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.

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?