Energy levels and the Aufbau Principle

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SUMMARY

The energy levels of the hydrogen atom, defined by the equation En=-me4/(32π2εohbarn2, are independent of the orbital angular momentum quantum number l. However, the Aufbau principle indicates that s, p, and d orbitals possess different energy levels due to factors such as shielding and penetration effects. A more accurate analysis requires considering relativistic effects, as the nonrelativistic Schrödinger equation does not account for the complexities of electron behavior. Experimental evidence supporting these conclusions can be found in the fine structure of the hydrogen atom.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of atomic structure and electron configurations
  • Concept of shielding and penetration in atomic orbitals
NEXT STEPS
  • Research the fine structure of the hydrogen atom
  • Study relativistic quantum mechanics and its implications
  • Explore the concept of electron shielding in multi-electron atoms
  • Examine the differences between s, p, and d orbital energies in various elements
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Students of quantum mechanics, physicists studying atomic structure, and educators explaining the Aufbau principle and energy levels in atoms.

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The energy levels of the hydrogen atom are given by En=-me4/(32\pi2\epsilonohbarn2, and are independent of the orbital angular momentum quantum number l, yet the Aufbau principle clealry implies that the energies of s, p, and d orbitals are different. Explain this apparent paradox and provide an example of experimental evidence that supports your conclusion.

I feel like I'm on the right track if I go about it from a shielding/penetration standpoint. But I could use the additional help! Thanks!
 
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There are certain approximations - things you neglected - that a more careful treatment will not neglect. Consider: the electron is actually a relativistic particle, yet you used the nonrelatavistic Schrödinger equation to derive those energy levels.

Look up the fine structure of the hydrogen atom.
 

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