A Conversation for The Pauli Principle

The Pauli Principle

Post 1

Dr Hell

In this thread anyone willing to help is more than welcome.

The problem is:

How to explain this rather simple piece of science guide-style.

I've tried, but came to a point where it seemed that a major retouch is needed...

So THIS is the forum to improve this entry. A WW of our own so to speak.



The Pauli Principle

Post 2


Hmmm, a bit tricky but how about this for a start...

As I recall this was linked to your periodic table entry. Did you specifically refer to the Pauli Principle there?
If not, I would suggest renaming it the Aufbau (building up) principle and simple describe the electron configurations - maybe quirkily mentioning that its all based on a terribly complicated theory called Quantum mechanics.

Ie say atoms have electronic shells and these shells have four different shapes of orbitals that electrons can occupy. s - or simply spherical orbitals, p - dumb bell shaped orbitals. d - orbitals, petal shaped orbitals consisting of four petals and f orbitals which are also flower shaped but have 8 petals (I know its more complex than that but that'll do for the layman I would say).
Each of these orbitals can only contain 2 electrons.

The first shell or energy level has only an s orbital so can take only 2 electrons.
The second shell has 1 s orbital and 3 p orbitals so can contain 8 electrons (2 in the s orbital and 2 in each of the p-orbitals).
The third shell has 1 s orbital 3 p orbitals and 5 d orbitals and so can contain 18 electrons.
The fourth shell has 1 s orbital, 3 p orbital, 5 d orbitals and 7 f orbitals. Hence it can contain 32 electrons.
The fifth shell has 1 s orbital, 3 p orbitals, 5 5 orbitals, 7 f orbitals and 9 g orbitals. No one has ever managed to make an element with enough electrons to utilise the g orbitals so this is as far as the current periodic table goes.

The atomic number of an element is the number of protons in its nucleus. Each proton is positively charged and to be electrically neutral the atom must possess the same number of electrons. Hence the atomic number also describes the number of electrons an atom has.

So if you know the number of electrons in an elemen you can work out its electronic configuration. You do this by using the so-called Aufbau or building up principle.

This means that you work out how many electrons you have to play with and then fill up the orbitals starting at the bottom.

The simples element hydrogen only has 1 electron and so its electronic configuration is 1s1. The first number represents the electron shell, the s the type of orbital and the second 1 indicates the number of electrons occupying this specific orbital.
Helium, having two electrons is 1s2. smiley - smiley

For Carbon, having 8 electrons, you fill the lowest energy orbital 1s with 2 electrons leaving 6. This is the lowest shell filled so you start building up the second shell. s orbitals are lower in energy than p orbitals so next you fill up the 2s orbital with another 2 electrons leaving 4 remaining which go into the 2p orbitals.

So the electronic configuration of Carbon is 1s22s22p4.

For each shell the s electrons are filled first and then the p orbitals. A funny thing happens in the heavier elements though.
For a bare nucleus, the s,p,d and f orbitals are of the same energy but once you start putting electrons in they become different. So that the building up becomes slightly more complicated. Its reasonably easy to remember that s is always filled first but once d orbitals are avaialable, these are filled next followed by the p-orbital. When f orbitals are available they are filled after s, followed by d then the p.

The chemical properties of the elements are determined by the outer electrons - those in unfilled shells. If all shells are filled - as in the nobel gases then the element is inert to chemistry. When shells are unfilled this is an unfavourable situation and atoms start combining with each other to share electrons and thus complete unfilled electronic shells.

Hence Lithium's electronic configuration is 1s22s1 so it has an extraneous electron in its outer shell. To have a complete shell it can either lose the outer electron to another species to give the Li+ ion (1s2) or it can gain 7 electrons to give the Li7- ion (1s22s2sp6). It is the former of these that is the easiest to achieve.
Fluorine in contrast has an electronic configuration of 1s22s22p5 and so to close its outer shell it must either lose 7 electrons to give F7+ or gain an electron to give the F- ion. The latter here is the only one possible under general conditions on earth.

So, if you mix Lithium and Fluorine they react - lithium gives up one electron and this electron is added to the fluorine giving the compound Lithium Fluoride - Li+F-.

