Statement 1: Though light of a single frequency (monochromatic light) is incident on a metal, the kinetic energies of emitted photoelectrons are not equal. Statement 2: The energy of electrons just after they absorb photons incident on metal surface may be lost in collision with other atoms in the metal before the electron is ejected out of the metal.

Options

A. Statement-1 is true, Statement-2: is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2: is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is true but statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the problem, we need to analyze the two statements given:

**Statement 1:** Though light of a single frequency (monochromatic light) is incident on a metal, the kinetic energies of emitted photoelectrons are not equal.

**Statement 2:** The energy of electrons just after they absorb photons incident on the metal surface may be lost in collision with other atoms in the metal before the electron is ejected out of the metal.

### Step-by-Step Solution:

1. **Understanding Photoelectric Effect:**
- The photoelectric effect states that when light of sufficient frequency strikes a metal surface, electrons are emitted from that surface. The energy of the incident photons is given by the equation \( E = hf \), where \( h \) is Planck's constant and \( f \) is the frequency of the light.

2. **Kinetic Energy of Emitted Electrons:**
- The kinetic energy (KE) of the emitted photoelectrons can be expressed as:
\[ KE = hf - \phi \]
where \( \phi \) is the work function of the metal (the minimum energy required to remove an electron from the metal surface).

3. **Analyzing Statement 1:**
- If monochromatic light is incident on the metal, all photons have the same energy \( hf \). However, the emitted electrons can have different kinetic energies due to various factors such as:
- Collisions with other atoms in the metal.
- Variations in the initial energy states of the electrons before absorption.
- Therefore, Statement 1 is **correct**: the kinetic energies of emitted photoelectrons are not equal.

4. **Analyzing Statement 2:**
- When a photon is absorbed by an electron, the electron gains energy. However, before the electron is emitted, it can collide with other atoms in the metal. These collisions can cause the electron to lose some of its energy.
- This energy loss can lead to variations in the kinetic energy of the emitted electrons, as not all absorbed energy is converted into kinetic energy due to these collisions.
- Thus, Statement 2 is also **correct**: energy can be lost in collisions before the electron is ejected.

5. **Conclusion:**
- Both statements are correct, and Statement 2 provides a valid reason for the observation made in Statement 1.

### Final Answer:
- Statement 1 is correct.
- Statement 2 is correct and provides a reason for Statement 1.