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 (RMS) velocity of the three gas molecules with velocities \( \sqrt{7} \), 4, and 5 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Square the Velocities**:
We start by squaring each of the given velocities.
\[ v_1^2 = (\sqrt{7})^2 = 7 \]
\[ v_2^2 = 4^2 = 16 \]
\[ v_3^2 = 5^2 = 25 \]

2. **Calculate the Mean of the Squared Velocities**:
Next, we find the mean of these squared values.
\[ \text{Mean} = \frac{v_1^2 + v_2^2 + v_3^2}{3} = \frac{7 + 16 + 25}{3} \]

3. **Sum the Squared Values**:
Now, we add the squared values together.
\[ 7 + 16 = 23 \]
\[ 23 + 25 = 48 \]

4. **Divide by the Number of Molecules**:
We divide the sum by the number of molecules (which is 3).
\[ \text{Mean} = \frac{48}{3} = 16 \]

5. **Take the Square Root of the Mean**:
Finally, we take the square root of the mean to find the RMS velocity.
\[ V_{rms} = \sqrt{16} = 4 \, \text{m/s} \]

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