How to Interpret Missing Energy Levels in Atomic Spectra?

[Clara Chung]

Homework Statement

Attached below

Relevant Equations

Attached below

I drew a picture of the information in the problem (not sure if it is right), the red lines are the given values and green line can be calculated using the formula given. I don't know how to find the defects because the energy from 100d to 100g is missing...

 

[Charles Link]

I think $E_{ion}=-\frac{Z^2 R}{n^2}$, (where $R$ is the Rydberg constant) and for hydrogen, $Z=1$ (atomic number) and $R_M=0$. I would need to do a little googling, which you perhaps should do on this one, but this equation is highly empirical, and not nearly as straightforward as the Bohr atom model for the hydrogen atom.
Incidentally, $n$ is the principal quantum number. You might consult an advanced spectroscopy textbook to find out what they call the other constants in this formula.

 

[DrClaude]

I think $E_{ion}=-\frac{Z^2 R}{n^2}$, (where $R$ is the Rydberg constant) and for hydrogen, $Z=1$ (atomic number) and $R_M=0$.

That won't work here. This question is about multi-electron atoms and quantum defect theory, so a quantum defect must be present in the equation. Also, $R_M$ is the Rydberg constant for a given isotope, so it can't be equal to zero.

@Clara Chung: I don't know how you can solve this problem. I agree with you that there appears to be some information missing. Can you post the spectrum that goes with the question?

 

[Clara Chung]

That won't work here. This question is about multi-electron atoms and quantum defect theory, so a quantum defect must be present in the equation. Also, $R_M$ is the Rydberg constant for a given isotope, so it can't be equal to zero.

@Clara Chung: I don't know how you can solve this problem. I agree with you that there appears to be some information missing. Can you post the spectrum that goes with the question?

I am so sorry that I forgot to post the spectrum in the question... Here is it...

 

[DrClaude]

It appears that the wavenumbers given in the spectrum are related to the energies of the levels, not to the transitions. In that case, there are no unknowns and you should be able to calculate the quantum defects.

 

[Clara Chung]

It appears that the wavenumbers given in the spectrum are related to the energies of the levels, not to the transitions. In that case, there are no unknowns and you should be able to calculate the quantum defects.

Why is it the energies of the levels¿ the question says from 3p to the 100 levels...

 

[DrClaude]

Why is it the energies of the levels¿ the question says from 3p to the 100 levels...

I interpreted this the same as you initially, but looking at the numbers given, the only way for this to make sense is to consider that these are energy levels, not transitions (compare to the energy level given for 100g).