Sp3 hybridization azimuthal quantum number

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Discussion Overview

The discussion centers on the azimuthal quantum number associated with sp3 hybridization, exploring the quantum mechanical properties of hybrid orbitals and their angular momentum characteristics. Participants examine the implications of hybridization on the quantum numbers and whether sp3 orbitals can be assigned a specific l value.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the s orbital corresponds to l=0 and the p orbital corresponds to l=1, questioning what l would be for an sp3 hybridization orbital.
  • Another participant suggests that the answer might be 1.5 but expresses uncertainty about the reasoning behind this value.
  • Several posts include tabulated quantum numbers, but their relevance to sp3 hybridization is questioned by a participant who notes that sp3 hybrid orbitals are not eigenstates of the orbital angular momentum operator, suggesting that discussing their l value may not be meaningful.
  • A participant expresses doubt about the validity of the image accompanying the quantum numbers, indicating it might not represent sp3 hybridization.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the azimuthal quantum number for sp3 hybridization, with multiple competing views and uncertainties remaining about the interpretation of the quantum numbers presented.

Contextual Notes

There is ambiguity regarding the assignment of quantum numbers to sp3 hybrid orbitals, particularly concerning their status as eigenstates of the orbital angular momentum operator. The discussion reflects differing interpretations of hybridization and quantum mechanics.

em3ry
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TL;DR
azimuthal quantum number for sp3 hybridization
The s orbital corresponds to l=0
The p orbital corresponds to l=1

For an electron in an sp3 hybridization orbital what is l?
 
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The answer appears to be 1.5 but I don't know why
 
nmℓmsmjj
mℓ + ms
21.51.5+0.522
21.50.5+0.512
21.5−0.5+0.502
21.5-1.5+0.5-12
21.5-1.5−0.5−22
21.5-0.5−0.5-11
21.50.5−0.501
21.51.5−0.511
 
Breit-rabi-Zeeman.png
 
em3ry said:
nmℓmsmjj
mℓ + ms
21.51.5+0.522
21.50.5+0.512
21.5−0.5+0.502
21.5-1.5+0.5-12
21.5-1.5−0.5−22
21.5-0.5−0.5-11
21.50.5−0.501
21.51.5−0.511
Where is that from?

sp3 hybrid orbitals are not eigenstates of the orbital angular momentum operator, so it makes no sense to talk about their ##l## value.
 
I am simply noting that the numbers match the image below it.

And I am no longer sure that it is an image of sp3 hybridization. It might be something else
 

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