The average velocity of gas is `2.9 xx 10^4 cms^(-1)`.Calculate the RMS velocity

Answer

To calculate the RMS (Root Mean Square) velocity of a gas given its average velocity, we can use the relationship between the two velocities. The formula for RMS velocity (v_rms) in terms of average velocity (v_avg) is:

\[ v_{rms} = \sqrt{\frac{3}{8}} \cdot v_{avg} \]

### Step-by-step Solution:

1. **Identify the given values**:
- Average velocity, \( v_{avg} = 2.9 \times 10^4 \, \text{cm/s} \)

2. **Use the formula for RMS velocity**:
\[ v_{rms} = \sqrt{\frac{3}{8}} \cdot v_{avg} \]

3. **Substitute the value of average velocity into the formula**:
\[ v_{rms} = \sqrt{\frac{3}{8}} \cdot (2.9 \times 10^4) \]

4. **Calculate \(\sqrt{\frac{3}{8}}\)**:
- First, calculate \(\frac{3}{8} = 0.375\).
- Then, find the square root:
\[ \sqrt{0.375} \approx 0.6124 \]

5. **Multiply by the average velocity**:
\[ v_{rms} = 0.6124 \cdot (2.9 \times 10^4) \]

6. **Calculate the final value**:
\[ v_{rms} \approx 0.6124 \cdot 29000 \approx 17761.6 \, \text{cm/s} \]

7. **Final Result**:
\[ v_{rms} \approx 1.776 \times 10^4 \, \text{cm/s} \]

### Final Answer:
The RMS velocity of the gas is approximately \( 1.776 \times 10^4 \, \text{cm/s} \).