A high purity metal with 8.5x1023 free electrons per cm³ has conductivity at room temperature of 298K = 5.92x107 S/m. A wire 1 mm in diameter and 100 cm long, was produced from this metal by wire drawing process. The process introduces many dislocations to the drawn material. Calculate: a) the resistance R of the wire (in 2) at room temperature b) If the wire is carrying a current of 1.3 Amps, what is the voltage U applied to the wire and the electrical field strength & developed within the wire? c) Calculate the relaxation time of electron between collisions = mv d) Calculate the mean free path of electron between collisions=vy T eɛ e) The wire was cooled to 4 K and its conductivity was measured at 4 K. It was 2000x higher than at room temperature i.e. σ4K = 1.18x10" S/m. Assuming that only dislocations contribute to the scattering, calculate density of dislocations Cp stored in the wire. the specific scattering of dislocation line is 1x10-19 cm³ - the phonon contribution to the resistivity at 298K is 1.5x10-62cm -the phonon contribution to the resistivity at 78K is 1.5x10-72cm the phonon contribution to the resistivity at 4K is 1.5x10-12 Qcm f) Discuss very briefly what is the main assumption/correction about the density of conductive electrons, which is used in the derivation of conductivity in quantum mechanical theory of conductivity

A high purity metal with 8.5x1023 free electrons per cm³ has conductivity at room temperature of 298K = 5.92x107 S/m. A wire 1 mm in diameter and 100 cm long, was produced from this metal by wire drawing process. The process introduces many dislocations to the drawn material. Calculate: a) the resistance R of the wire (in 2) at room temperature b) If the wire is carrying a current of 1.3 Amps, what is the voltage U applied to the wire and the electrical field strength & developed within the wire? c) Calculate the relaxation time of electron between collisions = mv d) Calculate the mean free path of electron between collisions=vy T eɛ e) The wire was cooled to 4 K and its conductivity was measured at 4 K. It was 2000x higher than at room temperature i.e. σ4K = 1.18x10" S/m. Assuming that only dislocations contribute to the scattering, calculate density of dislocations Cp stored in the wire. the specific scattering of dislocation line is 1x10-19 cm³ - the phonon contribution to the resistivity at 298K is 1.5x10-62cm -the phonon contribution to the resistivity at 78K is 1.5x10-72cm the phonon contribution to the resistivity at 4K is 1.5x10-12 Qcm f) Discuss very briefly what is the main assumption/correction about the density of conductive electrons, which is used in the derivation of conductivity in quantum mechanical theory of conductivity