Phew, rambled on a bit there but how's that for an alternative suggestion? smiley - erm

The Pauli Principle

Post 3



Just realised you've already written the article I just sketched out above smiley - erm

The Pauli Principle

Post 4

Dr Hell

Exactly... It's in the 'electron shells & orbitals'

But hey... there's some useful stuff in here, that might be added to the 'shells & orbitals' entry, what do you think? On the other hand that entry is quite complete as it is right now. Maybe it's just useful to add one or two examples?

This one is explicitly on the 'pauli principle'. In the beginning (See Orcus? We are chemists, we immediately think about the 'Aufbau' when we think of Pauli...) that was sort of my original intention, a short entry with the rule and some minor comments that it is way deeper than that, and that there is alot more to it. But while researching, peer reviewing and retouching the entry I found out that the Pauli thing in the outside-of-chemistry-world is a totally different thing that extends to stuff like quarks and hadrons and all *THAT* kindsa weird stuff...


A chemist when asked on the Pauli Princilple shoots one special case off the hip... But it's far broader than that.

*sigh again*

Well I don't even know where to start.

. . . - - - . . .


The Pauli Principle

Post 5

Marjin, After a long time of procrastination back lurking

Maybe that's where I drop in. Hi guys.
As chemists, you seem just to look at a smal subset of fermions, the electrons filling up atom shells.
As a physisist, I started with the general quantum mechanical side, where all particles have either whole numbered spins (bosons) or half numbered (fermions).
In the other discussion I used another way to express the principle:
No two fermions can be in exactly the same quantum mechanical state.

Maybe you/we can start with defining spin in laymen terms, introduce bosons and fermions and then state the principle.
After that a few examples can be given about the consequences (like the filling of atom shells).
How's that for a start?

The Pauli Principle

Post 6

Dr Hell

Hey Marijn.. So you found your way here - Good.

First. The entry's introduction (the forst two sentences) is still quite good, I think. After that it goes on just like Marijn said, explaining fermions and bosons first and then going on into the details.

BUT: There is a bigger problem that comes first.

- People might not know what quanta are, so there might be the need to explain *that* in a short way first (without hitting the pedanto-alarm(R) of other scientific people like us...)

- The classification into fermions and bosons: WHY is the classification like that? Answer: *Because* of the Pauli Principle. (If I remember correctly Pauli was there first, and the subdivision came afterwards) So we'd start explaining one thing on the premise that a consequence is already known.

- We'd have to start off earlier then: What led Pauli to include his nifty little Principle into the world of science? Why was there a NEED for that piece of theory?

After that we'd have to explain why may bosons have the same quantum numbers, and why may fermions NOT. But WITHOUT introducing integrals and symmetry elements of wave-functions.

I have a partial solution for that last problem: We'd have to tell the reader to trust us, because it's to complicated to explain it in easy terms, and because events in the quantum world (and particularly the spin) cannot be associated to anything anyone has ever seen (or felt) in real-life before. That is a solution, but it will make some people think it all is *excrements*.

The alternative explanation would prove it:

If we'd tell the reader the TRUTH: I.e. that the quantum mechanical approach has no pendant whatsoever to real-reality... The problem is that *THIS* normally excites people to higher energy states (I've seen that on my teachers before: They get red and start to rotate) and gets them so confused that it's really hard to bring them back to the negotiations table...

Well, we'll find a way out.

The Pauli Principle

Post 7


The trouble is I've never really been able visualise spin myself as I was taught that it is incorrect to imagine it as something simply spinning like the earth around its axis for example. This is of course the correct way to deal with quantum theory in my experience. If you start trying to visualise it then you are generally wrong. After all, how does a standing wave (electron in say an s orbital) 'spin'. Its kinda weird. smiley - erm
Must say I think I may enjoy this discussion. I did a special advanced course in quantum chemistry during my first degree because I do find it fascinating smiley - biggrin
All this has inspired me a bit and I think I may well attempt an article on the origins of the quantum theory as that should be reasonably easy to keep understandable. Problems with classical physics as in explaining the photoelectric effect and the ultraviolet explosion are the things I shall refer to.

