The following data are for intrinsic germanium at `300 K. n_(i) = 2.4 xx 10^(19)//m^(3), mu_(e) = 0.39 m^(2)//Vs, mu_(h) = 0.19 m^(2)//Vs`. Calculate the coductivity of intrinsic germanium.

Options

A. `4.3 Sm^(-1)`
B. `1.21 Sm^(-1)`
C. `2.22 Sm^(-1)`
D. `4.22 Sm^(-1)`

Explanation

To calculate the conductivity of intrinsic germanium at 300 K, we can follow these steps:

### Step 1: Understand the Formula for Conductivity
The conductivity (\( \sigma \)) of a semiconductor can be expressed as the sum of the contributions from electrons and holes:
\[ \sigma = \sigma_e + \sigma_h \]
where:
- \( \sigma_e = n_e \cdot \mu_e \cdot e \) (conductivity due to electrons)
- \( \sigma_h = n_h \cdot \mu_h \cdot e \) (conductivity due to holes)

### Step 2: Identify the Parameters
For intrinsic germanium, the concentration of electrons (\( n_e \)) is equal to the concentration of holes (\( n_h \)), which is equal to the intrinsic carrier concentration (\( n_i \)):
\[ n_e = n_h = n_i = 2.4 \times 10^{19} \, \text{m}^{-3} \]
The mobilities are given as:
- \( \mu_e = 0.39 \, \text{m}^2/\text{Vs} \)
- \( \mu_h = 0.19 \, \text{m}^2/\text{Vs} \)

The charge of an electron (or hole) is:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

### Step 3: Substitute Values into the Formula
Now we can substitute the values into the formula for conductivity:
\[ \sigma = n_i \cdot \mu_e \cdot e + n_i \cdot \mu_h \cdot e \]
Factoring out \( n_i \cdot e \):
\[ \sigma = n_i \cdot e \cdot (\mu_e + \mu_h) \]

### Step 4: Calculate the Total Mobility
Calculate the total mobility:
\[ \mu_e + \mu_h = 0.39 + 0.19 = 0.58 \, \text{m}^2/\text{Vs} \]

### Step 5: Substitute All Values into the Conductivity Formula
Now substitute all values into the conductivity formula:
\[ \sigma = (2.4 \times 10^{19}) \cdot (1.6 \times 10^{-19}) \cdot (0.58) \]

### Step 6: Perform the Calculation
Calculating the above expression:
\[ \sigma = 2.4 \times 1.6 \times 0.58 \]
Calculating step by step:
1. \( 2.4 \times 1.6 = 3.84 \)
2. \( 3.84 \times 0.58 = 2.2272 \)

Thus, the conductivity is:
\[ \sigma \approx 2.22 \, \text{S/m} \]

### Final Answer
The conductivity of intrinsic germanium at 300 K is approximately:
\[ \sigma \approx 2.22 \, \text{S/m} \]