If the velocities of three gas molecules are `sqrt(7)`, 4 and 5 m/s, then there `V_(rms)` ( in m/s) will be

Options

A. 4
B. `4/(sqrt(3))`
C. `(2-sqrt(7))/3`
D. `4sqrt(3)`

Explanation

To find the root mean square velocity (V_rms) of the gas molecules, we can follow these steps:

### Step 1: Identify the velocities of the gas molecules
The velocities given are:
- \( v_1 = \sqrt{7} \) m/s
- \( v_2 = 4 \) m/s
- \( v_3 = 5 \) m/s

### Step 2: Square each velocity
Now, we will square each of the velocities:
- \( v_1^2 = (\sqrt{7})^2 = 7 \)
- \( v_2^2 = 4^2 = 16 \)
- \( v_3^2 = 5^2 = 25 \)

### Step 3: Calculate the mean of the squared velocities
Next, we will find the mean of these squared velocities:
\[ \text{Mean} = \frac{v_1^2 + v_2^2 + v_3^2}{3} = \frac{7 + 16 + 25}{3} \]
Calculating the sum:
\[ 7 + 16 + 25 = 48 \]
Now, divide by 3:
\[ \text{Mean} = \frac{48}{3} = 16 \]

### Step 4: Take the square root of the mean
Finally, we take the square root of the mean to find V_rms:
\[ V_{rms} = \sqrt{16} = 4 \text{ m/s} \]

### Final Answer
Thus, the root mean square velocity \( V_{rms} \) is \( 4 \) m/s.

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