Pauli Prinicple:
Bosons obey Bose-Einstein statistics
Fermions obey Fermi-someone else statistics.
smiley - erm
I'll have to do a little reading on this one I must say.
But that's smiley - cool

The Pauli Principle

Post 8

Marjin, After a long time of procrastination back lurking

I looked again at the entry as it is now, and I think that after the principle it should start with the piece 'Quantum mechanics is a curious little piece of' up to (so for us things look like they are finely continuous).' After that we can focus on spin, saying that the physisists originally thought this concerned really the spinning of the particles in a classical manner, hence the name. They discovered it was quantisized, characterized by the numbers n/2. It is not exactly a fast turning of the particle, but it still describes an intrinsic internal angular momentum.
The way how a lot of these particles should act together statistically was described by Bose and Einstein, hence the name bosons. I cannot remember why the other kind was named fermions.
Experiments then revealed an unexpected difference between even and odd numbered particles. Odd numbers seemed more restricted in their possibillities. Pauli was the guy who tried to describe the difference with what is now called the Pauli principle. As usual, he just postulated it as the way things seemed to work, without any idea why.
This will have to be brushed up of course.
After it, some examples can be given, maby even the Bse-Einstein condensate.

The Pauli Principle

Post 9

Dr Hell

Orcus: Fermi-Dirac-Statistics (DIRAC!!!! - Da One!!)

Marijn: Fermions are named Fermions because of Fermi.

Marijn: OK so inverting the order of those paragraphs should be easy for a start.

Orcus: Heey, when you start that entry, can I help out.. Or do you prefer doing it by yourself?

Cheers to you all,

The Pauli Principle

Post 10

Dr Hell

Hey y'all look at the entry. I've done some rewriting.

Is it better now?

Remark: I think that Bose-Einstein condensates would be off scope, but well worth a separate entry.


It's getting better in my oppinion.


The Pauli Principle

Post 11


Dirac! Yeah, that's the bloke smiley - biggrin

I'd love you to help our Hell, that would be great. Input prior to Peer Review on such a subject would hopefully eliminate any violent 'discussions'. I'll try and make a start tonight and post a link in when I've got somewhere smiley - smiley
I have to say I don't really at this stage want to get involved in a university project though as I may well have a lot of RL w*rk to do soon and I don't particularly want any deadlines.

Anyway, looked up the Pauli Principle in Atkins' Physical Chemistry textbook now.Hmmm
Psi(1,2)=-Psi(2,1) where 1 and 2 are two fermions
Psi(1,2)=Psi(2,1) where 1 and 2 are fermions

it then decends into hamiltonian operators and stuff smiley - erm Not much help there.

How about this for what quanta are...

Clasical (Newtonian physics) told us that energy was continuous - ie that any give particle could exist in any energy state whatsoever. However, this led to a number of problems when dealing with extremely small paricles and was eventually shown to be incorrect. This led max Planck to postulate his 'Quantum theory' stating that energy was in fact not continous but was arranged in discrete 'packets' or quanta. The energy of a given state is given by his equation E=hf where E is the energy, f is the frequency of electromagnetic radiation (further quantum theory has shown that particles can also be observed as waves with frequency f). h is called Planck's constant and is in a very very small number.
A quantum is therefore simply a small packet of energy.

The Pauli Principle

Post 12

Dr Hell

Yeah... Hmmm...

I too would not want a university project, for

a) the same rasons (RL university)
b) I do not really like the concept of h2g2 university (or maybe just didn't understand it)

Anyway. Post the entry, and I'll pop up in there soon with unimaginable amounts of input smiley - smiley


About quanta... Do you think that this explanation is needed in this entry? Wouldn't it be too far out of scope? Do you think we could settle for"A basic feature of quantum mechanics is that certain properties come in very small discrete packs (called quanta) and not in a continuous form"? And then head on to the explanation why things seem to be continuous for us (i.e. because the quanta - or the grid - is too small for us to notice)

BTW... What you wrote in your post on Quanta would be good for the 'history of QM'-Entry you are planning.

BTW(2): Planck did NOT like his own theory at all, even though it explained the black-body radiation quite well, he refused to accept quantisation of nature. He formulated it that way: Absorbtion of Energy is quantised. And THAT liguistic bit IS quite of big importance, since he never said that emission or undisturbed systems are quantised. And all you can measure will only work with absorbtion. Ingenious, no?

BTW(3): Newtonian Physics is not incorrect, newtonian physics is a extension of quantum mechanics for very high quantum numbers. QM is also regarded by some as being "a neat mathematical joke that fails to explain anything even nearly related to reality". (I'll never ever again say anything is correct or incorrect after the discussion on centrifugal force)

OK, see you later.


