A one dimensional crystal is 10 periods long, and we apply periodic boundary conditions. The potential in each period is very weak. Assume that the lattice spacing is a.

(A)    draw an appropriate E(k) diagram

(B)    mark any small changes that result of the slight potential wells

(C)    idicate the edge of the Brillioun zone, and give the approximate values of k and E at the edge

(D)    draw circles in the approximate locations of electronic states, being sure to get the total number correct

(E)    if there are a total of 6 electrons in the lattice, indicate where they would be at low temperatures on the diagram by filling in the circles

(F)    roughly redraw the E(k) diagram for much stronger periodic potential

(G)    is the effective mass at low energies higher or lower for the crystal in part (F) than it is for the crystal in part (A)? (explain)