What will be conductance of pure sillicon crystal at 300 K temp? if electron hole pairs per `cm^(3)` is `1.072xx10^(10)` at this temp. `mu_(n)=1350 cm^(2)//"volt"` sec and `mu_(p)=480 cm^(2)//"volt"` sec-

Options

A. `3.14xx10^(-6) "mho/cm"`
B. `3xx10^(6) "mho/cm"`
C. `10^(-6) "mho/cm"`
D. `10^(6) "mho/cm"`

Answer

To find the conductance of pure silicon crystal at 300 K, we can follow these steps:

### Step 1: Identify the given values
- Electron-hole pairs per cm³, \( n = 1.072 \times 10^{10} \) cm⁻³
- Electron mobility, \( \mu_n = 1350 \) cm²/V·s
- Hole mobility, \( \mu_p = 480 \) cm²/V·s
- Charge of an electron, \( e = 1.6 \times 10^{-19} \) C

### Step 2: Write the formula for conductance
The conductance \( K \) of a semiconductor can be calculated using the formula:
\[ K = n \cdot e \cdot (\mu_n + \mu_p) \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ K = (1.072 \times 10^{10}) \cdot (1.6 \times 10^{-19}) \cdot (1350 + 480) \]

### Step 4: Calculate the sum of mobilities
First, calculate the sum of mobilities:
\[ \mu_n + \mu_p = 1350 + 480 = 1830 \text{ cm}^2/\text{V·s} \]

### Step 5: Substitute the sum back into the equation
Now substitute this back into the equation for conductance:
\[ K = (1.072 \times 10^{10}) \cdot (1.6 \times 10^{-19}) \cdot 1830 \]

### Step 6: Perform the multiplication
Calculating the product step-by-step:
1. First, calculate \( (1.072 \times 1.6) = 1.7152 \)
2. Then, multiply by \( 10^{10} \) and \( 10^{-19} \):
\[ 1.7152 \times 10^{10 - 19} = 1.7152 \times 10^{-9} \]
3. Now multiply by \( 1830 \):
\[ K = 1.7152 \times 1830 \times 10^{-9} \]
- Calculate \( 1.7152 \times 1830 = 3148.656 \)

### Step 7: Finalize the conductance value
Thus, we have:
\[ K = 3148.656 \times 10^{-9} \text{ S/cm} = 3.148656 \times 10^{-6} \text{ S/cm} \]
Rounding this to two decimal places gives:
\[ K \approx 3.14 \times 10^{-6} \text{ S/cm} \]

### Answer
The conductance of pure silicon crystal at 300 K is approximately \( 3.14 \times 10^{-6} \) S/cm.

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