In sample of pure silicon `10^(13) "atom"//cm^(3)` is mixed of phosphorus. If all doner atoms are active then what will be resistivity at `20^(@)C` if mobility of electron is `1200 cm^(2)//"Volt"` sec :-

Options

A. `0.5209` ohm cm
B. `5.209` ohm cm
C. `52.09` ohm cm
D. `520.9` ohm cm

Explanation

To find the resistivity of the silicon sample mixed with phosphorus, we can follow these steps:

### Step 1: Understand the given data
- The concentration of phosphorus (donor atoms) in silicon: \( n = 10^{13} \, \text{atoms/cm}^3 \)
- Mobility of electrons: \( \mu = 1200 \, \text{cm}^2/\text{V} \cdot \text{s} \)
- Charge of an electron: \( e = 1.6 \times 10^{-19} \, \text{C} \)

### Step 2: Use the formula for resistivity
The resistivity \( \rho \) of a semiconductor can be calculated using the formula:
\[ \rho = \frac{1}{n \cdot e \cdot \mu} \]
where:
- \( n \) is the number of charge carriers (electrons in this case),
- \( e \) is the charge of an electron,
- \( \mu \) is the mobility of the charge carriers.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ \rho = \frac{1}{(10^{13} \, \text{cm}^{-3}) \cdot (1.6 \times 10^{-19} \, \text{C}) \cdot (1200 \, \text{cm}^2/\text{V} \cdot \text{s})} \]

### Step 4: Calculate the denominator
Calculating the denominator:
\[ n \cdot e \cdot \mu = 10^{13} \cdot 1.6 \times 10^{-19} \cdot 1200 \]
Calculating step-by-step:
1. \( 10^{13} \cdot 1.6 = 1.6 \times 10^{13} \)
2. \( 1.6 \times 10^{13} \cdot 1200 = 1.92 \times 10^{16} \)

### Step 5: Calculate resistivity
Now substituting back into the resistivity formula:
\[ \rho = \frac{1}{1.92 \times 10^{16}} \approx 5.208 \times 10^{-17} \, \Omega \cdot \text{cm} \]

### Step 6: Final calculation
To express this in a more standard form:
\[ \rho \approx 5.208 \times 10^{-2} \, \Omega \cdot \text{cm} = 0.05208 \, \Omega \cdot \text{cm} \]

### Step 7: Conclusion
Thus, the resistivity of the sample is approximately \( 0.05208 \, \Omega \cdot \text{cm} \) or \( 520.8 \, \Omega \cdot \text{cm} \).