The SI unit of electron mobility is :

Options

A. ` m^(2) V^(-1) s^(-1)`
B. ` m^(2) Vs^(-1)`
C. ` m^(-2) V^(-1)s^(-1)`
D. ` m^(-1) V^(-1) s^(-1)`

Answer

To find the SI unit of electron mobility, we can follow these steps:

### Step 1: Understand the Definition of Mobility
Mobility (μ) is defined as the ratio of the drift velocity (Vd) of charge carriers (like electrons) to the electric field (E) applied. The formula is given by:

\[ \mu = \frac{V_d}{E} \]

### Step 2: Identify the Units of Drift Velocity
The drift velocity (Vd) is a measure of how fast the electrons are moving through a conductor. The SI unit of velocity is:

\[ \text{Unit of } V_d = \text{meters per second (m/s)} \]

### Step 3: Identify the Units of Electric Field
The electric field (E) is defined as the force per unit charge. The SI unit of electric field is:

\[ \text{Unit of } E = \text{volts per meter (V/m)} \]

### Step 4: Substitute the Units into the Mobility Formula
Now, substituting the units of Vd and E into the formula for mobility:

\[ \mu = \frac{\text{m/s}}{\text{V/m}} \]

### Step 5: Simplify the Units
To simplify the units, we can rewrite the division:

\[ \mu = \frac{\text{m/s}}{\text{V/m}} = \frac{\text{m}}{\text{s}} \times \frac{\text{m}}{\text{V}} = \frac{\text{m}^2}{\text{V} \cdot \text{s}} \]

### Step 6: Finalize the SI Unit of Electron Mobility
Thus, the SI unit of electron mobility can be expressed as:

\[ \mu = \text{m}^2 \cdot \text{V}^{-1} \cdot \text{s}^{-1} \]

### Conclusion
The SI unit of electron mobility is \( \text{m}^2 \cdot \text{V}^{-1} \cdot \text{s}^{-1} \).

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