Identify spectral lines

• John Greger
In summary: Fine structure has to do with different j values for the same n and l. The allowed j values for a given n and l are j=l+s, l+s-1, l+s-2, ... |l-s| with s=1/2 for electrons, so for l=2, j=5/2,3/2,1/2. The allowed j values for a triplet state are then j=1,2,3. The fine structure constant is A=sqrt((j+1/2)/(j+1/2+1))*alpha^2, where alpha is the fine structure constant for the hydrogen atom.In summary, the conversation discusses the use of a Fourier Transform Spectrometer to record a Ca

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).

Homework Equations

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$$I=F_{max} - J (1)$$

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

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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?

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The relative intensity doesn't help you much here I think, but you can work with the energies.

mfb said:
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?

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.

mfb said:
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?

There are seven numbers or six differences, that should be sufficient to find both unknowns.

This is a fine structure question, not hyperfine, so Eq. 3 is the wrong equation to use. There is no I.

1. What are spectral lines?

Spectral lines are specific wavelengths of light emitted or absorbed by an atom or molecule. They are unique to each element or compound and can be used to identify the composition of a substance.

2. How are spectral lines produced?

Spectral lines are produced when electrons in an atom or molecule transition between energy levels. When an electron moves from a higher energy level to a lower one, it releases energy in the form of light, creating a spectral line.

3. What is the importance of identifying spectral lines?

Identifying spectral lines is important in various fields of science, including astronomy, chemistry, and physics. It allows us to determine the composition of stars and planets, understand the chemical makeup of substances, and study the behavior of atoms and molecules.

4. How are spectral lines used to identify elements?

Each element has a unique arrangement of electrons, resulting in a distinct set of spectral lines. By comparing the spectral lines of an unknown substance to a known element's spectral lines, scientists can identify the elements present in the substance.

5. Can spectral lines change over time?

Yes, spectral lines can change over time. This can occur due to variations in temperature, pressure, or the chemical state of the substance. It is essential to consider these factors when identifying spectral lines to ensure accurate results.