(a) Show for a simple square lattice (i.e., in two
dimensions which possesses a lattice constant
*
a
*
) that the energy of a
free electron at a corner of the first Brillouin Zone (BZ) is higher than that
of an electron at midpoint of a side edge (i.e., a face) of the 1
^{
st
}
BZ by a factor of 2.

(b) What is the corresponding factor for a simple
cubic lattice possessing a lattice constant
*
a
*
in three dimensions (3D)?

(c) What bearing might the result of (b) have on the conductivity of divalent metals? Explain.