Consider a collision between an argon molecule and a nitrogn molecule in a mixture of argon and nitrogen kept at room temperature. Which of the following are possible?

Options

A. The kinetic energies of both the molecules increase.
B. The kinetic energies of both the molecules decrease.
C. The kinetic energy of the argon molecule increases and that of the nitrogen molecule decrease.
D. The kinetic energy of the nitrogen molecules increase and that of the argon molecule decrease.

Explanation

To solve the problem regarding the collision between an argon molecule and a nitrogen molecule in a mixture, we will analyze the possible outcomes based on the principles of kinetic theory of gases (KTG).

### Step-by-Step Solution:

1. **Understanding Elastic Collisions**:
The first step is to recognize that according to the kinetic theory of gases, the collisions between gas molecules are considered elastic. This means that during the collision, the total kinetic energy of the system is conserved.

**Hint**: Recall that in elastic collisions, the total kinetic energy before and after the collision remains the same.

2. **Kinetic Energy Conservation**:
Since the collisions are elastic, the change in kinetic energy for the entire system is zero. This implies that if one molecule gains kinetic energy, another must lose an equivalent amount of kinetic energy to keep the total energy constant.

**Hint**: Think about how energy can be transferred between two colliding objects while keeping the total energy constant.

3. **Analyzing the Options**:
- **Option A**: The kinetic energy of both molecules increases.
- This is not possible because if both molecules increase their kinetic energy, the total kinetic energy would increase, violating the conservation principle.

- **Option B**: The kinetic energy of both molecules decreases.
- This is also not possible for the same reason as option A; if both decrease, the total kinetic energy would decrease, which is not allowed in elastic collisions.

- **Option C**: The kinetic energy of the argon molecule increases and that of the nitrogen molecule decreases.
- This is possible because the increase in kinetic energy of one molecule can be balanced by the decrease in the other, maintaining the total kinetic energy.

- **Option D**: The kinetic energy of the nitrogen molecule increases and that of the argon molecule decreases.
- This is also possible for the same reason as option C; the energy lost by one molecule can be gained by the other.

4. **Conclusion**:
Based on the analysis, options C and D are valid outcomes of the collision between the argon and nitrogen molecules. The kinetic energy can be transferred between the two molecules while conserving the total kinetic energy.

### Final Answer:
The possible outcomes of the collision are:
- The kinetic energy of the argon molecule increases and that of the nitrogen molecule decreases (Option C).
- The kinetic energy of the nitrogen molecule increases and that of the argon molecule decreases (Option D).