In a quantum wire experiment we measure a wire resistance of 3.23 k (after accounting for all other resistance in the circuit). We know from other observations that the resistance in the wire is quantized and that the electron concentration in the wire is 1E18 /cm3 . a. If the wire has square cross section, what is the approximate width and length of the wire? b. Suppose that the wire can be reduced in cross section by etching while maintaining a square cross section. What other values of wire resistance are possible after such an operation