The energy e of an electron in the conduction band of a one-dimensional metal is given by asin2(ka) e = where a is a constant, k is the electron wavevector, and a is the atomic spacing. (a) determine the width of the first brillouin zone. (b) if a 2 x 10-10 m, the fermi wavevector is 2.618 x 103 m-1 and the fermi energy is 1 ev, determine the effective mass of electrons at the fermi level (c) this material is found to generate phonons when exposed to infrared light. in point form, describe a mechanism to account for this phenomenon.