Assertion: A photosensitive surface is illuminated by a monochromatic light of wavelength `lambda` and intensity I. The number of photoelectrons emitted per second is doubled when the intensity of light is doubled. However, the maximum speed of emitted electrons remains unchanged.
Reason: The number of electrons emitted per second is directly proportional to the intensity of the incident light. The kinetic energy of the emitted photoelectrons is independent of the intensity of the light.

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 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.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that when a photosensitive surface is illuminated by monochromatic light of wavelength \( \lambda \) and intensity \( I \), the number of photoelectrons emitted per second doubles when the intensity of light is doubled. However, the maximum speed of emitted electrons remains unchanged.

- **Analysis**: According to the photoelectric effect, the number of emitted photoelectrons is directly proportional to the intensity of the incident light. This is because intensity is related to the number of photons striking the surface per unit time. Therefore, if the intensity is doubled, the number of emitted photoelectrons will also double.

### Step 2: Understand the Reason
The reason states that the number of electrons emitted per second is directly proportional to the intensity of the incident light and that the kinetic energy of the emitted photoelectrons is independent of the intensity of the light.

- **Analysis**: This is also correct. The number of emitted electrons is indeed proportional to the intensity of light. The kinetic energy of the emitted photoelectrons, however, depends on the frequency of the incident light (as per Einstein's photoelectric equation: \( KE_{max} = h\nu - h\nu_0 \)). Since the intensity does not affect the frequency, the kinetic energy remains unchanged when only the intensity is varied.

### Step 3: Conclusion
Both the assertion and reason are correct. The reason correctly explains the assertion because it highlights the relationship between intensity and the number of emitted electrons as well as the independence of kinetic energy from intensity.

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

### Options:
- A. If both the assertion and reason are correct and the reason is a correct explanation.
- B. Both are correct but the reason is not a correct explanation.
- C. Assertion is correct, reason is incorrect.
- D. Assertion is not correct and reason is correct.

**Correct Option: A**

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