Question

At temperature 0K, germanium behaves as a/an
a) conductor
b) insulator
c) super conductor
d) ferromagnetic

Answer 1

Hint: Germanium is a semiconductor. It conducts electricity at room temperature or temperature higher than room temperature. In semiconductors the valence band and the conduction band do not overlap each other but at higher temperature, the electrons from the valence band cross the conduction band. 0K is the least possible temperature on the thermodynamic temperature scale. Therefore we can conclude what will be the effect of decrease of temperature on germanium.

Complete step by step answer:
In semiconductors i.e. germanium the energy gap is small. Hence at room temperatures some of the valence electrons gain enough thermal energy and jump to the conduction band. More the thermal energy available, the more electrons will get excited and jump to the conduction band. According to the Boltzmann law, the number of thermally excited electrons (n )is given by,
$n\propto {{e}^{-{{E}_{g}}/KT}}$ where ${{E}_{g}}$ is the energy gap for a particular substance, T is the temperature of the substance and K is the Boltzmann constant.
If we consider the above equation the number of thermally excited electrons keeps on increasing as we increase the temperature T. If the temperature of the semiconductor is brought down to 0K then the number of thermally excited electrons will literally be nil. Hence there won’t be any electrons in the valence band. Hence we can conclude that at 0K, germanium will behave as an insulator.

Note:
Usually semiconductors have a low resistivity to the flow of current at high temperatures. But for metals it's totally different. The resistivity of metal increases with the increase in temperature due to increased collisions between the electrons thus obstructing the flow of current.