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 order of root mean square speed (VRMS) at Normal Temperature and Pressure (NTP) for the gases CH₄ (methane), H₂ (hydrogen), He (helium), and F₂ (fluorine), we will follow these steps:

### Step 1: Understand the formula for VRMS
The formula for root mean square speed is given by:
\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]
Where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature (constant at NTP),
- \( M \) is the molar mass of the gas.

### Step 2: Identify the relationship between VRMS and molar mass
From the formula, we can see that VRMS is inversely proportional to the square root of the molar mass (\( M \)):
\[ V_{RMS} \propto \frac{1}{\sqrt{M}} \]
This means that the lower the molar mass, the higher the VRMS.

### Step 3: Determine the molar masses of the gases
Now, we will find the molar masses of the given gases:
- **Hydrogen (H₂)**: 2 g/mol
- **Helium (He)**: 4 g/mol
- **Methane (CH₄)**: 12 (C) + 4 (H) = 16 g/mol
- **Fluorine (F₂)**: 19 (F) × 2 = 38 g/mol

### Step 4: Arrange the gases by increasing molar mass
Now, we can arrange the gases in order of increasing molar mass:
1. H₂: 2 g/mol
2. He: 4 g/mol
3. CH₄: 16 g/mol
4. F₂: 38 g/mol

### Step 5: Determine the order of VRMS
Since VRMS is inversely proportional to the square root of the molar mass, we will reverse the order of the molar masses to find the order of VRMS:
1. H₂ (highest VRMS)
2. He
3. CH₄
4. F₂ (lowest VRMS)

### Conclusion
Thus, the order of root mean square speeds for the gases at NTP is:
\[ \text{H₂} > \text{He} > \text{CH₄} > \text{F₂} \]

### Final Answer
The correct order of root mean square speeds at NTP for the gases CH₄, H₂, He, and F₂ is:
\[ \text{H₂} > \text{He} > \text{CH₄} > \text{F₂} \]