The exhibition of highest co-ordination number depends on the availability of vacant orbitals in the central atom. Which of the following elements is not likely to act as central atom in `MF_(6)^(3-)` ?

Options

A. B
B. Al
C. Ga
D. In

Explanation

To solve the question regarding which element is not likely to act as a central atom in the complex ion \( MF_6^{3-} \), we need to analyze the elements provided: boron (B), aluminum (Al), gallium (Ga), and indium (In). The key factor here is the availability of vacant orbitals in the central atom.

### Step-by-Step Solution:

1. **Identify the Elements and Their Electron Configurations**:
- **Boron (B)**: Atomic number 5, electron configuration: \( 1s^2 2s^2 2p^1 \). Boron has 3 valence electrons and does not have d-orbitals.
- **Aluminum (Al)**: Atomic number 13, electron configuration: \( [Ne] 3s^2 3p^1 \). Aluminum has 3 valence electrons and has d-orbitals available.
- **Gallium (Ga)**: Atomic number 31, electron configuration: \( [Ar] 3d^{10} 4s^2 4p^1 \). Gallium has 3 valence electrons and has d-orbitals available.
- **Indium (In)**: Atomic number 49, electron configuration: \( [Kr] 4d^{10} 5s^2 5p^1 \). Indium has 3 valence electrons and has d-orbitals available.

2. **Determine Coordination Numbers**:
- Coordination number refers to the number of bonds formed by the central atom.
- **Boron** can form a maximum of 4 bonds due to the absence of vacant d-orbitals. Therefore, its coordination number is limited to 4.
- **Aluminum, Gallium, and Indium** can utilize their d-orbitals to expand their coordination number beyond 4, allowing them to form complexes like \( MF_6^{3-} \).

3. **Conclusion**:
- Since boron lacks vacant d-orbitals, it cannot achieve a coordination number of 6, which is necessary for the complex \( MF_6^{3-} \).
- Therefore, the element that is not likely to act as the central atom in \( MF_6^{3-} \) is **Boron (B)**.

### Final Answer:
**Boron (B)** is not likely to act as the central atom in \( MF_6^{3-} \).