[xstrae]

I have been asked to find out the spin multiplicity of the 3d⁷ elecron. The options given are:

A:  1/2
B:  3/2
C:  1
D:  0
E:  5/2

Can someone explain what the question means?? I have no clue on what spin multiplicity is.. please help.

[Mitch]

What is the spin of 1 electron?

[xstrae]

+ or - 1/2... thats what i thought was the answer initially. But my teacher said its B 3/4 because there are 3 unpaired electrons. so i was then thinking multiplicity must mean the sum of the spins of all the unpaired electrons.
anyway, i looked it up in the net and that got me all the more confused.Here is what wikipedia says:

"2S+1 is the spin multiplicity, i.e., the (maximum) number of different possible states of * J for a given (L,S) combination. L is the total orbital quantum number in spectroscopic notation, and J is the total angular momentum quantum number.S=n/2 where 'n' is the number of unpaired electrons."According to this the spin multiplicity must be equal to 5/2..

so then should the answer be 5/2 or 1/2 or 3/4?

[Mitch]

Careful you may get youself confused reading more advanced sources on the subject. You said that an electron is +/- 1/2 that is correct. Do you know how electrons like to allign in orbitals? Will the un-paired electrons all be facing the same direction or will they be randomly oriented?

[xstrae]

The first 5 electrons would have clockwise spin and the remaining 2 would be paired with the electons in the first and second orbitals(these would would have anti-clockwise spin). So therefore, the remaining 3 unpaired electrons would have clockwise spin. So is +3/2 the answer?

[Borek]

So is +3/2 the answer?

Correct

[xstrae]

ok thanks.. just out of curiousity though..

"2S+1 is the spin multiplicity, i.e., the (maximum) number of different possible states of * J for a given (L,S) combination. L is the total orbital quantum number in spectroscopic notation, and J is the total angular momentum quantum number.S=n/2 where 'n' is the number of unpaired electrons."

what is all that about?

[Mitch]

You said that the atom would be 3/2 since all the unpaired electrons would align. Atoms can have higher energy states where they don't all align anymore and thus some will have opposite directions. The numer of permutations possible is given by the spin multiplicity. The other states can only be accessed by studing the atom's spectroscopy.