Re: Pauli Exclusion

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

At 12:55 PM 7/22/2004, David,  you wrote:
> Regarding Brian W's focusing of the discussion:
>
> >In responding to David's puzzlement, I will acknowledge that's a
> >state quite well known to me, too.
>
> I think it is quite a universally common state.
>
> >So I had better narrow down the field:
> >Does the puzzlement arise from the assertion that:
> >there was an electron occupancy paradox?
>
> Yes.  I don't believe I have heard of this paradox.

Perhaps David is looking for more texture than the
treatment I had in mind:

The Bohr model using a single quantum number gives the right answer
for the energy of the electron orbitals.
A parameter n, the principal quantum number, is associated with the
 total energy,  so that calculating the energy from the quantum
mechanical wave function gives the expression Bohr derived for the energy.

This leaves inconvenient paradoxes:  why do not more electrons occupy given
energy levels etc., etc.

A developed  quantum mechanical model requires four quantum numbers
to explain away (..er I mean "characterize") the actual electron orbitals.
The principal quantum number, the orbital quantum number, the magnetic
quantum number, and the spin quantum number are associated with
observable properties.
The orbital quantum number is connected to the total angular momentum
of the electron.
The magnetic quantum number, is related to a component of the angular
momentum.
 The energy of any orbital is found to depend on the magnetic quantum
number  when the atom is in an external magnetic field.
This quantum number has a magnitude less than or equal to the orbital
quantum number.
The spin quantum number is related to the spin angular momentum of the
 electron with two known states:  for convenience called spin up and
spin down.
As usual, for historical reasons there is more than one way to characterize
an electron state in an atom, using the 4 quantum numbers, or the notion
of shells and subshells.
 A shell consists of all those states with the same value of n, the principal
quantum number. A subshell groups all the states within one shell with
the same value of the orbital quantum number.
The subshells are usually referred to by letters, rather than by the
 corresponding value of the orbital quantum number.

This paragraph is essentially a condensation of an on line article
which may be found here:

<http://www.nationmaster.com/encyclopedia/Electron-configuration>

I expect David is perfectly familiar with this material, though as always,
 the physicist spin is to offer 'Laws' bolstered (here)
 by multidimensional math confections, rather than as a model which is
 bolstered so as to explain the observations as they
consecutively appear.

> The only
> Fermi Paradox with which I'm familiar is the one concerning the
> question of where all the ETs are given the size and age of the
> universe and the tendency of technology to improve over time.
>
> >that Fermi offered a proposal to avoid a paradox or catastrophe?
>
> That too.  It goes along with my unfamiliarity with the original
> paradox.  I'm thus also unfamiliar with any proposed solutions to it.
>
> >that there are four quantum properties of interest in this case?
> >that Fermi's quantum model is upheld?
> >that the Fermi model works in some sense?
>
> Yes.
>
> Please elaborate on:
>
> 1) Why the concept of electron indistinguishability is unhelpful.
>
> 2) What this paradox is.
>
> 3) What Fermi's solution to it is.
>
> 4) What the 4 properties are.
>
> 5) Why the model is "pragmatic" and how it relates to the
> the conventional quantum theory explanation of quantum
> statistics.

> David Bowman


I hope this modest offering went some way to describe one (at least my)
 mindset on the topic.


Brian Whatcott    Altus OK    Eureka!