`6 xx 10^(22)` gas molecules each of mass `10^(-24) kg` are taken in a vessel of 10 litre. What is the pressure exerted by gas molecules? The root mean square speed of gas molecules is 100 m/s.

Options

A. 20 Pa
B. `2 xx 10^(4)` Pa
C. `2 xx 10^(5)` Pa
D. `2 xx 10^(7)` Pa

Explanation

To find the pressure exerted by the gas molecules, we can use the formula for pressure in terms of the root mean square speed of gas molecules. The formula is given by:

\[ P = \frac{1}{3} \frac{n \cdot m \cdot C^2}{V} \]

where:
- \( P \) = pressure
- \( n \) = number of molecules
- \( m \) = mass of each molecule
- \( C \) = root mean square speed
- \( V \) = volume of the gas

### Step-by-Step Solution

1. **Identify the given values**:
- Number of molecules, \( n = 6 \times 10^{22} \)
- Mass of each molecule, \( m = 10^{-24} \, \text{kg} \)
- Root mean square speed, \( C = 100 \, \text{m/s} \)
- Volume of the vessel, \( V = 10 \, \text{liters} = 10 \times 10^{-3} \, \text{m}^3 \)

2. **Convert volume from liters to cubic meters**:
- \( V = 10 \, \text{liters} = 10 \times 10^{-3} \, \text{m}^3 = 0.01 \, \text{m}^3 \)

3. **Substitute the values into the pressure formula**:
\[ P = \frac{1}{3} \cdot \frac{(6 \times 10^{22}) \cdot (10^{-24}) \cdot (100)^2}{0.01} \]

4. **Calculate \( C^2 \)**:
\[ C^2 = (100)^2 = 10000 \]

5. **Now substitute \( C^2 \) back into the equation**:
\[ P = \frac{1}{3} \cdot \frac{(6 \times 10^{22}) \cdot (10^{-24}) \cdot (10000)}{0.01} \]

6. **Calculate the numerator**:
\[ (6 \times 10^{22}) \cdot (10^{-24}) \cdot (10000) = 6 \times 10^{22} \cdot 10^{-24} \cdot 10^4 = 6 \times 10^{22 - 24 + 4} = 6 \times 10^{2} = 600 \]

7. **Now substitute back into the pressure equation**:
\[ P = \frac{1}{3} \cdot \frac{600}{0.01} \]

8. **Calculate \( \frac{600}{0.01} \)**:
\[ \frac{600}{0.01} = 60000 \]

9. **Now calculate the pressure**:
\[ P = \frac{1}{3} \cdot 60000 = 20000 \, \text{Pa} \]

10. **Final result**:
\[ P = 2 \times 10^{4} \, \text{Pa} \]

### Conclusion
The pressure exerted by the gas molecules is \( 2 \times 10^{4} \, \text{Pa} \).