A piece of copper and another of germanium are cooled from room temperature to 100 K. The resistance of:

The correct option is: copper decreases and germanium increases.

To understand why this happens, we must analyze the electrical properties of the two materials, copper and germanium, and how their resistance changes with temperature.

1. Behavior of Copper (a Conductor):
Copper is a metallic conductor. In conductors, a large number of free electrons are already available for conduction at room temperature. When a conductor is cooled (its temperature decreases), the thermal vibrations of the metal lattice ions decrease. This reduction in lattice vibrations decreases the scattering of charge carriers (electrons), allowing them to flow more easily. Consequently, the resistivity and resistance of copper decrease as the temperature is lowered from room temperature to 100 K.

2. Behavior of Germanium (a Semiconductor):
Germanium is a semiconductor. In semiconductors, the valence band is completely filled and the conduction band is empty at absolute zero temperature. At room temperature, some covalent bonds are broken due to thermal energy, creating free electrons and holes for conduction. When a semiconductor is cooled, the available thermal energy decreases. As a result, fewer covalent bonds are broken, and charge carriers recombine, significantly reducing the concentration of free charge carriers in the conduction band. The decrease in carrier concentration outweighs any decrease in lattice scattering, causing the resistivity and resistance of germanium to increase as it is cooled from room temperature to 100 K.

Therefore, when cooled from room temperature to 100 K, the resistance of copper decreases and the resistance of germanium increases.