| Topic: |
Science > Physics |
| User: |
"G Patel" |
| Date: |
16 Nov 2006 06:39:47 PM |
| Object: |
wave mechanics - orbitals |
In multielectron atoms, each "orbital" can have 2 electrons with
opposite spins.
Say we're talking about 1s orbital, so the two electrons would have the
following quantum numbers:
n= 1, l=0, m_l=0, m_s=+1/2
n= 1, l=0, m_l=0, m_s=-1/2
Are there 2 totally different wave functions (orbitals) for each set of
quantum numbers above, or are they the same orbital?
The gist of my question is:
In a hydrogen atom the 1s orbital has a certain shape (95% of charge
density/ prob. density in a sphere centered at nucleus). In a helium
atom, we have 2 electrons in the 1s orbital, with different spin
numbers.
Are these two electrons [in] two different (95% probability) spheres or
[in] the same sphere?
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| User: "tadchem" |
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| Title: Re: wave mechanics - orbitals |
17 Nov 2006 05:48:07 PM |
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G Patel wrote:
In multielectron atoms, each "orbital" can have 2 electrons with
opposite spins.
Say we're talking about 1s orbital, so the two electrons would have the
following quantum numbers:
n= 1, l=0, m_l=0, m_s=+1/2
n= 1, l=0, m_l=0, m_s=-1/2
Are there 2 totally different wave functions (orbitals) for each set of
quantum numbers above, or are they the same orbital?
The gist of my question is:
In a hydrogen atom the 1s orbital has a certain shape (95% of charge
density/ prob. density in a sphere centered at nucleus). In a helium
atom, we have 2 electrons in the 1s orbital, with different spin
numbers.
Are these two electrons [in] two different (95% probability) spheres or
[in] the same sphere?
That depends...
The quantum number m is also called the 'magnetic' quantum number.
The presence of a magnetic field will separate the two electrons in
terms of energy because the magnetic quantum numbers interact directly
with the magnetic field to contribute to the total energy: the magnetic
field will elevate the energy of one electron and reduce the energy of
the other depending on the relative orientation of the magnetic dipole
of the electron and the applied magnetic field.
As long as there is no significant magnetic field present, the energies
of the two electrons will remain equal and the orbitals will remain
spherically symmetrical and indistinguishable.
Tom Davidson
Richmond, VA
Personal aside: I went to a G.P. physician in Amarillo, Texas, named
Dr. G. Patel. I know 'Patel ' is a rather common surname, but is there
any chance you two are closely related?
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| User: "malibu" |
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| Title: Re: wave mechanics - orbitals |
17 Nov 2006 08:40:02 AM |
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G Patel wrote:
In multielectron atoms, each "orbital" can have 2 electrons with
opposite spins.
Say we're talking about 1s orbital, so the two electrons would have the
following quantum numbers:
n= 1, l=0, m_l=0, m_s=+1/2
n= 1, l=0, m_l=0, m_s=-1/2
Are there 2 totally different wave functions (orbitals) for each set of
quantum numbers above, or are they the same orbital?
The gist of my question is:
In a hydrogen atom the 1s orbital has a certain shape (95% of charge
density/ prob. density in a sphere centered at nucleus). In a helium
atom, we have 2 electrons in the 1s orbital, with different spin
numbers.
Are these two electrons [in] two different (95% probability) spheres or
[in] the same sphere?
http://users.accesscomm.ca/john/He.GIF
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| User: "Rock Brentwood" |
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| Title: Re: wave mechanics - orbitals |
18 Nov 2006 03:18:30 PM |
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G Patel wrote:
In multielectron atoms, each "orbital" can have 2 electrons with
opposite spins.
n= 1, l=0, m_l=0, m_s=+1/2
n= 1, l=0, m_l=0, m_s=-1/2
Are there 2 totally different wave functions (orbitals) for each set of
quantum numbers above, or are they the same orbital?
The shapes of the Hydrogen orbitals with these numbers are the same.
But the HELIUM orbitals ... that's a different matter. You have to take
into account the interaction of the electrons with each other. The
Helium orbitals are distortions (or perturbations) of the corresponding
Hydrogen orbitals. The same for the H_2 molecule.
A problem with asking what "each" electron is, in the combined system,
or where "each" one is, is that there is no "each". The totality is an
inseparable whole and the electrons making it up don't have any more
individual identity than two waves on an ocean would. It would be like
mixing two cups of coffee together and then asking where each cup is.
I'm not sure what a combined 1S-1S orbital might look like, but the one
thing I do recall is that there is a rather involved math behind
determining what the actual spin eigenstates of the various
combination-orbitals are and the whole affair breaks any mould you had
in your mind, behind the question you posed, about the items in
question. It's a whole nuther subject to learn.
A few references found at random on Yahoo...
Introduction to Molecular Orbital Theory
http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html
The Helium Atom
http://user.mc.net/~buckeroo/HELI.html
There's a million other references on the topic and related topics.
This is also standard material in a chemistry course.
Examples of references on the Helium atom
http://www.iop.org/EJ/abstract/0022-3700/5/7/005/
A theorem on the Hartree-Fock equations for the nsms 1S states of
Helium with orthogonal orbitals
http://www.iop.org/EJ/abstract/0022-3700/1/6/303/
On the Hartree-Fock equations for helium with non-orthogonal orbitals
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