The mobility of free electrons is greater then that of free holes because

Options

A. Carry negative charge
B. Are light
C. Mutually collide less
D. Require low energy to continue their motion

Answer

To solve the question regarding why the mobility of free electrons is greater than that of free holes, we can analyze the options provided and the underlying physics principles.

### Step-by-Step Solution:

**Step 1: Understand Mobility**
- Mobility (\( \mu \)) is defined as the ability of charge carriers (electrons and holes) to move through a semiconductor material when an electric field is applied. It is given by the formula:
\[ \mu = \frac{q \cdot \tau}{m^*} \]
where \( q \) is the charge of the carrier, \( \tau \) is the average time between collisions, and \( m^* \) is the effective mass of the carrier.

**Step 2: Compare the Mass of Electrons and Holes**
- The mass of an electron is approximately \( 9.1 \times 10^{-31} \) kg.
- The mass of a hole (which can be approximated as the mass of a proton) is about \( 1.6 \times 10^{-27} \) kg.
- Since the mass of the hole is significantly greater than that of the electron, we can conclude that electrons are lighter than holes.

**Step 3: Analyze the Implications of Mass on Mobility**
- Since mobility is inversely proportional to mass, lighter particles (like electrons) will have higher mobility compared to heavier particles (like holes).
- This means that electrons can accelerate more easily under an electric field than holes can.

**Step 4: Consider Other Factors**
- Although the other options (like charge, collision frequency, and energy required) may have some relevance, the primary reason for the difference in mobility is the mass of the charge carriers.
- Electrons carry a negative charge, but this does not directly affect their mobility compared to holes; it is their mass that plays a crucial role.

**Step 5: Conclusion**
- Therefore, the correct explanation for why the mobility of free electrons is greater than that of free holes is primarily due to the fact that electrons are much lighter than holes.

### Final Answer:
The mobility of free electrons is greater than that of free holes because electrons are lightweight compared to holes.