Solid state physics

Electrons in the solid state a) It is assumed that the electrons can move freely in two-dimensional crystal. Draw this. - The dispersion relation E(k) to the wave vector k. - The density of states D(E) to the energy E. - The density of states D(llgl) to the magnitude of the wave vector k. I) It is now assumed that the electrons sense the atomic truncation of the lattice. How does this change the dispersion relation and the density of states? 0) What is the effective mass and how can it be determined from the dispersion relation