Please show your work in detailed steps for each part.

Consider a crystal with a rectangular lattice where b = a/2: a b oo. . X(a) (10 points) On the same plot, sketch the rst Brilloiun zone dispersion relations E(kx) and E (ky). (b) (10 points) When an electron travels through the crystal, in which direction will the electron have a lighter effective mass? (c) (I Opoz'nrs) A material has two bands that look like the following. In which band will the electrons behave more like free electrons? Why? 500 Band A Band B (d) (5 points) For iron, which of the two bands would you expect to be the 0' band? Which would you expect to be the 3 band? Explain why