The root mean square speed at NTP for the gases `CH_4,H_2,He and F_2` are in the order

Options

A. `CH_4ltH_2ltHeltF_2`
B. `H_2ltHeltCH_4ltF_2`
C. `H_2ltHeltF_2ltCH_4`
D. `F_2ltCH_4ltHeltH_2`

Answer

To determine the root mean square (RMS) speed of the gases CH₄, H₂, He, and F₂ at Normal Temperature and Pressure (NTP), we will follow these steps:

### Step 1: Understand the Formula for RMS Speed
The formula for the root mean square speed (Vrms) of a gas is given by:

\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]

Where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( M \) is the molar mass of the gas in kg/mol.

### Step 2: Identify the Molar Masses of the Gases
Next, we need to find the molar masses of the gases involved:

- **CH₄ (Methane)**: Molar mass = 12 (C) + 4 (H) = 16 g/mol
- **H₂ (Hydrogen)**: Molar mass = 2 g/mol
- **He (Helium)**: Molar mass = 4 g/mol
- **F₂ (Fluorine)**: Molar mass = 19 (F) + 19 (F) = 38 g/mol

### Step 3: Compare the Molar Masses
Now, we can compare the molar masses to determine their order:

- H₂ = 2 g/mol
- He = 4 g/mol
- CH₄ = 16 g/mol
- F₂ = 38 g/mol

### Step 4: Determine the Order of RMS Speed
Since the RMS speed is inversely proportional to the square root of the molar mass, the gas with the lowest molar mass will have the highest RMS speed. Thus, we can arrange them based on their molar masses:

1. H₂ (2 g/mol) - Highest Vrms
2. He (4 g/mol) - Second highest Vrms
3. CH₄ (16 g/mol) - Third highest Vrms
4. F₂ (38 g/mol) - Lowest Vrms

### Conclusion
The order of root mean square speeds at NTP for the gases CH₄, H₂, He, and F₂ is:

\[ \text{H₂} > \text{He} > \text{CH₄} > \text{F₂} \]

### Final Answer
Thus, the answer is option 4: H₂, He, CH₄, F₂.

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