Complex `[ML_(5)]` can exhibit trigonal bipyramidal and square pyramidal geometry. Determine total number of `180^@, 90^@ & 120^@` L-M-L bond angles.

Options

A. (a) 14
B. (b) 20
C. (c) 10
D. (d) 25

Explanation

To determine the total number of 180°, 90°, and 120° L-M-L bond angles in the complex [ML₅] that exhibits trigonal bipyramidal (TBP) and square pyramidal geometries, we will analyze each geometry step by step.

### Step 1: Analyze Trigonal Bipyramidal Geometry
In trigonal bipyramidal geometry, the arrangement of ligands around the central metal atom is such that there are two axial positions and three equatorial positions.

1. **180° Angles**:
- There is only **1 angle** of 180° between the two axial ligands (L1 and L3).

2. **90° Angles**:
- Each equatorial ligand (L2, L4, L5) forms a 90° angle with the axial ligands (L1 and L3).
- There are **6 angles** of 90° (3 angles with L1 and 3 angles with L3).

3. **120° Angles**:
- The equatorial ligands (L2, L4, L5) form 120° angles with each other.
- There are **3 angles** of 120° (L2-L4, L2-L5, and L4-L5).

**Total for TBP**:
- 180°: 1
- 90°: 6
- 120°: 3

### Step 2: Analyze Square Pyramidal Geometry
In square pyramidal geometry, there are four ligands in a square plane and one ligand above the plane.

1. **180° Angles**:
- There are **2 angles** of 180° (between L2 and L4, and L3 and L5).

2. **90° Angles**:
- The ligand above the plane (L1) forms 90° angles with all four ligands in the square plane (L2, L3, L4, L5).
- Additionally, the ligands in the square plane also form 90° angles with each other.
- There are **8 angles** of 90° (4 with L1 and 4 between the ligands in the square plane).

3. **120° Angles**:
- There are **0 angles** of 120° in square pyramidal geometry.

**Total for Square Pyramidal**:
- 180°: 2
- 90°: 8
- 120°: 0

### Step 3: Combine Results
Now, we will combine the results from both geometries:

- **Total 180° Angles**: 1 (TBP) + 2 (Square Pyramidal) = 3
- **Total 90° Angles**: 6 (TBP) + 8 (Square Pyramidal) = 14
- **Total 120° Angles**: 3 (TBP) + 0 (Square Pyramidal) = 3

### Final Count of Bond Angles
- **Total 180° angles**: 3
- **Total 90° angles**: 14
- **Total 120° angles**: 3

### Total Number of L-M-L Bond Angles
Adding all the bond angles together:
- Total = 3 (180°) + 14 (90°) + 3 (120°) = **20**

### Conclusion
The total number of L-M-L bond angles in the complex [ML₅] is **20**.