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

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In summary, the quantum defect is a measure of the difference between an energy level and the corresponding one in hydrogen, which can be determined by comparing the energies of an electron in a particular energy state in an atom with the same set of quantum numbers to the energy of an electron in a hydrogen atom. The term is mainly used to describe the difference in energy for weakly bound, highly excited electrons in Rydberg atoms. However, it is not as relevant for tightly bound electrons that strongly interact with other electrons. This concept is further explored in the book "Theoretical Atomic Physics" by Harald Friedrich.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
Thank you very much DrDo!
 

1. What is a quantum defect?

A quantum defect is a term used in quantum mechanics to describe the discrepancy between the observed energy levels of an atom and the predicted values based on classical physics. It is caused by the quantum nature of particles and their interactions.

2. Why is the concept of quantum defect important?

The concept of quantum defect is important because it helps explain the behavior of atoms and molecules and their interactions with light. It also plays a crucial role in understanding the electronic structure of atoms and the stability of chemical bonds.

3. How is quantum defect calculated?

Quantum defect is calculated by comparing the observed energy levels of an atom with the theoretical values predicted by the Rydberg formula. The difference between these two values is the quantum defect.

4. How does quantum defect affect the spectrum of an atom?

The quantum defect has a significant impact on the spectrum of an atom. It causes a shift in the energy levels, resulting in the formation of new lines in the spectrum. This leads to a more complex and detailed spectrum, allowing scientists to study the properties of atoms and molecules in greater depth.

5. Can quantum defect be observed in everyday life?

No, quantum defect is a concept that is only observed in the microscopic world of atoms and molecules. Its effects are not noticeable in everyday life, but it is crucial for understanding the fundamental principles of matter and energy in the universe.

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