Explanation around Fermi Wave Vector and Metallic Behaviour

[bennyq]

Homework Statement

I was to calculate the Fermi Wave Vector $K_F$ for a metallic structure then explain why the nearly free elctron model is consistent with its behaviour?

The Attempt at a Solution

After calculating the wave vector, I see that the fermi wave vector is within an energy band, hence the energy band is only partially filled allowing easy promotion of electrons into higher energy states.. Allowing for easy conduction? Would this explain why the nearly free electron model is consistent?

 

[kau]

Homework Statement

I was to calculate the Fermi Wave Vector $K_F$ for a metallic structure then explain why the nearly free elctron model is consistent with its behaviour?

The Attempt at a Solution

After calculating the wave vector, I see that the fermi wave vector is within an energy band, hence the energy band is only partially filled allowing easy promotion of electrons into higher energy states.. Allowing for easy conduction? Would this explain why the nearly free electron model is consistent?

I didn't get the question exactly...But I think what you said is ok. we can say in nearly free electron model that in the edge there is a gap due to superposition of traveling waves directed opposite to each other..Now if the band is filled then it's insulator...and if the fermi momentum lies within a band and it's nt filled then it's a metal...