What will be conductivity of pure silicon crystal at 300 K temperature .If electron hole pairs per `cm^(3)` is 2 x `10^(10)` at this temperature ,µe=1350 `cm^(2)` /volt-sec and ,µh=480 `cm^(2)` /volt-sec

Explanation

To find the conductivity of pure silicon crystal at 300 K, we can use the formula for conductivity (σ):

\[ \sigma = n_i e (\mu_h + \mu_e) \]

Where:
- \( n_i \) = number of electron-hole pairs per cm³
- \( e \) = charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs)
- \( \mu_h \) = mobility of holes
- \( \mu_e \) = mobility of electrons

### Step-by-Step Solution:

1. **Identify the given values**:
- \( n_i = 2 \times 10^{10} \, \text{cm}^{-3} \)
- \( \mu_e = 1350 \, \text{cm}^2/\text{V·s} \)
- \( \mu_h = 480 \, \text{cm}^2/\text{V·s} \)
- \( e = 1.6 \times 10^{-19} \, \text{C} \)

2. **Substitute the values into the conductivity formula**:
\[ \sigma = n_i e (\mu_h + \mu_e) \]
\[ \sigma = (2 \times 10^{10}) \times (1.6 \times 10^{-19}) \times (480 + 1350) \]

3. **Calculate the sum of mobilities**:
\[ \mu_h + \mu_e = 480 + 1350 = 1830 \, \text{cm}^2/\text{V·s} \]

4. **Substitute the sum back into the equation**:
\[ \sigma = (2 \times 10^{10}) \times (1.6 \times 10^{-19}) \times (1830) \]

5. **Calculate the product**:
\[ \sigma = (2 \times 1.6 \times 1830) \times 10^{10} \times 10^{-19} \]
\[ = (5.856) \times 10^{-9} \, \text{mho/cm} \]

6. **Final result**:
\[ \sigma = 5.856 \times 10^{-6} \, \text{mho/cm} \]

### Final Answer:
The conductivity of pure silicon crystal at 300 K is \( 5.856 \times 10^{-6} \, \text{mho/cm} \).