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Identify spectral lines

  • #1
Skärmavbild 2018-07-30 kl. 16.44.00.png

Homework Statement


The Ca spectrum below, recorded using a Fourier Transform Spectrometer (FTS), shows the resolved ##3d4s ^3D - 3d4p ^3D## multiplet. The wavenumbers and their relative intensities are given in the table. Identify all the lines and determine the fine structure constants in the two triplets (both are positive).
Skärmavbild 2018-07-30 kl. 16.39.50.png


Homework Equations


[/B]
$$I=F_{max} - J (1)$$

Landé interval rule: ##\frac{F_{max}}{F_{max-1}} = ##energy ratio between the F numbers(2)

$$ E_{hfs} = A/2 * [F(F+1) - J(J+1)-I(I+1)] (3)$$

The Attempt at a Solution


[/B]
I can determine the quantum numbers F,,J,I. But how do I know what rel. int. correspond to what transition?
And once I have the transitions. How do I use eq.(3) to solve for A?

Very grateful for any reply!
 

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Answers and Replies

  • #2
34,039
9,881
The relative intensity doesn't help you much here I think, but you can work with the energies.
 
  • #3
The relative intensity doesn't help you much here I think, but you can work with the energies.
Thanks!

I see. But how do I know what energy belong to what set of quantum numbers?
 
  • #4
34,039
9,881
You have formulas for the energies of the different levels. The transitions correspond to differences between these energies. If you have states with energies E1, E2 and E3 in ascending order, then in general you expect transitions with energy (E2-E1), (E3-E2) and (E3-E1). You won't necessarily see all in your spectrum and you won't necessarily know all energy levels, but if you know E2-E1 then you can know that two different spectral lines will differ by this energy.
 
  • #5
You have formulas for the energies of the different levels. The transitions correspond to differences between these energies. If you have states with energies E1, E2 and E3 in ascending order, then in general you expect transitions with energy (E2-E1), (E3-E2) and (E3-E1). You won't necessarily see all in your spectrum and you won't necessarily know all energy levels, but if you know E2-E1 then you can know that two different spectral lines will differ by this energy.
Joining this thread. But since we don't have the finestructure constants the expressions for the energies won't tell us anything. Jut E_1 = A * some number. Will be impossible to solve that set of equations.

How do one identify the lines given the figures above?
 
  • #6
34,039
9,881
There are seven numbers or six differences, that should be sufficient to find both unknowns.
 
  • #7
mjc123
Science Advisor
Homework Helper
946
437
This is a fine structure question, not hyperfine, so Eq. 3 is the wrong equation to use. There is no I.
 

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