Pauli exclusion principle

[montezuma110]

Can anyone explain what a quantum number is in terms of the Pauli exclusion principle and quantum degeneracy pressure. I understand that no two fermions can have the same quantum number, but I'm not quite sure what that is.

Thanks

[JulianO]

It says that no two identical fermions (usually electrons) can have the same 4 quantum numbers. It means in an atom, you can't have two electrons in the same quantum state.

The numbers are

the spin

the shell

the subshell

and the orbital.

I'm not sure if there is actually a reasoning behind this, or it is just a well understood rule.

Degeneracy pressure is when basically all the electrons are squashed into their lowest allowed positions whilst maintaining the PEP so they resist being squashed further because the electrons can't be pushed into the fully occupied lower energy states.

This pressure can be overcome by sufficient amounts of gravity, and it forces the electrons to combine with protons to make neutrons, and then you get a new type of pressure. Neutron degeneracy, which is much like electron degeneracy, but with neutrons replacing the electrons and again filling energy levels.

At least that's my understanding of it, without going into wave functions and stuff!

[Merlin66]

I'd recommend "Spectroscopy: The Key to the Stars" by Keith Robinson as a general introduction. He covers the quatum side of things with some easy to understand examples.

[acey]

I'm not sure if there is actually a reasoning behind this, or it is just a well understood rule.

Only thing I'd add to JulianO's excellent summary is that the reasoning is something called the "spin-statistics theorem". There are two types of fundamental particle, bosons and fermions, which have different kinds of wave function ("symmetric" or anti-symmetric"). Electrons are examples of fermions, and fermions have "anti-symmetric" wave functions.

By analogy (it's no more than that!), think of the equation 3-2 = 1. If I swap the numbers I get 2 - 3 = -1. Electrons are a bit like this: if you interchange a pair of them then the wave function gets a minus sign (this is the "antisymmetry").

Suppose my two electrons are identical, e.g. like the number 3. We've got 3-3 = 0. If I swap them I get the same answer (it's symmetric), which shouldn't happen - it should be antisymmetric.

(To make the analogy more precise, instead of subtracting numbers we would multiply matrices - but never mind about that).

So I can't have a wave function involving two electrons with the same quantum state. The same applies for any fermions (e.g. quarks), but not for bosons (e.g. photons). I could, for example, have lots and lots of photons all in the same quantum state: that's the principle of a laser.

Neutrons are themselves fermions, like electrons, so in a neutron star you get the same issue of degeneracy pressure. Under the most extreme conditions, it's hypothesised that you might get a further stage, a quark star.

Quark star - Wikipedia, the free encyclopedia

Spin-statistics theorem - Wikipedia, the free encyclopedia

[Macavity]

I think the remarkable thing is that the basic theory extends over other quantum numbers too... It predicts / excludes elementary particles, based on coloured quark combos etc. Of course, quantitative calculations, one leaves to theorists!

[Photosbykev]

Did anyone else hear that ????

I think it was the sound of this thread going way over my head

[Macavity]

Didn't you listen to ol' Prof. Brian Cox. [just teasing!] I think he left more "armchair physicists" (as he now terms us?) baffled by his (rather unconventional) musings on the Pauli exclusion principle, than many... and in recent years too?

[montezuma110]

Thanks, i think i understand now.

A quark star is a very interesting concept, i have never heard that before. If something overcame its neutron degeneracy pressure and split into its component quarks, would its radius shrink again, therefore getting close or even becoming smaller than its shwarzschild radius?

[acey]

Maybe, but you don't need super-dense matter to make a black hole. If you were to fill a sphere as big as the solar system with sand then its Schwarzschild radius would be smaller than its physical radius: it would become a black hole.

You'd need a lot of sand, though.