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### Topic: Stability of half filled orbitals  (Read 31050 times)

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#### xstrae

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##### Stability of half filled orbitals
« on: July 21, 2006, 09:43:32 AM »
can someone explain why half filled orbitals are more stable than partially filled orbitals??

#### Dan

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##### Re: Stability of half filled orbitals
« Reply #1 on: July 21, 2006, 10:41:09 AM »
Basically it is because after the half full point, electrons coming in will have to pair with another electron. Electrons are negatively charged and repel each other, so this is a relatively high energy process - ie. it's relatively difficult to do.

I'm not sure how in depth you want/have to go, but here is a more detailed explaination:

This is to do with the multiplicity of the state. If the shell is half full, the total spin (and therefore multiplicity) is at a maximum - all the electron spins are aligned. This means that the electrons tend to avoid each other - an often used analogy is cars going round a roundabout, if they all travel in the same direction, they tend to avoid each other.
When you add more electrons, the spins start to pair up. Basically, the cars coming in now are going the other way round the roundabout and often come close to each other. Electrons are negatively charged and repel each other, so having a state in which the electrons must get close is relatively high in energy. This is the basis of Hund's rule of maximum multiplicity.

Search for 'Hunds rule of maximum multiplicity', and 'Fermi holes' and 'Fermi heaps'
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#### xstrae

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##### Re: Stability of half filled orbitals
« Reply #2 on: July 21, 2006, 11:13:48 AM »
ok i got what you mean and did a bit of reading on fermi holes too. thanks. i actually got this doubt when i was going through the electronic configurations of elements. if the above were true, then why cant the electronic configuration of carbon be  1s22s12p3
wont this configuration be more stable since both the 2s and 2p orbitals are only half full??

#### tamim83

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##### Re: Stability of half filled orbitals
« Reply #3 on: July 21, 2006, 11:35:51 AM »
No, becacuse that would violate the Aufbau principle, which pretty much says that lower energy orbitals are filled before higher energy orbitals.  So in the case of carbon, you cannot partially fill the lower energy 2s orbital and then begin filling the p orbitals.  This is more unfavorable  energywise in the case of carbon than having partially filled p subshell.

#### Dan

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##### Re: Stability of half filled orbitals
« Reply #4 on: July 21, 2006, 11:54:42 AM »
why cant the electronic configuration of carbon be  1s22s12p3
wont this configuration be more stable since both the 2s and 2p orbitals are only half full??

As tamim83 pointed out, it is because the energy required to promote a 2s electron into the 2p is much greater than the energy gain from unpairing the electrons.

However, it's a good question! There are some cases when this can happen. Cr (I am led to believe) has a ground state config [Ar]4s13d5
In this case, the energy difference between the levels (4s and 3d) is very small, and the energy gain from unpairing electrons does overcome the energy gap.
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#### xstrae

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##### Re: Stability of half filled orbitals
« Reply #5 on: July 21, 2006, 01:17:00 PM »
ok it seems Cu too doesnt follow the usualy rules. it ends up with a ground state configuration of [Ar]4s13d10.
thanks for clearing this!

#### tamim83

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##### Re: Stability of half filled orbitals
« Reply #6 on: July 21, 2006, 02:14:16 PM »
Quote
it seems Cu too doesnt follow the usualy rules

Yep, there is a whole list of elements that do not follow the rules.  It happens more as the atomic number increases.