What is the Quantum Defect and Its Relation to Energy Levels in Hydrogen?

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Discussion Overview

The discussion centers around the concept of quantum defect and its relationship to energy levels in hydrogen and other atomic systems. Participants explore how quantum defect measures the difference in energy levels between various atoms and hydrogen, particularly in the context of outer electrons and their penetration into inner shells.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant defines quantum defect as the measure of the difference between an energy level of an atom and the corresponding one in hydrogen, questioning the meaning of "corresponding" in this context.
  • Another participant notes that while the electronic states of isolated atomic systems are similar to those of hydrogen, differences in nuclear charge and electron interactions can perturb energy levels, suggesting a correspondence can still be found.
  • A third participant explains that to compare energy levels, one must identify the quantum numbers of an electron in a specific energy state and find the corresponding energy in hydrogen, indicating that this comparison reveals the extent of electron penetration and defines quantum defect.
  • Another participant argues that quantum defect primarily applies to weakly bound, highly excited electrons in Rydberg atoms, suggesting it may not be relevant for more tightly bound electrons that interact strongly with others.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of quantum defect to various atomic systems, with some suggesting it is relevant primarily for Rydberg atoms while others argue for its broader applicability. The discussion remains unresolved regarding the precise implications and definitions of quantum defect.

Contextual Notes

Participants highlight the need for clarity on the definitions and assumptions regarding quantum numbers and energy levels, as well as the conditions under which quantum defect is applicable. There is also mention of the limitations of the discussion in terms of visual aids, such as energy level diagrams.

Who May Find This Useful

This discussion may be of interest to those studying atomic physics, particularly in understanding the behavior of electrons in various atomic systems and the concept of quantum defect.

spaghetti3451
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"The quantum defect is a measure of the difference between an energy
level and the corresponding one in hydrogen i.e. the extent to which an outer (valence)
electron of a given angular momentum penetrates the inner shell of the atom."

So, if i pick an energy level of one atom, how do i know what the corresponding energy level of the hydrogen atom is? In other words, what does corresponding mean in this case?

"the extent to which an outer (valence) electron of a given angular momentum penetrates the inner shell of the atom": I don't see how this acts as an explanation for the difference between an energy level and the corresponding one in hydrogen.

Any help would be greatly appreciated.
 
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The electronic states of isolated atomic systems is very similar to that of the hydrogen atom. The biggest two differences is (1) the nucleus has greater positive charge, and (2) there are electron interactions. These two differences serve to perturb the energy levels a bit in heavier atomic systems, but one should be able to find a pretty good correspondence.

An energy level diagram comparing the two cases to illustrate my point is in order, but I don't have the time or ambition to make one.
 
failexam when you take up an enegry level and check it with the corresponding in H - atom , means that you have to find the quantum numbers of an electron in a particular energy state in and atom and find the its (electron's) energy and for the same set of quantum nos. find the energy of an electron in a H-atom compare these energies the comparision gives you the amount of penetration of an electron of the atom under consideration, and the last statement is just the definition of quantum defect.
 
The term quantum defect is used mainly to describe the difference between the energy of a weakly bound highly excited electron bound to a positive ionic core in so called Rhydberg atoms. I don't think it makes much sense for more tighly bound electrons which stronlgy interact with the other electrons.
A good book on atomic physics treating this subject is "Theoretical atomic physics", by Harald Friedrich.
 
Thank you very much DrDo!
 

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