Question

In a semiconductor crystal, the total number of electrons in the outer shell is 4N . At absolute zero, the number of energy states of valence and conduction band are respectively

• A. 0 and 4N
• B. 4N and 4N
• C. 4N and 0
• D. 8N and 0
• E. 0 and 8N

Hint:

At absolute zero, all energy states in the valence band are occupied, while the conduction band has the same number of states but remains unoccupied due to the lack of thermal energy.

Answer 1

The Correct Option is B

In a semiconductor crystal, the behavior of electrons at absolute zero temperature ( T = 0 \, \text{K} ) is governed by the properties of the valence band and the conduction band. Let us analyze the situation step by step:
Step 1: Understanding the Valence Band
- The valence band is the energy band where electrons are normally present at absolute zero.
- At absolute zero, all available energy states in the valence band are fully occupied by electrons.
- Given that the total number of electrons in the outer shell is 4N , all these electrons will occupy the valence band.
- Therefore, the number of energy states in the valence band that are occupied is 4N .
Step 2: Understanding the Conduction Band
- The conduction band is the energy band above the valence band, where electrons can move freely to conduct electricity.
- At absolute zero, no electrons have enough energy to jump from the valence band to the conduction band because there is no thermal energy available.
- However, the number of energy states in the conduction band is equal to the number of electrons in the valence band, as each electron in the valence band corresponds to an empty state in the conduction band. - Therefore, the number of energy states in the conduction band is also 4N , but these states are unoccupied at absolute zero.
Step 3: Conclusion - At absolute zero, the number of energy states in the valence band that are occupied is 4N .
- The number of energy states in the conduction band is 4N , but they are unoccupied.
Thus, the number of energy states of the valence and conduction bands at absolute zero are 4N and 4N , respectively.
Hence, the correct answer is (B) 4N and 4N .