Statement-1: The photoelectrons produced by a monochromatic light beam incident on a metal surface have a spread in their kinetic energies.
Statement-2: The work function of the metal varies as a function of depth form the surface.

Options

A. If both Assertion & 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 the correct expalanation of the assertion
C. if assertion is true , but reason is false
D. both assertion and reason are false statements.

Explanation

To solve the question, we need to analyze both statements provided:

**Statement 1:** The photoelectrons produced by a monochromatic light beam incident on a metal surface have a spread in their kinetic energies.

**Statement 2:** The work function of the metal varies as a function of depth from the surface.

### Step-by-Step Solution:

1. **Understanding Photoelectric Effect:**
- When monochromatic light (light of a single frequency) strikes a metal surface, it can cause electrons to be ejected from the surface. This phenomenon is known as the photoelectric effect.

2. **Kinetic Energy of Photoelectrons:**
- The kinetic energy (KE) of the emitted photoelectrons can be described by the equation:
\[ KE = E_{incident} - \phi \]
where \(E_{incident}\) is the energy of the incoming photons and \(\phi\) is the work function of the metal.

3. **Spread in Kinetic Energies:**
- The energy of the incident photons is constant for monochromatic light, but the work function \(\phi\) can vary slightly due to factors like electron binding energies and the energy levels of electrons within the metal. This leads to a spread in the kinetic energies of the emitted photoelectrons.

4. **Conclusion for Statement 1:**
- Therefore, Statement 1 is **correct** because the photoelectrons do indeed have a spread in their kinetic energies due to variations in the work function and the energy levels of electrons in the metal.

5. **Understanding Work Function:**
- The work function \(\phi\) is a characteristic property of the material and is defined as the minimum energy needed to remove an electron from the surface of the metal.

6. **Depth Dependence of Work Function:**
- Statement 2 claims that the work function varies as a function of depth from the surface. However, the work function is primarily determined by the electronic structure and properties of the material itself, not by the depth from which the electron is emitted. While there may be some variations in electronic properties at very high depths, the work function is generally considered a constant for a given material.

7. **Conclusion for Statement 2:**
- Thus, Statement 2 is **incorrect** because the work function does not vary significantly with depth in a typical metal.

8. **Final Assessment:**
- Since Statement 1 is true and Statement 2 is false, the correct answer is that the assertion is true but the reason is false.

### Final Answer:
- The assertion is true (Statement 1) but the reason is false (Statement 2).