# Is the order of orientation of electron box diagrams meaningful or arbitrary?

Here is my interpretation when asked to:

By drawing arrows in the appropriate boxes, complete the outer electron structures for Cu and Cu2+

I had no problem in drawing out the electron structure, but am a little confused by the orientation of my arrows. I understand that each normal box has to have arrows in opposing directions to represent the opposite spins on the electrons, but the mark scheme defines which way round they want them to go:

Ordinarily I would have said that whether you go up or down first (or even consistently) is irrelevant and arbitrary, but the comment in the guidance

ALLOW single arrow in either direction

suggests to me that with the paired arrows, the order of directions matter.

Is there any chemical reason for putting the downwards spin arrow first? I would happily accept by convention as a reason but I just want to be sure that I'm not missing anything chemically relevant.

• I dont think so.. Your teacher seems to have subcontracted the correction to non-teaching staff :/. Note that unpaired electrons all have the same direction of spin, that's the only remotely related rule. Commented May 31, 2012 at 16:05
• I'd say it doesn't make a difference, since in atoms and ions the energy levels for two states with different spins (but all the other quantum numbers the same) are degenerate. Furthermore, the choice of the system's $z$-direction, to which $\uparrow$ and $\downarrow$ refer for the spins refer, is arbitrary in a spherically symmetric system. Commented May 31, 2012 at 16:13

Raise hell with the grader. There's no reason whatsoever for this answer to be rejected. A Google book search can substantiate your argument, and the first example from a textbook is actually in your order:

I think the guidance “allow single arrow in either direction” is not exclusive with “allow double arrows in either order”, and maybe only single arrows were explicitly mentionned because it was obvious to the writer that order in double arrows doesn't matter.

• That's what I found also. Commented May 31, 2012 at 22:27

I just cracked open five textbooks (Silberberg, Housecroft and Sharpe, West, McMurray, Simons) and they all adopt the $\uparrow\downarrow$ convention.

The only conceivable reason to prefer any order (namely, alphabetic ordering of the spin orbitals $\alpha$ and $\beta$) would actually suggest your chosen order. There is no chemically meaningful distinction between $\uparrow\downarrow$ and $\downarrow\uparrow$. I would love to know the marker's rationale here.

The order definitely does not matter.

This sort of diagram is for representing the quantum numbers of the electrons in the system. The 3d boxes mean the quantum numbers n=3, l=2 with ml =-2,-1,0,+1,+2 for the 5 boxes.

If a box has an up and a down arrow in it, this means there are 2 electrons with those quantum numbers, one with s=1/2, and one with 2=-1/2. It is completely meaningless which order your draw these in, the result is still the same two electrons with the same set of quantum numbers. Electrons are indistinguishable from each other. If you had a complex system with an exotic lepton such as a tau or muon then the order might matter, but in this case it certainly does not!

I can only assume that the writer of the mark-scheme assumed that UP DOWN and DOWN UP being identical would be obvious to anyone, and so didn't bother to write it. If the answer to a maths question was x * y, most mark-schemes wouldn't bother to write y * x also acceptable, as its obvious to anyone with any subject knowledge.

This is intended as an extension of RichardTerret's answer.

I personally have used/been taught uparrow first (not _explicitly taught, just that the teachers did it).

Anyway, I wanted to address the "Allow single arrow in either direction" issue.

I think that you have misinterpreted this. Basically, it's allowing some deviation from Hund's rule

Normally, Hund's rule forbids stuff like $[\uparrow\downarrow][\uparrow][\downarrow]$, since the spins cancel out (Hund's rule valls for maximum total spin). The second two ought to be both up or both down.

In early stages, this aspect of Hund's rule is not necessarily taught--Hund's rule is just portrayed as the thing that prevents pairing (from my experience). So, the paper setter may have decided to allow violations of the other aspect(if it is that) of Hund's rule, and thus the "Allow single arrow in either direction". They mean that the directions of single arrows can be mixed up.

• There's only a single “single arrow” in each case, so I don't think that can be the reason why…
– F'x
Commented May 31, 2012 at 20:42
• @F'x: Hmm, yeah. Though it may be a boilerplate for all such questions... :\ Commented Jun 1, 2012 at 3:44