Find the number of geometrical isomer of `Ma_(2)bcde` which have identical ligands at maximum distance. (a, b, c, d and e are monodentate ligand)

Explanation

To find the number of geometrical isomers of the coordination compound \( MA_2BCDE \) with the condition that identical ligands are at maximum distance, we can follow these steps:

### Step 1: Identify the structure
The coordination compound \( MA_2BCDE \) consists of a central metal atom \( M \) bonded to two identical ligands \( A \) and four different monodentate ligands \( B, C, D, \) and \( E \).

### Step 2: Determine the coordination geometry
The coordination number of the metal \( M \) is 6 (2 from \( A \) and 4 from \( B, C, D, \) and \( E \)). This typically leads to an octahedral geometry.

### Step 3: Analyze the arrangement of ligands
In an octahedral complex, the two identical ligands \( A \) can be arranged in different positions relative to the other ligands. The goal is to maximize the distance between the two \( A \) ligands.

### Step 4: Positioning the identical ligands
To achieve maximum distance between the two \( A \) ligands, they should be positioned opposite each other. This arrangement allows for the other four ligands \( B, C, D, \) and \( E \) to occupy the remaining four positions.

### Step 5: Count the arrangements of the other ligands
The four different ligands \( B, C, D, \) and \( E \) can be arranged in the four remaining positions. The number of ways to arrange four different ligands is given by the factorial of the number of ligands:

\[ \text{Number of arrangements} = 4! = 24 \]

### Step 6: Conclusion
Thus, the total number of geometrical isomers of \( MA_2BCDE \) with the identical ligands at maximum distance is 24.

### Final Answer:
The number of geometrical isomers of \( MA_2BCDE \) with identical ligands at maximum distance is **24**.

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