The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the

Options

A. crystal structure
B. variation of the number of charge carriers with temperature
C. type of bonding
D. variation of cattering mechanism with temperature

Answer

To solve the question regarding the difference in the variation of resistance with temperature in metals and semiconductors, we can break down the explanation into clear steps:

### Step-by-Step Solution:

1. **Understanding Resistance in Metals:**
- In metals, as the temperature increases, the atoms in the metal lattice vibrate more vigorously. This increased vibration leads to more frequent collisions between the conduction electrons and the vibrating atoms.
- As a result of these collisions, the resistivity of the metal increases with temperature. Since resistance (R) is directly proportional to resistivity (ρ), we can conclude that the resistance of metals increases with an increase in temperature.

2. **Understanding Resistance in Semiconductors:**
- In semiconductors, the behavior is quite different. When the temperature of a semiconductor increases, more electrons gain enough energy to jump from the valence band to the conduction band, thus increasing the number of charge carriers (electrons and holes).
- This increase in charge carriers more than compensates for any increase in scattering due to temperature. Consequently, the resistivity of the semiconductor decreases with an increase in temperature, leading to a decrease in resistance.

3. **Comparing the Two:**
- In summary, for metals, resistance increases with temperature due to increased scattering and higher resistivity.
- In contrast, for semiconductors, resistance decreases with temperature due to an increase in the number of charge carriers.

4. **Conclusion:**
- The fundamental difference in the variation of resistance with temperature between metals and semiconductors arises due to the difference in the variation of the number of charge carriers with temperature.

5. **Selecting the Correct Option:**
- Based on the analysis, the correct option is that the difference in the variation of resistance with temperature in metals and semiconductors arises essentially due to the difference in the variation of the number of charge carriers with temperature.

### Final Answer:
The correct option is **B**: The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the variation of the number of charge carriers with temperature.