Quantum spin numbers for ground-state electron configurations

[spaghettibretty]

Homework Statement

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Please redraw this figure by assuming that an electron can have spin quantum number m_s = +1/2 (arrow up), m_s = 0 (marked as "I"), or m_s = -1/2 (arrow down). It is important to clearly state your arguments/reasoning.
http://s30.postimg.org/jz7tfeha9/wow.png

Homework Equations

None

The Attempt at a Solution

I think I'm oversimplifying this question too much. In the image, there are arrows that point up and down and they represent the spin of an electron. I know there are two electrons per orbital. If there are two arrows, one pointing up and one pointing down, wouldn't the arrows cancel out and be equal to 0? Then any atoms that don't have all their states equal to zero would be positive, since the positive spin number always go first. Wouldn't this mean I would just have to put a zero where there are two arrows and a +1/2 where there is an arrow pointing up? This seems too simple to be correct.

 

[Borek]

I can be missing something, but I think this is a stupid question.

My bet is that whoever asked it wanted you to remember the Pauli exclusion principle. Commonly taught version of the Pauli exclusion principle says that you can't have two identical electrons (with identical set of quantum numbers) in an atom/molecule. Normally it means two electrons in an orbital, and they probably expect you to put three electrons on the orbital.

There is a problem though - Pauli exclusion principle doesn't say "two identical electrons", it says "you can' have two identical fermions". And fermion is any particle with a half integer spin. Spin zero is not a "half integer spin" so the particle with spins 1/2, 0, -1/2 is not a fermion, and we don't know if the Pauli exclusion principle applies to it. So in reality the question asks "how do the laws of nature work when they not work", and as such doesn't make much sense.