The ratio of cis and trans-isomers of the complex `[Ma_(2)bcde]^(n+-)` is:

Options

A. `5:3`
B. `2:1`
C. `7:3`
D. `3:1`

Explanation

To determine the ratio of cis and trans isomers of the complex \([Ma_{2}bcde]^{n+}\), we will follow a systematic approach:

### Step 1: Understand the Structure of the Complex
The complex \([Ma_{2}bcde]^{n+}\) consists of a central metal atom \(M\) bonded to two identical ligands \(A\) and four different ligands \(b\), \(c\), \(d\), and \(e\).

### Step 2: Identify the Isomer Types
In coordination chemistry, isomers can be classified as cis or trans based on the relative positions of the ligands around the central metal atom.
- **Cis Isomer**: Ligands of the same type are adjacent to each other.
- **Trans Isomer**: Ligands of the same type are opposite each other.

### Step 3: Draw the Cis Isomers
1. Place the two \(A\) ligands adjacent to each other.
2. The remaining ligands \(b\), \(c\), \(d\), and \(e\) can occupy the remaining positions around the metal center.
3. By varying the positions of \(b\), \(c\), \(d\), and \(e\) while keeping \(A\) ligands in cis, we can generate different cis isomers.

### Step 4: Count the Cis Isomers
After systematically placing the \(b\), \(c\), \(d\), and \(e\) ligands in various configurations while keeping \(A\) in cis positions, we find that there are **6 distinct cis isomers**.

### Step 5: Draw the Trans Isomers
1. Place the two \(A\) ligands opposite each other.
2. Again, vary the positions of \(b\), \(c\), \(d\), and \(e\) around the metal center while keeping \(A\) in trans positions.

### Step 6: Count the Trans Isomers
Following a similar approach to the cis isomers, we find that there are **3 distinct trans isomers**.

### Step 7: Calculate the Ratio
Now that we have the counts:
- Number of cis isomers = 6
- Number of trans isomers = 3

The ratio of cis to trans isomers is:
\[ \text{Ratio} = \frac{\text{Number of cis isomers}}{\text{Number of trans isomers}} = \frac{6}{3} = 2:1 \]

### Final Answer
The ratio of cis and trans isomers of the complex \([Ma_{2}bcde]^{n+}\) is **2:1**.

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