Explain how the energy diagrams for H and Na differ

[Poirot]

Homework Statement

Referencing to the gross and fine structure, explain how the energy diagrams differ for Hydrogen and Sodium. What effect does this have on the observed spectra?

Homework Equations

Sodium config: 1s²1s²2p⁶3s¹
Hydrogen : 1s¹

The Attempt at a Solution

I think that the diagram would be the same if you covered up the energy diagram before 3s. And I know that the spectra lines for "s" transitions are the brightest, with lines getting dimmer through the letters (p,d,f...). But I'm not to clear on what this means in reference to the gross and fine structures, nor if the energy gaps of the transitions have an effect on the brightness or just the wavelength of given off photons (I'd assume the brightness is due to the probability of a transition occurring)? (The question is worth 5 marks out of 20 so I suspect there's a lot to mention)

Any help would be greatly appreciated, thanks in advance.

 

[mfb]

Just looking at the gross structure: Can you have a transition between n=1 and n=2 in hydrogen, can you have it in sodium? How would the electron configuration look like afterwards?
What about between other transitions? At which energy do you expect those transitions roughly?

What do you know about the fine structure?

 

[Poirot]

Hi thanks for your reply,

So you can have transition between n=1 and n=2 for hydrogen but not for sodium as it is filled up to 3s1 i.e n=3. Then the electron configuration for hydrogen would be 2p1 with 1s0 free as the l quantum number must change +/-1. Then I'm not sure what you mean by other transitions and wouldn't not sure how to find the energies of these transitions other than simply looking them up.
Then fine structure I know is for energy differences ΔE=0.001-0.01ev, and are harder to observe. I think it comes about from the interaction between the electron spin and the orbital angular momentum which causes an internal B-field and a kind of Zeeman Effect internally.
But I'm not sure how to related these effects to each other and the elements and their energy diagrams.

 

[mfb]

All the formulas for the fine-structure depend on the charge of the nucleus.

and wouldn't not sure how to find the energies of these transitions other than simply looking them up.

You should know the formula for atoms with a single electron. What do you expect to happen if there are additional electrons?

 

[Poirot]

We haven't been given any equations relating to fine structure yet, apart from the fine structure constant, fine structure has only been discussed briefly from the Zeeman effect.

Since sodium has more electrons the ionisation energy is smaller than hydrogen, so one could argue that observed spectra for hydrogen would relate to larger energy differences?

 

[mfb]

Since sodium has more electrons the ionisation energy is smaller than hydrogen

That is just an effect of different occupied shells, but not the point.

How would the sodium spectrum look like if there is just a single electron around it - compared to the hydrogen spectrum?

We haven't been given any equations relating to fine structure yet

Okay, then I don't see how you could do that part.