In a semiconductor,

Options

A. there are no free electrons at 0K
B. there are no free electorns at any temperature
C. the number of free electrons increases with temperature
D. the number of free electrons is less that in a conductor.

Answer

To solve the question regarding the properties of free electrons in a semiconductor, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Free Electrons at 0 Kelvin**:
- At 0 Kelvin, all thermal motion of particles ceases. This means that electrons in a semiconductor will not have enough energy to break free from their atomic bonds. Therefore, there are no free electrons available for conduction at 0 Kelvin.
- **Conclusion**: Option 1 is correct.

2. **Free Electrons at Any Temperature**:
- The statement claims that there are no free electrons at any temperature. However, at temperatures above 0 Kelvin, thermal energy allows some electrons to gain enough energy to break free from their bonds, creating electron-hole pairs. Thus, there will always be some free electrons present in a semiconductor at temperatures above absolute zero.
- **Conclusion**: Option 2 is incorrect.

3. **Effect of Temperature on Free Electrons**:
- As the temperature increases, the thermal energy provided to the semiconductor increases, causing more covalent bonds to break. This results in the generation of more free electrons and holes. Therefore, the number of free electrons increases with temperature.
- **Conclusion**: Option 3 is correct.

4. **Comparison with Conductors**:
- In conductors, the energy gap between the valence band and conduction band is very small or nonexistent, allowing a large number of free electrons to participate in conduction. In semiconductors, the energy gap is larger, resulting in fewer free electrons compared to conductors.
- **Conclusion**: Option 4 is correct.

### Final Summary:
- **Correct Options**:
- Option 1: Correct (No free electrons at 0 Kelvin)
- Option 2: Incorrect (There are free electrons at temperatures above 0 Kelvin)
- Option 3: Correct (Number of free electrons increases with temperature)
- Option 4: Correct (Number of free electrons is less than in a conductor)