The metallic lustre exhibited by sodium is explained by

Options

A. Diffusion of `Na^(+)` ions
B. Oscillation of loose electrons
C. Excitation of free protons
D. Existence of body centred cubic lattice

Answer

To explain the metallic lustre exhibited by sodium, we can analyze the options provided and determine the correct reasoning behind this phenomenon.

### Step-by-Step Solution:

1. **Understanding Metallic Lustre**:
- Metallic lustre refers to the shiny appearance of metals. This property arises due to the behavior of electrons in the metal.

2. **Analyzing the Options**:
- **Option 1: Diffusion of Na⁺ ions**:
- This option is not correct. The diffusion of ions does not contribute to the metallic lustre. Metallic lustre is primarily due to the behavior of electrons, not ions.

- **Option 2: Oscillation of Loose Electrons**:
- This is the correct answer. In metals like sodium, there are free or delocalized electrons that can oscillate. When these electrons absorb energy (for example, from light), they can jump to higher energy levels and then fall back, releasing energy in the form of light (photons). This oscillation and subsequent emission of light give metals their characteristic shine.

- **Option 3: Excitation of Free Photons**:
- This option is incorrect. Photons themselves do not get excited; rather, electrons get excited and can emit photons when they return to lower energy states. Thus, this option does not explain the metallic lustre.

- **Option 4: Existence of Body-Centered Cubic Lattice**:
- While sodium does have a body-centered cubic lattice structure, this alone does not explain the metallic lustre. The lattice structure contributes to the overall properties of the metal but does not directly cause the shiny appearance.

3. **Conclusion**:
- The correct explanation for the metallic lustre exhibited by sodium is due to the **oscillation of loose electrons**. These electrons can move freely and oscillate when they interact with light, which results in the emission of light and thus the shiny appearance.

### Final Answer:
The metallic lustre exhibited by sodium is explained by **oscillation of loose electrons**.