Assertion : Though light of a single frequency (monochromatic) is incident on a metal , the energies of emitted photoelectrons are different.
Reason : The energy of electrons emitted from inside the metal surface is lost in collision with the other atoms in the metal.

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when monochromatic light (light of a single frequency) is incident on a metal, the energies of the emitted photoelectrons are different.
- This is true because, even though the light has a single frequency, the photoelectrons can originate from different depths within the metal.

2. **Understanding the Photoelectric Effect**:
- The photoelectric effect explains that when light hits a metal surface, it can impart energy to electrons, allowing them to escape from the metal. The energy of the emitted electrons is given by the equation:
\[ KE = hf - \phi \]
where \( KE \) is the kinetic energy of the emitted electron, \( hf \) is the energy of the incident photon, and \( \phi \) is the work function of the metal.

3. **Energy Variations**:
- Electrons that are emitted from deeper within the metal may lose energy due to collisions with other atoms before they escape. This results in a range of kinetic energies for the emitted electrons, even though they are all being struck by photons of the same energy.

4. **Understanding the Reason**:
- The reason provided states that the energy of electrons emitted from inside the metal surface is lost in collisions with other atoms in the metal.
- This is a valid explanation for the assertion. Electrons that are emitted from deeper layers may collide with atoms and lose some of their kinetic energy, leading to a distribution of energies among the emitted photoelectrons.

5. **Conclusion**:
- Both the assertion and the reason are true. The reason correctly explains why the assertion is true. Therefore, the assertion and reason are both valid and related.

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

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