The SI unit of electron mobility is :

Options

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

Explanation

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

### Step 1: Understand the definition of electron mobility
Electron mobility (μ) is defined as the ratio of the drift velocity (v_d) of electrons to the electric field (E) applied. Mathematically, this can be expressed as:
\[ \mu = \frac{v_d}{E} \]

### Step 2: Identify the units of drift velocity
Drift velocity is a type of velocity, which has the SI unit of meters per second (m/s). Therefore, we can write:
\[ [v_d] = \text{m/s} \]

### Step 3: Identify the units of electric field
The electric field (E) is defined as the force per unit charge. Its SI unit is volts per meter (V/m). Thus, we can express the unit of electric field as:
\[ [E] = \text{V/m} \]

### Step 4: Substitute the units into the equation for mobility
Now, substituting the units of drift velocity and electric field into the equation for electron mobility gives us:
\[ [\mu] = \frac{[v_d]}{[E]} = \frac{\text{m/s}}{\text{V/m}} \]

### Step 5: Simplify the units
To simplify this expression, we can multiply by the reciprocal of the electric field unit:
\[ [\mu] = \frac{\text{m/s}}{\text{V/m}} = \text{m/s} \cdot \frac{m}{\text{V}} = \frac{\text{m}^2}{\text{s} \cdot \text{V}} \]

### Step 6: Final unit of electron mobility
Thus, the SI unit of electron mobility is:
\[ \text{m}^2/\text{s} \cdot \text{V} \]
or equivalently:
\[ \text{m}^2 \cdot \text{s}^{-1} \cdot \text{V}^{-1} \]

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

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