The velocities of 4 molecules are 4m/s, 5m/s, 6m/s and 2m/s respectively. What is their rms velocity?

Options

A. `5/2m//s`
B. `7/2m//s`
C. `9/2m//s`
D. `3/2m//s`

Explanation

To find the root mean square (rms) velocity of the given molecules, we will follow these steps:

### Step 1: List the velocities
The velocities of the molecules are given as:
- \( v_1 = 4 \, \text{m/s} \)
- \( v_2 = 5 \, \text{m/s} \)
- \( v_3 = 6 \, \text{m/s} \)
- \( v_4 = 2 \, \text{m/s} \)

### Step 2: Calculate the squares of the velocities
Next, we will calculate the square of each velocity:
- \( v_1^2 = 4^2 = 16 \)
- \( v_2^2 = 5^2 = 25 \)
- \( v_3^2 = 6^2 = 36 \)
- \( v_4^2 = 2^2 = 4 \)

### Step 3: Sum the squares of the velocities
Now, we add these squared values together:
\[ v_1^2 + v_2^2 + v_3^2 + v_4^2 = 16 + 25 + 36 + 4 = 81 \]

### Step 4: Calculate the mean of the squares
To find the mean of the squares, we divide the sum by the number of molecules (which is 4):
\[ \text{Mean} = \frac{81}{4} = 20.25 \]

### Step 5: Take the square root of the mean
Finally, we take the square root of the mean to find the rms velocity:
\[ v_{\text{rms}} = \sqrt{20.25} = 4.5 \, \text{m/s} \]

### Final Answer
The root mean square velocity of the molecules is \( 4.5 \, \text{m/s} \).

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