The width of depletion region in p-n junction diode is `500 nm` and an intrinsic electric field of `6xx 10^(5) Vm^(-1)` is also found to exist in it. What is the kinetic energy which a conduction electron must have in order to diffuse from the n-side to p-side?

Options

A. 0.30 V
B. 0.40 V
C. 3 V
D. 4 V

Answer

To solve the problem, we need to find the kinetic energy that a conduction electron must have in order to diffuse from the n-side to the p-side of a p-n junction diode. The given parameters are the width of the depletion region (D) and the intrinsic electric field (E).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Width of the depletion region (D) = 500 nm = \(500 \times 10^{-9}\) m
- Intrinsic electric field (E) = \(6 \times 10^{5}\) V/m

2. **Calculate the Potential Barrier (V):**
The potential barrier across the depletion region can be calculated using the formula:
\[ V = E \times D \]
Substituting the values:
\[ V = (6 \times 10^{5} \, \text{V/m}) \times (500 \times 10^{-9} \, \text{m}) \]

3. **Perform the Calculation:**
\[ V = 6 \times 10^{5} \times 500 \times 10^{-9} \]
\[ V = 6 \times 500 \times 10^{-4} \]
\[ V = 3000 \times 10^{-4} = 0.30 \, \text{V} \]

4. **Determine the Kinetic Energy (K.E.):**
The kinetic energy required for the conduction electron to overcome the potential barrier is given by:
\[ K.E. = e \times V \]
where \(e\) is the charge of an electron, approximately \(1.6 \times 10^{-19}\) C. Now substituting the values:
\[ K.E. = (1.6 \times 10^{-19} \, \text{C}) \times (0.30 \, \text{V}) \]

5. **Calculate the Kinetic Energy:**
\[ K.E. = 1.6 \times 10^{-19} \times 0.30 \]
\[ K.E. = 0.48 \times 10^{-19} \, \text{J} \]

6. **Convert Kinetic Energy to Electron Volts (eV):**
Since \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ K.E. = \frac{0.48 \times 10^{-19}}{1.6 \times 10^{-19}} \, \text{eV} \]
\[ K.E. = 0.30 \, \text{eV} \]

### Final Answer:
The kinetic energy required for a conduction electron to diffuse from the n-side to the p-side of the p-n junction diode is **0.30 eV**.