513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
of Elements

      

Kittel problem 9.4

Show for a simple square lattice in two dimensions that the kinetic energy of a free electron at a corner of the first zone is higher than that of an electron at the midpoint of a side face of the zone by a factor of 2.

What is the corresponding factor for a simple cubic lattice in three dimensions?

For one valence electron per unit cell, how large is kF compared with k at the corners of the Brillouin zone and k in the middle of one of the faces of the Brillouin zone?

How does this change for two valence electrons per unit cell?

Often metals with one valence electron per unit cell like Ag, Au, Cu, Pt are better conductors than metals with two valence electrons per unit cell like Ca or Sr because kF is closer to the Brillouin zone boundary for divalent metals.