To understand why different term symbols are used in tetrahedral and octahedral crystal field splitting, we need to consider the geometrical arrangement and the symmetry of the ligands around the central metal ion.
### Explanation
1. **Octahedral Splitting**:
- In an octahedral complex, the ligands approach the central metal ion along the axes of the coordinate system (the x, y, and z axes).
- This leads to a specific splitting of the d-orbitals:
- The \( t_{2g} \) set (lower energy) includes the \( d_{xy}, d_{xz}, d_{yz} \) orbitals, which are oriented between the axes and are less affected by the ligand’s repulsion.
- The \( e_g \) set (higher energy) consists of the \( d_{x^2-y^2} \) and \( d_{z^2} \) orbitals, which point directly towards the ligands and experience greater repulsion.
- The term symbols \( e_g \) and \( t_{2g} \) are used because they reflect this arrangement and the symmetry of the octahedral environment.
2. **Tetrahedral Splitting**:
- In a tetrahedral complex, the ligands approach the central metal ion from the corners of a tetrahedron, which means they are not aligned along the axes.
- This results in a different splitting pattern of the d-orbitals:
- The \( e \) set (lower energy) includes the \( d_{x^2-y^2} \) and \( d_{z^2} \) orbitals, which are less affected by the ligand’s repulsion.
- The \( t_2 \) set (higher energy) consists of the \( d_{xy}, d_{xz}, d_{yz} \) orbitals, which point more towards the ligands and experience higher repulsion.
- The term symbols \( e \) and \( t_2 \) are used to denote the orbital arrangements in a tetrahedral field.
### Answer to the Question
Given the explanations above, the correct answer to the question is:
**(C) Due to the symmetry present in the octahedral system.**
This is because the distinct terms used in both splitting patterns arise from how the ligands approach the metal ion and the symmetry of the respective geometrical arrangements. In octahedral complexes, the specific alignment of ligands along the axes allows for a different naming convention than in tetrahedral complexes, where the approach is not along the coordinate axes.
