Assertion: In a mixture of gases at a fixed temperatue, the heavier molecule has the lower average speed.
Reason: Temperature of a gas is a measure of the average kinetic energy of a molecule.

Options

A. If both assertion and reason are true and reason is the correct explanation os assertion.
B. If both assertion and reason are true but reason is not be correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the question, we need to analyze the assertion and reason given:

**Assertion**: In a mixture of gases at a fixed temperature, the heavier molecule has the lower average speed.

**Reason**: Temperature of a gas is a measure of the average kinetic energy of a molecule.

### Step-by-Step Solution:

1. **Understanding Temperature and Kinetic Energy**:
- The temperature of a gas is directly related to the average kinetic energy of its molecules. The formula for the average kinetic energy (KE) of a gas molecule is given by:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

2. **Kinetic Energy and Speed Relationship**:
- The kinetic energy of a single molecule can also be expressed in terms of its mass (m) and speed (v):
\[ KE = \frac{1}{2} mv^2 \]
- From this equation, we can derive that:
\[ v = \sqrt{\frac{2 KE}{m}} \]
- This shows that speed \( v \) is inversely proportional to the square root of the mass \( m \).

3. **Analyzing the Assertion**:
- Since the average kinetic energy is constant for all molecules at a fixed temperature, if we consider two molecules with different masses (where one is heavier), the heavier molecule will have a lower speed because:
\[ v \propto \frac{1}{\sqrt{m}} \]
- Therefore, the assertion that "the heavier molecule has the lower average speed" is true.

4. **Analyzing the Reason**:
- The reason states that "the temperature of a gas is a measure of the average kinetic energy of a molecule." This is also true, as we have established that temperature correlates directly with the average kinetic energy of gas molecules.

5. **Conclusion**:
- Both the assertion and the reason are true, and the reason explains the assertion. Therefore, the final answer is:
- Assertion: True
- Reason: True
- They explain each other.