Suppose a gas sample in all have `6xx10^(23)` molecules Each `1//3rd` of the molecules have rms speed `10^(4) cm//sec, 2 xx 10^(4) cm//sec` and `3 xx 10^(4) cm//sec` Calculate the rms speed of gas molecules in sample .

Explanation

To calculate the root mean square (RMS) speed of the gas molecules in the sample, we will follow these steps:

### Step 1: Identify the number of molecules and their speeds
We have a total of \( 6 \times 10^{23} \) molecules. Each speed category has one-third of the total molecules:
- \( N_1 = N_2 = N_3 = \frac{6 \times 10^{23}}{3} = 2 \times 10^{23} \)

The speeds are:
- \( U_1 = 10^4 \, \text{cm/s} \)
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