Why Is the Conduction Band in Na Metal Half-Filled and Non-Magnetic?

[slimjim]

Homework Statement

Describe the ”conduction band” in Na metal. Why it is half-filled and
non-magnetic?

The Attempt at a Solution

Na has electron configuration: [Ne]3s^1

the 3s band is highest in energy and is the conduction band for Na. since Na has 1 electron in the 3s band, and the 3s band can hold 2 electrons, the conduction band is half filled.

this single electron is not spin paired, so this gives a net magnetic moment to the conduction band.

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Why would the conduction band be half filled AND non magnetic? Am I misunderstanding what a conduction band is?

 

[psmt]

this single electron is not spin paired, so this gives a net magnetic moment to the conduction band.

It's not spin-paired in a single sodium atom, but in a solid the situation changes completely. Are you aware of Bloch's theorem?