Question

A pure germanium crystal at absolute zero is:
A. an insulator
B. a good conductor
C. a semiconductor
D. none of the above.

Answer 1

Hint-We know that semiconductors are the materials which have a small band gap. So even a small amount of energy in the form of thermal energy can cause conduction. Germanium is a semiconductor. At absolute zero the thermal energy is zero hence there is no energy for exciting the valence band electrons to the conduction band. Using this information, we can choose the correct answer.

Step by step solution:
The answer to this question can be explained using the band theory. With the help of this theory we can understand the difference between insulator, conductor and semiconductor.

In a conductor the valence band and conduction band overlap. Hence electrons from valence band can easily go to the conduction band making it a good conductor. In an insulator the conduction band and valence band are separated by a large band gap. Hence electrons from valence band cannot go to the conduction band easily. Hence, they are bad conductors.

The semiconductors are the materials that have conductivity in between insulators and conductors. In a semiconductor the band gap is small. So even a small amount of energy can excite the electrons from the valence band into the conduction band. Usually the energy given to excite the electrons is in the form of thermal energy.

The conductivity of a semiconductor increases with increase in temperature and decreases with decreasing temperature.

We know that germanium is an example of a semiconductor. But at absolute zero it behaves as an insulator. The electrons from the valence band can go to the conduction band only if we supply energy in the form of thermal energy. At absolute zero there is no sufficient energy for the valence band electrons to move to the conduction band. Hence no conduction takes place. So, it acts as an insulator at absolute zero.

Thus, the correct answer is option A.

Note:If temperature is not specified then we can say that pure germanium crystal is a semiconductor. But since we are asked about the nature of the germanium crystal at absolute zero we got the answer as an insulator. Same is the case for any other semiconductor. All semiconductors behave as insulators at absolute zero.