On increasing the temperature the work function of metal will

Options

A. Increase
B. Decrease
C. Remains same
D. First increase and then decrease

Answer

To solve the question regarding the effect of temperature on the work function of a metal, we can follow these steps:

### Step 1: Understand the 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 the material.

**Hint:** Remember that the work function is related to the energy needed to free an electron from the metal.

### Step 2: Consider the Effect of Temperature
When the temperature of a metal increases, the thermal energy of the electrons also increases. This means that the electrons gain additional vibrational energy due to the increased temperature.

**Hint:** Think about how thermal energy affects the motion of electrons in the metal.

### Step 3: Relate Thermal Energy to Work Function
As the temperature rises, the increased thermal energy can help in overcoming the work function barrier. This means that less external energy (in the form of light or other means) is required to free the electrons from the metal.

**Hint:** Consider how the increased energy from temperature affects the energy needed to remove an electron.

### Step 4: Conclusion on Work Function
Since the increased thermal energy allows electrons to be freed more easily, the effective work function decreases. Therefore, the work function does not remain constant; it decreases with an increase in temperature.

**Hint:** Remember that a decrease in the energy required to remove an electron indicates a decrease in the work function.

### Final Answer
On increasing the temperature, the work function of the metal will **decrease**.