Assertion: Light of frequency `1.5` times the threshold frequency is incident on photo-senstive material. If the frequency is halved and intensity is doubled, the photo current remains unchanged.
Reason: The photo electric current varies directely with the intensity of light and frequncy of light.

Options

A. If both, Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. If both, Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
C. If Assertion is true but the Reason is false.
D. If both Assertion and Reason are false.

Explanation

To solve the given question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that light of frequency \(1.5 \times \nu_0\) (where \(\nu_0\) is the threshold frequency) is incident on a photo-sensitive material. If the frequency is halved (to \(0.75 \times \nu_0\)) and the intensity is doubled, the photo current remains unchanged.

**Analysis**:
- The threshold frequency \(\nu_0\) is the minimum frequency required to eject electrons from the material.
- The initial frequency \(1.5 \times \nu_0\) is above the threshold, so photoelectric emission occurs.
- When the frequency is halved to \(0.75 \times \nu_0\), this frequency is below the threshold frequency. Therefore, no photoelectric emission can occur, and the photo current will be zero.

### Conclusion for Assertion:
The assertion is **false** because the photo current cannot remain unchanged when the frequency is below the threshold frequency.

### Step 2: Understanding the Reason
The reason states that the photoelectric current varies directly with the intensity of light and frequency of light.

**Analysis**:
- The photoelectric current does indeed vary with the intensity of light. Higher intensity means more photons, which can lead to more emitted electrons, thus increasing the current.
- However, the current does not vary with frequency in the sense that increasing frequency does not increase the number of emitted electrons; it only affects the energy of the emitted electrons. The current is dependent on the number of photons (intensity), not their energy (frequency).

### Conclusion for Reason:
The reason is also **false** because while the current varies with intensity, it does not vary directly with frequency.

### Final Conclusion:
Both the assertion and the reason are false.

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