A piece of copper and another of Ge are cooled from room temp. to 80 K. The resistance of - (a) Each of them increases (b) Cu increases and that of Ge decrease (c) Cu decrease and that of Ge increases (d) Each of them decreases

When we cool materials like copper (Cu) and germanium (Ge) from room temperature to 80 K, their electrical resistance behaves quite differently due to their distinct properties as conductors and semiconductors. Let's break down what happens to each material in this scenario.

Understanding Resistance in Metals and Semiconductors

Resistance in materials is influenced by temperature. In metals, such as copper, the resistance typically increases as the temperature decreases. This is because, at lower temperatures, the thermal vibrations of the metal lattice decrease, allowing electrons to move more freely. However, the reduced thermal energy also means that the electrons encounter fewer scattering events, which can lead to an increase in resistance.

On the other hand, germanium, which is a semiconductor, behaves differently. As the temperature drops, the number of charge carriers (electrons and holes) in germanium decreases. At higher temperatures, more electrons can jump from the valence band to the conduction band, allowing for better conductivity. However, at lower temperatures, fewer charge carriers are available, which leads to an increase in resistance.

Analyzing the Options

• (a) Each of them increases: This is incorrect. While copper's resistance increases, germanium's resistance also increases, but the overall behavior is not the same.
• (b) Cu increases and that of Ge decreases: This is not accurate. Copper's resistance increases, but germanium's resistance does not decrease.
• (c) Cu decreases and that of Ge increases: This option is also incorrect. Copper's resistance does not decrease.
• (d) Each of them decreases: This is false. Copper's resistance increases, while germanium's resistance also increases.

Conclusion on Resistance Behavior

To summarize, as we cool copper and germanium to 80 K, the resistance of copper increases due to reduced thermal vibrations and increased electron scattering. In contrast, germanium's resistance also increases because the number of charge carriers decreases at lower temperatures. Therefore, the correct understanding is that the resistance of copper increases, and the resistance of germanium also increases, but they do not behave the same way.

In essence, the answer to the question is that both materials experience an increase in resistance as they are cooled to 80 K, reflecting their different electrical properties. This distinction between metals and semiconductors is crucial in understanding their applications in electronics and materials science.