Do they spin, or orbit around the nucelous of the atom?
Very crudely- an electron is smeared out like a cloud around the +ve nucleus.
It is possible to make measurements of the rotational angular momentum of the electron and get 'sensible' answers, but quantum mechanics is weird. Strictly speaking, the electron can't be viewed as having an instantaneous position and velocity like macroscopic objects. Its properties are more 'blurry'.
This applet might give you some idea
Is that mostly due to the uncertainty in knowing it's position and momentum simultaneously?
Yes- that's a good way of looking at it. There's a big debate however on what that uncertainty actually means. Standard quantum theory says that it's more than just our ignorance of the electron (i.e. our uncertainty)- the blurriness is actually a property of the electron (or its 'wavefunction') itself. The puzzling thing is though that if you actually measure the position of an electron (e.g. with a bank of detectors) you never actually see that blurriness- it only registers a hit at one spot at one time. However, the actual result you get for the electron's position is unpredictable- before you make the measurement you can only know a probability for where the electron is going to be.
Hope that confuses you enough.
what's the 2 more circular, and dense spots then? where's the nucleous? The centre is empty, certianly the nucleous is in the centre of the atom??
Excellent question, and one that leads to very profound consequences. There are numerous explanations for this to be found (Google is your friend), but let me take a stab and see how this strikes you.Can anyone explain why does an electron have intrinsic spin? Pauli and Dirac matrices show the existence of spin, but this doesn't really explain the physical origins of the spin.
The reason that we have particles with intrinsic spin actually has to do with the symmetries of space-time. You don't get spin automatically unless you're working with relativistic mechanics, with its space-time symmetries. Without getting too deep into it, I'll just say that it turns out that the space we live in has the property that not everything is unchanged by a rotation of 360 degrees - some things pick up negative signs. Those things require a rotation by 720 degrees in order to return to their initial state. Electrons have this kind of symmetry, and that's what leads to their intrinsic spin.
There's an argument that intrinsic spin is actually due simply to a rotating current of the electron's wavefunction (just like orbital spin, for that matter). I've probably cited the article on PF before (it's also in the footnotes of Griffiths).[Spin] is not due to rotation of an extended object - it's really a fundamental quality of the particle, which just happens to have the characteristics of angular momentum.
Oh, gosh ... I was just thinking of the explanation that is often given when Dirac spinors are first introduced for describing the possible states of an electron in relativistic QM. Not having any quick references on the top of my head, I just did a Google search for "Dirac scissors", as this problem is often called, after the famous demonstration by Paul Dirac. He used a pair of scissors with a string looped the handles and tied to the back of a chair. Rotate the scissors once and the string is irretrievably tangled, but rotate through another 360 degrees, and the string can be untangled without further rotation of the scissors. In other words, the final state (after 720 degree rotation) is equivalent to the initial state in a way that the intermediate state (after 360 degrees) was not.Could you perhaps give a citation to where this 720-as-specifically-opposed-to-360 thing is shown to give rise to spin? I find it quite.. surprising, since as far as I knew there was no way to actually observe this lesser-symmetry of the spinor/wavefunction.
It's the Balinese candle-dance trick, and if you don't know it, go find someone who can show you how to do it. You hold the coffee cup with your right hand underneath it, straight out in front of you. Now bring it left, under your underarm, awkwardly around front with your elbow straight up in the air. That's 360 degrees, and you're a pretzel. Keep going around counterclockwise, this time swinging your arm around over your head. At 720 degrees the coffee cup is back where it started, unspilled, and your arm is straight once more.
Well, I can confirm the "very bizarre" part - about the rest, I'll just have to wing it and hope I'm not too far off the mark.I'm also wondering about what you wrote: "... this particular symmetry gives rise (through Noether's theorem) to intrinsic spin...". Sure. But what does it mean? From a strict physics point of view, how can an intrinsic property act in the same way as a motion, without being motion itself? Very bizarre.