The Pauli Principle

Post 13

Marjin, After a long time of procrastination back lurking

I just read the revised article, it is much better now. I am only not happy with the part about the smeared out electrons, it just falls out of thin air with new difficult terms. More and more I get the idea we should stay with the original errounous semi classical models.

Let me try.
Since the Bohr model, scientist were convinced electrons could only be found in certain orbits around the nucleus of an atom. Each atom would try to get into a state containing the lowest energy, by having the electron jump to a lower orbit while emitting a foton. They expected that for all elements all electrons would fall into the lowest orbit, as boson theories predicted.
Alas, many experiments proved this untrue. It worked for the first elements, Hydrogen and Helium, but with the next, Lithium, there was allways at least one electron in the second orbit. Comparing this with the periodic table, a new orbit was starting to fill after each noble gas. Why oh why?
When you look at all the known quantum numbers of each electron in an orbit, there is allways at least one difference somewhere. That is what Pauli states: There can be no two fermions with exactly the same quantum numbers.
He did not know why, it just seemed to happen that way. (I do not know whether the latest models of 'the whichness of the why' predict this principle). And as far as it is known, there has never been found a fermion that violates this principle.

The Pauli Principle

Post 14

Marjin, After a long time of procrastination back lurking

While I as writing my part, you were going on to quanta. To explain Pauli, I do not think we have to go deep into quanta, that is mor fore the 'quantum mechanics' entry, with other nice things as wave functions, Heisenbergs uncertaincy, wave-particle duality and things like that.

The Pauli Principle

Post 15

Dr Hell


You are right: that part with the smeared electrons comes in without context.

The part you would want to insert would go somewhere in here:


Smart scientists in the beginning of the 20th century went on to calculate systems with many particles in a quantum mechanical approach.

Many experiments proved that electrons would at most show up in pairs (and not three or four). Looking at all the known quantum numbers of each electron in an atom, there is always at least one difference somewhere, the tiniest of them being the so called spin. This is the basis for the Pauli principle. Pauli found out that the reason for that lies in the mathematics of those systems, and that this rule would not only be valid for electrons but for any particle with an odd multiple of the spin.

According to this rule a different statistic would apply to particles for odd and even multiples of the spin:

Fermi-Dirac statistics for particles obeying Pauli's principle (i.e. odd multiples -- 1/2, 3/2, 5/2 etc...). The particles are therefore called fermions. Some important fermions are: quarks, prontons, neutrons and electrons.

Bose-Einstein statistics for the ones that must not obey Pauli's rule (i.e. even multiples 1, 2, 3 etc...). These particles are called bosons. Some prominent bosons are: 4He-Nucleus, photons and gluons.

This is all wild theory, but as far as it is known, there has never been found a fermion that violates this principle.


What do you say?

The Pauli Principle

Post 16

Dr Hell

Entry rewritten again. Checkout please (smeared electron part has been removed)

The Pauli Principle

Post 17

Marjin, After a long time of procrastination back lurking

It looks like it is going somewhere.smiley - ok
A question. You say:
Pauli found out that the reason for that lies in the (very complicated) mathematics of those systems
Does this mean he could explain this from theory when he formulated the rule? I thought he just stated an empirically found property, and I don't remember whether it can be derived from a theoretical model.

Something else. You start three times with 'Wild theory', That may be a bit overdone.

P.S. Of those 3 or 4 people, 2 will be dead by now.smiley - winkeye

The Pauli Principle

Post 18

Dr Hell


Yea it can be derived from the theoretical model... I can't remember it all, but he found out that that's something to do with symmetry and vanishing integrals.

He actually calculated the whole stuff, and not just adapted empirically... Getting a Nobel biscuit is not *that* easy after all.

OK 'wild theory' IS overdone.

PS: Everytime some bright spark understands the theory one of the 3 or 4 has to die. (That's also paraphrasing Feynman) so - fortunately - at any point in time there's 3 or 4 (the 'or' is probably due to uncertainty) people that understand QM. smiley - winkeye

The Pauli Principle

Post 19


Does that mean if a fifth appears he has to go and shoot one of the others? smiley - winkeye

The Pauli Principle

Post 20

Marjin, After a long time of procrastination back lurking

A fifth should be impossible. It would be a violation of the conservation of the total amount of knowledge.smiley - smiley
Maybe that why the number of people with scientific knowledge seems to decrease.smiley - sadface

Key: Complain about this post