Electron Spin 'technicality' of sorts

[stmoe]

I can't really find the section to put this in, it has to do with Chemistry .. but . really.. Quantum Chemistry and like..well, doing quantum numbers my teacher asked whether or not the first electron in an orbital was + 1/2 or -1/2. When doing it on my own I always just write 1/2 , and then +/- when the electron is paired , but my teacher is forcing a "class consensus." I kind of argued that it doesn't matter because its about the perspective , but he swears that there is something that dictates it.

My reasoning for the 1/2 has always been that while its just the electron by itself it doesn't matter if its plus or minus, i just make sure that they all fillt he same , as soon as another is put in there, then I write its spin to characterize it with accordance to the other.

I've searched high and low on the internet , and haven't had any luck finding anything that talks about it to any great depth. However I'm probably using some dumb vocabulary for what I'm wanting.

So, for example.. you fill the up to the 2p orbital ... and then you put 2 electrons in .. 1 to the x and the other to the y ... Have I assumed correctly in that the spin of these is going tobe the same , spin x = spin y, or can the one in the x be -1/2 while the one in the y be 1/2? .. And, Is there any order for noting them? first e- in the px is +1/2 and 2nd is -1/2 or something?

 

[vanesch]

I can't really find the section to put this in, it has to do with Chemistry .. but . really.. Quantum Chemistry and like..well, doing quantum numbers my teacher asked whether or not the first electron in an orbital was + 1/2 or -1/2. When doing it on my own I always just write 1/2 , and then +/- when the electron is paired , but my teacher is forcing a "class consensus." I kind of argued that it doesn't matter because its about the perspective , but he swears that there is something that dictates it.

Hmmm, now or you missed completely what your teacher told you, OR he/she is, eh, how should I put this without missing respect towards him/her...
You are of course totally right that it doesn't matter whether you call it +1/2 or -1/2 ! Change the direction of the z-axis and you flip the sign
Now, if for some odd reason he wants you all to normalize to a certain convention, why not, but you are right that this is purely conventional. But sometimes conventions are useful (for instance, to speed up correcting homework)

HOWEVER, when filling in 2 or more electrons into two orbitals, it DOES matter what RELATIVE spin they have, and that's because there's a tiny interaction between the spins that favors "equal spin" a very small amount over "opposite spin". This is called Hund's rule http://en.wikipedia.org/wiki/Hund's_rule

cheers,
Patrick.

 

[stmoe]

yeah, i always just made sure that when i had the general 1/2 out there that when I had to pick a sign I did.
Example : px1 py1 pz1 all with 1/2... px2 py1 pz1 3 with +1/2 and 1 with -1/2, or visa versa

thanks