The total number of isomers for a square planer complex [M(F)(Cl)(Br)(`NO_(2)`)] is _________.

Explanation

To determine the total number of isomers for the square planar complex [M(F)(Cl)(Br)(NO2)], we can follow these steps:

### Step 1: Identify the Ligands
The complex contains four different ligands: F (fluoride), Cl (chloride), Br (bromide), and NO2 (nitro).

### Step 2: Consider the Geometry
Since the complex is square planar, we need to consider the arrangement of these ligands around the central metal atom (M).

### Step 3: Determine the Isomers
1. **Arrangement of Ligands**: In a square planar geometry, the ligands can be arranged in different ways. The arrangement can lead to different geometric isomers.
2. **Ambidentate Ligand**: The nitro group (NO2) can coordinate to the metal through either nitrogen (N) or oxygen (O), which adds to the number of possible isomers.

### Step 4: Count the Isomers
1. **Geometric Isomers**: For the ligands F, Cl, and Br, we can have different arrangements:
- One arrangement can have NO2 coordinated through N.
- Another arrangement can have NO2 coordinated through O.
- Each arrangement can lead to different geometric isomers.

2. **Calculating Total Isomers**:
- For the arrangement where NO2 is bonded through N, we can have different configurations:
- F, Cl, Br in different positions.
- For the arrangement where NO2 is bonded through O, we can again have different configurations.

Since there are 3 ligands (F, Cl, Br) that can be arranged in different ways, we can use the formula for the number of isomers:
- Total isomers = (Number of arrangements for one configuration) * (Number of configurations for NO2)
- For 3 different ligands, the arrangements can be calculated as 3! (which equals 6).
- Since NO2 can bind in two different ways (through N or O), we multiply by 2.

### Final Calculation
- Total Isomers = 6 (from arrangements of F, Cl, Br) * 2 (from NO2 binding) = 12.

### Conclusion
The total number of isomers for the square planar complex [M(F)(Cl)(Br)(NO2)] is **12**.

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