A metal is heated up to a certain temperature, the work function changes from `phi_1 " to " phi_2 (phi_1 gt phi_2)` photoelectric current before and after change are `I_1 and I_2` Keeping all other condition unchanged, the correct relation between `I_1 and I_2`

Options

A. `I_1 gt I_2`
B. `I_1 = I_2`
C. `I_1 lt I_2`
D. `I_1 ne I_2`

Explanation

To solve the problem, we need to analyze the relationship between the work function of a metal and the photoelectric current produced when light shines on it.

### Step-by-Step Solution:

1. **Understanding Work Function**:
The work function (φ) is the minimum energy required to eject an electron from the surface of a metal. In this case, we have two work functions: φ₁ (initial) and φ₂ (final), where φ₁ > φ₂. This means that the work function has decreased when the metal is heated.

**Hint**: Remember that a lower work function means that it is easier for electrons to be ejected from the metal.

2. **Photoelectric Current**:
The photoelectric current (I) is directly related to the number of photoelectrons emitted from the metal surface when it is illuminated by light. The current produced is proportional to the number of electrons ejected.

**Hint**: The photoelectric current increases with an increase in the number of emitted photoelectrons.

3. **Effect of Work Function on Photoelectric Current**:
When the work function decreases (from φ₁ to φ₂), it becomes easier for electrons to be emitted from the metal. This means that for the same intensity of light, more electrons will be ejected.

**Hint**: A decrease in work function leads to an increase in the number of emitted electrons, which in turn increases the current.

4. **Intensity of Light**:
The problem states that all other conditions remain unchanged, including the intensity of the light. The intensity of light is related to the number of photons striking the surface of the metal. Since the intensity is unchanged, the number of photons remains constant.

**Hint**: The intensity of light affects the number of photons, but since it is constant, we focus on the change in work function.

5. **Conclusion on Current Relation**:
Since the work function has decreased, the number of photoelectrons emitted will increase, leading to an increase in the photoelectric current. Therefore, we can conclude that the photoelectric current after the change (I₂) will be greater than the photoelectric current before the change (I₁).

However, since the problem asks for the correct relation between I₁ and I₂, we can summarize this as:
- If φ₁ > φ₂, then I₁ < I₂.

**Final Relation**:
I₂ > I₁

### Summary:
The correct relation between the photoelectric currents before and after the change in work function is:
\[ I_2 > I_1 \]