[UPSC CSE 2001] Superconductivity (Q140, (10+10+10)M)

(i) Give a qualitative account of BCS theory of superconductivity. (ii) Obtain an expression for conductivity of an intrinsic semiconductor. How does it vary with temperature? (iii) The resistivity of an intrinsic semiconductor is 4.5\text{ ohm-m} at 20^\circ\text{C} and 2.0\text{ ohm-m} at 32^\circ\text{C}. Calculate the energy band gap.