Assertion : The work function of a metal is different at different temperature .
Reason : The increases in the temperature of metals decreases the work function of metal.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect
D. If assertion is incorrect but reason is correct.

Answer

To analyze the assertion and reason provided in the question, we will break down the concepts of work function, temperature, and their relationship step by step.

### Step-by-Step Solution:

1. **Understanding Work Function**:
- The work function (Φ) of a metal is defined as the minimum energy required to remove an electron from the surface of the metal. It is a characteristic property of each metal.

2. **Effect of Temperature on Electrons**:
- As the temperature of a metal increases, the kinetic energy of the electrons within the metal also increases. This is due to the thermal agitation of the atoms in the metal, which causes the electrons to gain energy.

3. **Relationship Between Kinetic Energy and Work Function**:
- With increased kinetic energy, electrons are more likely to overcome the work function barrier. This means that less energy is required to remove an electron from the metal's surface when the temperature is higher.

4. **Conclusion on Work Function and Temperature**:
- As the temperature increases, the work function effectively decreases because the electrons have more energy to escape from the metal. Therefore, the assertion that the work function of a metal is different at different temperatures is true.

5. **Evaluating the Reason**:
- The reason states that an increase in the temperature of metals decreases the work function of the metal. This statement is also true, as explained in the previous steps.

6. **Final Evaluation**:
- Both the assertion and the reason are correct, and the reason provides a correct explanation for the assertion. Therefore, the conclusion is that both the assertion and reason are true, and the reason is a valid explanation of the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason is a correct explanation of the assertion.

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