Quantum numbers for the third electron in lithium

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KingBigness
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Homework Statement



Lithium has an atomic number Z = 3. Two of its electrons have the quantum numbers {n, L, m{l}, m{s}} = {1,0,0,+1/2} and {1,0,0,-1/2}. Write down the corresponding set of quantum numbers for the third electron in the lowest energy state of the Li atom. Briefly explain the factors motivating the set of quantum numbers

Homework Equations


The Attempt at a Solution



Haven't done quantum numbers in a while.

The first shell is full so n=2. It is Lithium so it is still in the s orbital so l = 0
Firstly is this correct?

Now is where I get a little confused. Do the electrons have a preference when it comes to the m{s} numbers? Does it prefer to fill m{s} +1/2 before -1/2

My final answer for this question is (2,0,0,+1/2) is this correct?

Thank you for your time.
 
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n=2, L=m(l)=0 should be correct for the reasons you have outlined above.
If you are being asked for the corresponding Set(!) of quantum numbers I believe you want to include both the spin-up and spin-down states in your answer.