How number of primitive cells in a material = number of K-States ?

[masyousaf1]

Dear All,

1) I am not able to understand the statement given by one of the professor. i,e., Number of primitive cells in a material = Number of K-States.
2) Additionally, if one atom is per primitive cell then why do we have NUMBER of k-states equivalent to number of atoms in this case ?
3) why Number of primitive cells in a material are of order of avogadro number ?

Kindly respond
Thanks

 

[BigJDubs]

1) The statement is referring to the number of k-states (or energy states) within each primitive cell of a material. Essentially, each primitive cell of a material can be thought of as a single atom, since they are the smallest repeating unit of the material. Therefore, the number of k-states within a primitive cell is equivalent to the number of k-states within an atom. 2) In this case, the number of atoms in the material is equal to the number of primitive cells, since each primitive cell contains only one atom. Therefore, the number of k-states in the material is equal to the number of atoms in the material. 3) The number of primitive cells in a material is typically of the order of Avogadro's number (6.02 x 10^23). This is because materials typically have a large number of atoms, and each atom is contained within a single primitive cell. Therefore, the number of primitive cells in the material is equal to the number of atoms, which is typically of the order of Avogadro's number.