Finding the spin-orbit coupling constants of an Alkai transition?

In summary, the conversation discusses the quantum numbers for the 4p and 4d orbitals and how they can be used to calculate energy differences and corresponding wavelengths for transitions between sub-levels. There is some discussion about using the differential form of the equation and assigning wavelengths to possible transitions.
  • #1
Ted55
3
0
Homework Statement
Find the spin-orbit Coupling constants of a 4p-4d transition of potassium given the following information:

There are three spectral lines in the transitions fine structure corresponding to wavelengths 693.9,696.4,696.5nm respectively.

The coupling constant for the 4d level is << 4p level. I.e] C_(4p) >> C_(4d)
Relevant Equations
Delta(E_j) = C/2 [ j(j+1) -l(l+1) -s(s+1)]
E = hc/x where x = wavelength
The set of quantum numbers for the 4p orbital is: 4, 1, {-1,1}, +-1/2 (n,l,m,s)
The set of quantum numbers for the 4d orbital: 4,2,{-2,2},+-1/2
Hence we can calculate DeltaE for the 4p sub levels for j=1+- 1/2
And for the 4d sub levels as j=2+-1/2.
Giving four total values for Delta E as:
C_4p /2, -C_4p , C_4d, -3/2 C_4d
Now given that E= hc/x where x is wavelength we can say that dE= hc dX/ X^2 for small energy splittings.
Now I get stuck, my thinking is to use the fact that the smaller E is the larger the lambda transition is and vice versa, however the 3 values for wavelength is throwing me off. This would give a value for C_4p as 2.6x10^-4 eV if this was the right thinking.

As the lambda split for the 4d level would be roughly 3nm, I’m not sure I could use the differential form of the equation here. So I am doubting my method.
Am I missing a trick here? Any pointers would be much appreciated! Thank you!
 
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  • #2
1. combining L=2 and S=1/2 gives which values of J?
2. Which selection rules apply?
 
  • #3
Ted55 said:
Now I get stuck, my thinking is to use the fact that the smaller E is the larger the lambda transition is and vice versa, however the 3 values for wavelength is throwing me off. This would give a value for C_4p as 2.6x10^-4 eV if this was the right thinking.
I don't understand what you are saying here. Maybe you should start by assigning the different wavelengths to the possible transitions.

Edit: @DrDu beat me to it.

Ted55 said:
As the lambda split for the 4d level would be roughly 3nm, I’m not sure I could use the differential form of the equation here. So I am doubting my method.
I think there is less possibility for errors if you first convert the wavelengths to energies.
 

1. What is spin-orbit coupling in Alkali transitions?

Spin-orbit coupling is a phenomenon that occurs in atoms when the spin of an electron interacts with its orbital motion. In Alkali transitions, this interaction is particularly strong due to the large difference in energy between the outermost electron and the inner core electrons.

2. How do scientists find the spin-orbit coupling constants in Alkali transitions?

Scientists use a variety of methods, such as spectroscopy and quantum mechanical calculations, to determine the spin-orbit coupling constants in Alkali transitions. These methods involve measuring the energy levels of the atoms and analyzing the data to determine the strength of the spin-orbit interaction.

3. Why is it important to know the spin-orbit coupling constants in Alkali transitions?

Knowing the spin-orbit coupling constants in Alkali transitions is important because it helps us understand the behavior of atoms in various environments. This information is also crucial for predicting and controlling chemical reactions and for developing new technologies.

4. Are the spin-orbit coupling constants the same for all Alkali transitions?

No, the spin-orbit coupling constants can vary depending on the specific Alkali transition and the atomic environment. They are affected by factors such as the nuclear charge, electron configuration, and external electric or magnetic fields.

5. How do the spin-orbit coupling constants affect the properties of Alkali atoms?

The spin-orbit coupling constants can affect the energy levels, spectral lines, and chemical reactivity of Alkali atoms. They also play a role in determining the magnetic properties and the stability of these atoms. Understanding these constants is essential for accurately describing and predicting the behavior of Alkali atoms.

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