A block of pure silicon at `300 K` has a length of `10 cm` and an area of `1.0 cm^(2)`. A battery of emf `2V` is connected across it. The mobility of electron is `0.14 m^(2) v^(-1) S^(-1)` and their number density is `1.5 xx 10^(16) m^(-3)`. The mobility of holes is `0.05 m^(2) v^(-1) S^(-1)`.
The electron current is

Options

A. `6.72 xx 10^(-4) A`
B. `6.72 xx 10^(-5) A`
C. `6.72 xx 10^(-6) A`
D. `6.72 xx 10^(-7) A`

Explanation

To find the electron current in a block of pure silicon at 300 K, we can follow these steps:

### Step 1: Calculate the Electric Field (E)
The electric field (E) across the silicon block can be calculated using the formula:
\[ E = \frac{V}{D} \]
Where:
- \( V \) is the voltage (2 V)
- \( D \) is the length of the silicon block (10 cm = 0.1 m)

Substituting the values:
\[ E = \frac{2 \, \text{V}}{0.1 \, \text{m}} = 20 \, \text{V/m} \]

### Step 2: Calculate the Electron Drift Velocity (vE)
The drift velocity of electrons can be calculated using the formula:
\[ v_E = \mu_E \cdot E \]
Where:
- \( \mu_E \) is the mobility of electrons (0.14 m²/V·s)
- \( E \) is the electric field (20 V/m)

Substituting the values:
\[ v_E = 0.14 \, \text{m}^2/\text{V·s} \cdot 20 \, \text{V/m} = 2.8 \, \text{m/s} \]

### Step 3: Calculate the Electron Current (IE)
The electron current can be calculated using the formula:
\[ I_E = n_E \cdot A \cdot e \cdot v_E \]
Where:
- \( n_E \) is the number density of electrons (\( 1.5 \times 10^{16} \, \text{m}^{-3} \))
- \( A \) is the cross-sectional area (1 cm² = \( 1 \times 10^{-4} \, \text{m}^2 \))
- \( e \) is the charge of an electron (\( 1.6 \times 10^{-19} \, \text{C} \))
- \( v_E \) is the drift velocity of electrons (2.8 m/s)

Substituting the values:
\[ I_E = (1.5 \times 10^{16} \, \text{m}^{-3}) \cdot (1 \times 10^{-4} \, \text{m}^2) \cdot (1.6 \times 10^{-19} \, \text{C}) \cdot (2.8 \, \text{m/s}) \]

Calculating this:
\[ I_E = 1.5 \times 10^{16} \cdot 1 \times 10^{-4} \cdot 1.6 \times 10^{-19} \cdot 2.8 \]
\[ I_E = 6.72 \times 10^{-7} \, \text{A} \]

### Final Answer
The electron current \( I_E \) is approximately:
\[ I_E \approx 6.72 \times 10^{-7} \, \text{A} \]

---