Orbital having more value of n+l has high energy.
If value of n+l is equal for two orbitals than orbital having higher principal quantum number has higher energy.

Okay. But that seems to be against the notion: The farther you pull an electron from the nucleus, the more potential energy it has.
 

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