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

[spaghetti3451]

"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.

 

[TriTertButoxy]

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.

 

[Deric Boyle]

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.

 

[DrDu]

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.

 

[Deric Boyle]

Thank you very much DrDo!