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

In summary, the conduction band in Na metal is the 3s band, which is the highest energy band. It is half-filled because Na has one electron in the 3s band, which can hold two electrons. This single electron is not spin-paired, giving a net magnetic moment to the conduction band. However, in a solid, the situation changes and the conduction band is non-magnetic due to Bloch's theorem.
  • #1
slimjim
11
0

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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  • #2
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?
 

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

What is the conduction band in Na metal?

The conduction band in Na metal is the highest energy level at which electrons are able to move freely and conduct electricity. It is located just above the valence band, which is the highest occupied energy level.

How does the conduction band in Na metal form?

The conduction band in Na metal forms when valence electrons gain enough energy to overcome the attraction of the positively charged nuclei and become delocalized. This allows them to move freely throughout the metal and contribute to electrical conductivity.

What is the significance of the conduction band in Na metal?

The conduction band in Na metal is significant because it is responsible for the high electrical conductivity of the metal. It allows for the flow of electricity, making Na metal useful for many applications.

How does temperature affect the conduction band in Na metal?

As temperature increases, the atoms in Na metal vibrate more vigorously, allowing electrons to gain more energy and move more freely in the conduction band. This leads to an increase in electrical conductivity.

Can the conduction band in Na metal be modified?

Yes, the conduction band in Na metal can be modified by adding impurities or alloying it with other metals. This can change the energy levels and affect the electrical and physical properties of the metal.

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