Residual electron-electron interactions, atomic terms

L+1)(2S+1) In summary, When an atom has an excited-state configuration of 1s22s22p63s23p64s23d14p1 and residual electron-electron interactions are taken into account, the configuration splits into 6 atomic terms labeled by their L and S quantum numbers. These terms are (1,0), (1,1), (2,0), (2,1), (3,0), and (3,1). The total degenerate states for these terms is 60. This is determined by multiplying (2L+1)(2S+1) for each term, which agrees with the number of valence electrons in the configuration.
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Homework Statement


An atom with an excited-state configuration
1s22s22p63s23p64s23d14p1
With residual electron-electron interactions are taken into account, this configuration splits into atomic terms. List these terms labelled by their L and S quantum numbers

Homework Equations


L=|l1-l2|, |l1-l2|+1,..., l1+l2-1, l1+l2
S=|s1-s2|, |s1-s2|+1,..., s1+s2-1, s1+s2

The Attempt at a Solution


With 3d14p1open would give l1=2 s1=1/2 and l2=1 s1=1/2
Thus L = 1, 2 and 3 and S = 0 and 1. Which give the pairs

(1,0)
(1,1)
(2,0)
(2,1)
(3,0)
(3,1)

Is this correct?

If these are correct then I looked at the degeneracy of each of the terms above and total degenerate states would be 60. How can I confirm that this agrees with the number expected from the l and s quantum numbers of the two valence electrons in the configuration above?
 
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From my question above can I look at (2L+1)(2S+1)? Is there another way from l and s
 
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1. What are residual electron-electron interactions?

Residual electron-electron interactions are the interactions between electrons within an atom that are not accounted for by the simpler Coulombic interactions.

2. How do these interactions affect atomic terms?

Residual electron-electron interactions can cause deviations from the expected energy levels and spectral lines of an atom, leading to the splitting of atomic terms and the appearance of new spectral lines.

3. What is the role of electron spin in these interactions?

Electron spin plays a crucial role in residual electron-electron interactions as it can lead to the exchange of energy and angular momentum between electrons, resulting in the splitting of atomic terms.

4. How do researchers study these interactions?

Researchers study residual electron-electron interactions through theoretical calculations, experimental measurements, and spectroscopic techniques. They also use advanced quantum mechanical models to understand the underlying mechanisms of these interactions.

5. What applications do these interactions have in science and technology?

Residual electron-electron interactions have important implications in fields such as atomic and molecular physics, materials science, and quantum computing. Understanding and controlling these interactions can lead to advancements in energy storage, communication, and information processing technologies.

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