Choose the correct arrangement, where the symbols have their usual meanings

Options

A. `vecu gt u_(p) gt u_(rms)`
B. `u_(rms) gt vecu gt u_(p)`
C. `u_(p) gt vecu gt u_(rms)`
D. `u_(p) gt u_(rms) gt vecu`

Answer

To solve the question regarding the correct arrangement of the speeds (Root Mean Square Speed, Average Speed, and Most Probable Speed), we need to analyze the formulas for each type of speed and compare their values.

### Step-by-step Solution:

1. **Identify the Formulas**:
- Root Mean Square Speed (RMS): \( v_{rms} = \sqrt{\frac{3RT}{M}} \)
- Average Speed: \( v_{avg} = \sqrt{\frac{8RT}{\pi M}} \)
- Most Probable Speed (MP): \( v_{mp} = \sqrt{\frac{2RT}{M}} \)

2. **Compare the Speeds**:
To compare these speeds, we can look at the coefficients under the square root for a fixed gas (where \( R \) and \( T \) are constants, and \( M \) is the molar mass):
- For \( v_{rms} \), the coefficient is \( \sqrt{3} \).
- For \( v_{avg} \), the coefficient is \( \sqrt{\frac{8}{\pi}} \).
- For \( v_{mp} \), the coefficient is \( \sqrt{2} \).

3. **Calculate the Numerical Values**:
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt{2} \approx 1.414 \)
- \( \sqrt{\frac{8}{\pi}} \approx 1.596 \)

4. **Arrange the Speeds**:
Now we can arrange these values from highest to lowest:
- \( v_{rms} \) (1.732) > \( v_{avg} \) (1.596) > \( v_{mp} \) (1.414)

5. **Final Arrangement**:
The correct arrangement from highest to lowest speed is:
- Root Mean Square Speed (RMS) > Average Speed > Most Probable Speed (MP)

### Conclusion:
The correct option is **B**: RMS > Average > MP.