- #1
RobL14
- 11
- 0
For a college project, I'm researching quantum defect theory. In my study, I'm using emission spectra to determine the quantum defect, treated as the correction term in the denominator of the Rydberg equation.
What I understand
In general, the Rydberg equation is effective for Hydrogen, because the nucleus provides a constant electrostatic potential. Beyond Hydrogen, however, the equation does not work, because the multi-electron system changes the electrostatic potential exerted on the outermost electron. When the outermost valence electron is in the s orbital, it has a high probability of approaching the nucleus, so it experiences extremely varied potential. When it is in the d orbital, it has a low probability of coming close to the nucleus, so it stays pretty far away from everything else; as a result, the electrostatic potential on the d electron is the aggregate charge of the ionic core, very much like Hydrogen's single-proton point charge. Because the potential is very different for the s orbital electron, its defect is much higher, whereas the defect for the d orbital is much lower.
What I don't understand
While I have the previous qualitative understanding of the quantum defect for emission spectra, I really have no understanding of its theoretical basis. I've tried reading multiple journal articles, but the literature is simply too advanced in its explanation for my current level of understanding.
What I have gathered is that the defect is related to the Coulomb Phase Shift by Seaton's Theorem. However, I need to know what the phase shift is and where it comes from. I appreciate anyone's help on the matter. It's really important that I gain an understanding of the theory, so I appreciate anyone's explanation and any mention of sources that I might consult.
What I understand
In general, the Rydberg equation is effective for Hydrogen, because the nucleus provides a constant electrostatic potential. Beyond Hydrogen, however, the equation does not work, because the multi-electron system changes the electrostatic potential exerted on the outermost electron. When the outermost valence electron is in the s orbital, it has a high probability of approaching the nucleus, so it experiences extremely varied potential. When it is in the d orbital, it has a low probability of coming close to the nucleus, so it stays pretty far away from everything else; as a result, the electrostatic potential on the d electron is the aggregate charge of the ionic core, very much like Hydrogen's single-proton point charge. Because the potential is very different for the s orbital electron, its defect is much higher, whereas the defect for the d orbital is much lower.
What I don't understand
While I have the previous qualitative understanding of the quantum defect for emission spectra, I really have no understanding of its theoretical basis. I've tried reading multiple journal articles, but the literature is simply too advanced in its explanation for my current level of understanding.
What I have gathered is that the defect is related to the Coulomb Phase Shift by Seaton's Theorem. However, I need to know what the phase shift is and where it comes from. I appreciate anyone's help on the matter. It's really important that I gain an understanding of the theory, so I appreciate anyone's explanation and any mention of sources that I might consult.