Why Is the d-Orbital Considered in Sc Term Symbols?

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The discussion focuses on deriving term symbols for various atoms, specifically addressing why the d-orbital is considered for Sc while the s-orbital is not. The participants clarify that filled subshells contribute zero to total angular momentum, thus only partially filled subshells are relevant for determining term symbols. There is confusion regarding the term symbol for F-, where the correct solution is identified as 1S0 instead of 1P0, emphasizing the importance of recognizing filled orbitals. The conversation also corrects a typo regarding the electron configuration of Sc. Overall, the thread highlights the significance of understanding electron configurations in determining term symbols.
physicisttobe
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Homework Statement
electron configuration of SC
Relevant Equations
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I've solved further Term Symbol problems. The task is: derive the term symbols of the ground states of the following atoms: a) H, b) F, c) Cu, d) F- , e) P, f) Na, g) Sc

Why is the d-orbital considered here in g)? Why isn't the s orbital taken into account here? The 4s orbital is energetically higher than the 3d orbital, so why don't you look at the 4s orbital. I also post the solution and my approach to this problem. I can't explain why my approach is incorrect. Can someone help me?

my approach:
C5D1F174-C00B-4242-A072-B400DE853580.jpeg


solution:
ECB91335-C5CF-470D-94EE-3DA783A57DF4.jpeg
 
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The s orbital is full. The net contribution of all filled subshells to L and S is zero, so you only need to consider partially filled subshells. (And I assume 3d14 is a typo for 3d1.)

Oh, and if you meant Sc you should have said so. SC is something very different!
 
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mjc123 said:
The s orbital is full. The net contribution of all filled subshells to L and S is zero, so you only need to consider partially filled subshells.
All right, but what about F-? We have the configuration [He]2s^2 2p^6, both orbitals are full.
I thought it would be 1P0 but it's wrong. The solution is 1S0, but I can't explain why 1S0.
I solved this problem like this:

EE4B9EA0-09D4-4259-8706-EEB25FFD77E8.jpeg

mjc123 said:
(And I assume 3d14 is a typo for 3d1.)
Yes, it's a typo, sorry for that.
mjc123 said:

Oh, and if you meant Sc you should have said so. SC is something very different!
Oh, sorry, I mean Sc, of course.
mjc123 said:
The s orbital is full. The net contribution of all filled subshells to L and S is zero, so you only need to consider partially filled subshells. (And I assume 3d14 is a typo for 3d1.)

Oh, and if you meant Sc you should have said so. SC is something very different!
 

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physicisttobe said:
All right, but what about F-? We have the configuration [He]2s^2 2p^6, both orbitals are full.
I thought it would be 1P0 but it's wrong. The solution is 1S0, but I can't explain why 1S0.

What is your reasoning for selecting ##P## in your solution ##^1P_0##?
A full orbital subshell has zero net orbital angular momentum.
 
Last edited:
physicisttobe said:
Oh, sorry, I mean Sc, of course.
{Fixed in thread title now)
 
TSny said:
What is your reasoning for selecting ##P## in your solution ##^1P_0##?
A full orbital subshell has zero net orbital angular momentum.
All right, I get it. Thank you so much for your help!
If any questions arise, I'll get in touch here
 
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I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

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