8. A piece of copper and other of germanium are cooled from the room temperature to 80 K, then ?

8. A piece of copper and other of germanium are cooled from the room temperature to 80 K, then ?

(a) resistance of each will increase

(b) resistance of copper will decrease

(c) resistance of copper will increase while that of germanium will decrease

(d) resistance of copper will decrease while that of germanium will increase

Answer :  (d) resistance of copper will decrease while that of germanium will increase

\(\rho = \frac{m}{n e^2 \tau}\)

When copper, a metal, is cooled, the atomic vibrations decrease, causing fewer collisions for the flowing electrons. This reduces resistance. In contrast, when germanium, a semiconductor, is cooled, the number of free charge carriers drops sharply, which makes it harder for current to flow. As a result, its resistance increases.