The velocity of three molecules, are `2 km s^(-1), 4 km s^(-1), 6 km s^(-1)`. Find
mean square velocity.

Answer

To find the mean square velocity of the three molecules with velocities \( V_1 = 2 \, \text{km/s} \), \( V_2 = 4 \, \text{km/s} \), and \( V_3 = 6 \, \text{km/s} \), we will follow these steps:

### Step 1: Square the velocities
First, we need to square each of the velocities:
- \( V_1^2 = (2 \, \text{km/s})^2 = 4 \, \text{km}^2/\text{s}^2 \)
- \( V_2^2 = (4 \, \text{km/s})^2 = 16 \, \text{km}^2/\text{s}^2 \)
- \( V_3^2 = (6 \, \text{km/s})^2 = 36 \, \text{km}^2/\text{s}^2 \)

### Step 2: Sum the squared velocities
Next, we add these squared values together:
\[ V_1^2 + V_2^2 + V_3^2 = 4 + 16 + 36 = 56 \, \text{km}^2/\text{s}^2 \]

### Step 3: Divide by the number of molecules
Now, we divide the sum of the squared velocities by the number of molecules (which is 3):
\[ \text{Mean Square Velocity} = \frac{V_1^2 + V_2^2 + V_3^2}{n} = \frac{56 \, \text{km}^2/\text{s}^2}{3} = \frac{56}{3} \, \text{km}^2/\text{s}^2 \approx 18.67 \, \text{km}^2/\text{s}^2 \]

### Final Result
Thus, the mean square velocity of the three molecules is approximately:
\[ \text{Mean Square Velocity} \approx 18.67 \, \text{km}^2/\text{s}^2 \]

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