PLEASE Help - interpreting an Atomic Structure question

[joker_900]

1. The problem statement, all variables and given/known data
It commonly happens that the hyperfine structure in a transition is dominated by the contribution of an s-electron in one of the levels. What property of s-electrons could be responsible for this?

A transition of this kind occurs at 494nm in singly ionised 133Cs between a level from the 5p5 6s config and one from the 5p5 6p config. Five hyperfine structure components are observed with wavenumbers relative to that with the lowest wavenumber as follows: 0.0, 8.1, 19.5, 33.7, 51.3 /m. The experimental uncertainty in the position of each component is of order 0.1 /m. Find the nuclear spin of 133Cs, and the value of J for the level arising from the 5p5 6s config.


2. Relevant equations
Earlier in the question we derived:

deltaE(F, F-1) * (F-1) = deltaE(F-1, F-2) * F


3. The attempt at a solution
Basically what I don't understand is what those wavenumbers refer to - are they for transitions or are they ionization energies, and which levels do they correspond to? You can read on to see what I've done so far if you wish:

So I think that J = 1/2 for the 6s config, as there is only one outer electron with l=0, so L=0 and so J=S=1/2.

I assume I>J, and got some allowed values of F. For the 6s config, I get 2 levels, for F=I+1/2 and F=I-1/2. For the 6p config I get J=3/2 or J=1/2, and so 6 levels for the 6p config overall. I think this is right, as even though for 6p, J=3/2 and J=1/2 both have F=+/-1/2 as allowed values, its for different J so the coefficient of the hyperfine energy will be different.

Now I have no idea what the given wavenumbers are.

Thanks

[Redbelly98]

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Five hyperfine structure components are observed with wavenumbers relative to that with the lowest wavenumber as follows: 0.0, 8.1, 19.5, 33.7, 51.3 /m.
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Basically what I don't understand is what those wavenumbers refer to - are they for transitions or are they ionization energies, and which levels do they correspond to?

The wavenumbers are equivalent to 1/λ for a transition from each hyperfine level to the lowest level in the group.

Note that a photon's energy is proportional to 1/λ, so giving the wavenumber (=1/λ) is another way of giving the energy difference of two levels ... so the lowest one is necessarily at 0.0/m, since that one is used as the reference point here.