How Does the Pauli Exclusion Principle Influence Orbital Stability in Atoms?

[JDude13]

The Pauli Exclusion Principle is the reason more than two electrons cannot occupy the same orbital. This is easy for me to grasp.
Why, then, does the Pauli Exclusion Principle make an orbital MORE stable with two electrons as opposed to one?
(This is in the interest of knowledge. I'm not doubting the validity of any physicist's theories.)

 

[tom.stoer]

The Pauli exclusion principle forbids to electrons two occupy the same state; so two electrons in one orbital differ by their spin. In the hydrogen atom one can label states using the quantum numbers n,l,m; n=1,2, ...; l=0,1,...,n-1; m=-l,-l+1,...,0,...,l-1,l; s=-1/2,+1/2

 

[Bill_K]

Why, then, does the Pauli Exclusion Principle make an orbital MORE stable with two electrons as opposed to one?

I don't think it does, does it? Do you have an example in mind?

There is an effect similar to this in the shell model of the nucleus, in which an even number of protons or neutrons makes the nucleus more stable, due to a 'pairing force' thought to be a residual effect of the nucleon-nucleon interaction.

 

[JDude13]

I don't think it does, does it? Do you have an example in mind?

In the case of ionic bonding, a non-metal (e.g. fluorine) will gain electrons to ensure that each of it's occupied electron orbitals are full (containing two electrons).

 

[alxm]

In the case of ionic bonding, a non-metal (e.g. fluorine) will gain electrons to ensure that each of it's occupied electron orbitals are full (containing two electrons).

An atom doesn't have the same orbitals when it's in a molecule as if it's a free atom. A molecule like HF is not more stable as H⁺ and F^-, if you pull it apart. You must be thinking about Lewis theory and how they 'want' a noble gas structure, but that doesn't have a lot to do with orbitals and the Pauli principle.

If you want to talk molecules in terms of QM, you'd normally describe it in terms of Valence-Bond (VB) theory or Molecular orbital (MO) theory. In which case a HF molecule bonds by forming a sigma bonding MO, alternately an sp-hybrid (in VB theory) from the hydrogen 1s orbital and one of the fluorine 2p orbitals.

The Pauli principle doesn't make an orbital more stable with two electrons than one. Electrons repel each other, and their mutual repulsion couldn't be larger than the one between electrons in the same orbital. They'll only share the same orbital if that orbital is low enough in energy. Otherwise they'll spread out as much as possible, to reduce overlap, but also to maximize the total spin. (Which reduces repulsion through the Pauli principle, since they can't be at the same place at the same time when they have the same spin) This is http://en.wikipedia.org/wiki/Hund%27s_rule_of_maximum_multiplicity" An example is the triplet ground-state of the oxygen molecule.

A non-metal atom will gain electrons to fill a Lewis octet or 18. But if you're going to talk about orbitals, the Pauli principle and quantum topics, you also need to drop the pre-quantum Lewis model for theories of bonding actually based on QM. Which means VB and/or MO theory.