Statement-`1`: High thermal conductivity of metals is due to presence of free electrons.
Statement-`2`: Electrons at same temperature have very high average velocity than atoms.

Options

A. Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`
B. Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`
C. Statement -`1` is True , Statement -`2` is False.
D. Statement -`1` is False , Statement -`2` is True.

Answer

To analyze the statements given in the question, we will evaluate each statement separately and determine their validity.

### Step-by-Step Solution:

**Step 1: Evaluate Statement 1**
- **Statement 1**: "High thermal conductivity of metals is due to the presence of free electrons."
- Metals have free electrons that can move easily throughout the metal lattice. This mobility allows metals to conduct heat effectively. When one part of a metal is heated, the free electrons gain energy and move faster, transferring energy to neighboring electrons and atoms, which results in the conduction of heat.
- **Conclusion**: Statement 1 is **True**.

**Step 2: Evaluate Statement 2**
- **Statement 2**: "Electrons at the same temperature have a very high average velocity than atoms."
- While it is true that electrons are lighter than atoms and can move quickly, the term "very high average velocity" is misleading. At a given temperature, the average kinetic energy of particles (both electrons and atoms) is related to temperature, but the average velocity of electrons is not necessarily "very high" compared to atoms. Electrons can have high speeds, but they also experience collisions and interactions that affect their effective motion. Thus, the statement exaggerates the situation.
- **Conclusion**: Statement 2 is **False**.

**Final Evaluation**:
- Since Statement 1 is True and Statement 2 is False, we conclude that the correct evaluation of the statements is:
- **Statement 1: True**
- **Statement 2: False**

### Final Answer:
- Statement 1 is true, and Statement 2 is false.