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

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SUMMARY

The conduction band in sodium (Na) metal is half-filled due to its electron configuration of [Ne]3s1, where the 3s band serves as the conduction band. This band can accommodate two electrons, but with only one present, it remains half-filled. Despite having an unpaired electron, the conduction band is non-magnetic in the solid state because of the effects described by Bloch's theorem, which alters the magnetic properties of the electrons in a collective manner.

PREREQUISITES
  • Understanding of electron configurations, specifically for sodium (Na)
  • Knowledge of conduction bands in solid-state physics
  • Familiarity with Bloch's theorem and its implications on electron behavior in solids
  • Basic concepts of magnetism and magnetic moments
NEXT STEPS
  • Research Bloch's theorem and its impact on electron behavior in solids
  • Study the properties of conduction bands in various metals
  • Explore the relationship between electron spin and magnetism in materials
  • Investigate the implications of half-filled conduction bands on electrical conductivity
USEFUL FOR

Students and researchers in solid-state physics, materials science, and anyone interested in the electronic properties of metals, particularly sodium.

slimjim
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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.

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

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