In a mixture of nitrogen and helium kept at room temperarture. As compared to a helium molecule nitrogen molecule hits the wall

Options

A. With greater average speed
B. with smaller average speed
C. with greater average kinetic energy
D. with smaller average kinetic energy

Answer

To solve the question regarding the behavior of nitrogen and helium molecules in a mixture at room temperature, we need to analyze the kinetic theory of gases and the properties of these two gases.

### Step-by-Step Solution:

1. **Understanding Kinetic Theory of Gases:**
- According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. Therefore, at room temperature, both nitrogen (N₂) and helium (He) will have the same average kinetic energy.

2. **Molecular Mass Consideration:**
- The molecular mass of helium (He) is approximately 4 g/mol, while the molecular mass of nitrogen (N₂) is approximately 28 g/mol. This difference in molecular mass will affect the speed of the molecules.

3. **Relationship Between Speed and Mass:**
- The root mean square speed (v_rms) of gas molecules can be expressed as:
\[ v_{rms} = \sqrt{\frac{3kT}{m}} \]
where \( k \) is the Boltzmann constant, \( T \) is the absolute temperature, and \( m \) is the mass of the gas molecule.
- Since nitrogen has a greater molecular mass than helium, the \( v_{rms} \) for helium will be higher than that for nitrogen.

4. **Comparing Molecular Speeds:**
- Since helium molecules are lighter, they move faster than nitrogen molecules at the same temperature. Therefore, the average speed of helium molecules will be greater than that of nitrogen molecules.

5. **Impact on Wall Collisions:**
- When considering the collisions with the wall, the frequency and force of the collisions depend on the speed of the molecules. Helium molecules, moving faster, will hit the walls more frequently and with greater momentum compared to nitrogen molecules.

6. **Conclusion:**
- As a result, in a mixture of nitrogen and helium at room temperature, a helium molecule will hit the wall more frequently and with greater speed than a nitrogen molecule.

### Final Answer:
In a mixture of nitrogen and helium kept at room temperature, as compared to a helium molecule, a nitrogen molecule hits the wall less frequently and with lower speed.