In a `p-n` junction the depletion region is `400 nm` wide and electric field of `5 xx 10^(5) Vm^(-1)` exists in it. The minimum energy of a conduction electron, which can diffuse from n-side to the p-side is.

Options

A. `4 eV`
B. `5 eV`
C. `0.4 eV`
D. `0.2 eV`

Explanation

To find the minimum energy of a conduction electron that can diffuse from the n-side to the p-side of a p-n junction, we can use the relationship between electric field, potential difference, and energy. The energy gained by the electron as it moves across the depletion region can be calculated using the formula:

\[ E = V \cdot q \]

Where:
- \( E \) is the energy gained by the electron (in joules),
- \( V \) is the potential difference (in volts),
- \( q \) is the charge of the electron (approximately \( 1.6 \times 10^{-19} \) coulombs).

### Step 1: Calculate the Potential Difference (V)
The potential difference across the depletion region can be calculated using the electric field (E) and the width of the depletion region (d):

\[ V = E \cdot d \]

Given:
- Electric field \( E = 5 \times 10^5 \, \text{V/m} \)
- Width of depletion region \( d = 400 \, \text{nm} = 400 \times 10^{-9} \, \text{m} \)

Substituting the values:

\[ V = (5 \times 10^5) \cdot (400 \times 10^{-9}) \]

### Step 2: Calculate the Potential Difference
Now, performing the calculation:

\[ V = 5 \times 10^5 \times 400 \times 10^{-9} \]

\[ V = 5 \times 400 \times 10^{-4} \]

\[ V = 2000 \times 10^{-4} \]

\[ V = 0.2 \, \text{V} \]

### Step 3: Calculate the Energy (E)
Now we can calculate the energy \( E \):

\[ E = V \cdot q \]

Substituting the values:

\[ E = 0.2 \, \text{V} \cdot (1.6 \times 10^{-19} \, \text{C}) \]

### Step 4: Calculate the Energy
Calculating the energy:

\[ E = 0.2 \cdot 1.6 \times 10^{-19} \]

\[ E = 0.32 \times 10^{-19} \, \text{J} \]

### Step 5: Convert Energy to Electron Volts
To convert joules to electron volts, we recognize that \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):

\[ E = \frac{0.32 \times 10^{-19}}{1.6 \times 10^{-19}} \]

\[ E = 0.2 \, \text{eV} \]

### Final Answer
The minimum energy of a conduction electron that can diffuse from the n-side to the p-side is:

\[ \boxed{0.2 \, \text{eV}} \]