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 \([Ma_2bcde]^{n+}\), we can follow these steps:

### Step 1: Identify the structure of the complex
The complex has a coordination number of 6, with two identical ligands (A) and four different ligands (B, C, D, E). This arrangement suggests that the complex can exhibit both cis and trans isomerism.

**Hint:** Remember that cis isomers have similar ligands adjacent to each other, while trans isomers have them opposite each other.

### Step 2: Determine the possible arrangements
For a complex of the type \([Ma_2bcde]^{n+}\), we can visualize the arrangement of ligands around the central metal atom (M). The two identical ligands (A) can be positioned in different ways relative to the other four ligands (B, C, D, E).

**Hint:** Draw a diagram to visualize the arrangements of the ligands around the metal center.

### Step 3: Identify cis and trans isomers
- **Cis Isomers:** In these isomers, the two identical ligands (A) will be adjacent to each other.
- **Trans Isomers:** In these isomers, the two identical ligands (A) will be opposite each other.

### Step 4: Count the number of isomers
1. **Cis Isomers:**
- The two A ligands can be adjacent, and we can arrange the other four different ligands (B, C, D, E) around them. The arrangements can be calculated based on the positions of the other ligands.
- For each arrangement of A's, the remaining ligands can be arranged in \(4!\) (24) ways.

2. **Trans Isomers:**
- The two A ligands are opposite each other. The remaining four ligands can still be arranged around the metal center, which can also be done in \(4!\) (24) ways.

### Step 5: Calculate the total number of isomers
- **Total Cis Isomers:** There are 6 distinct arrangements of the two A ligands adjacent to each other, leading to \(6 \times 4! = 6 \times 24 = 144\) cis isomers.
- **Total Trans Isomers:** There are 3 distinct arrangements of the two A ligands opposite each other, leading to \(3 \times 4! = 3 \times 24 = 72\) trans isomers.

### Step 6: Calculate the ratio of cis to trans isomers
The ratio of cis to trans isomers can be calculated as follows:
\[ \text{Ratio} = \frac{\text{Number of Cis Isomers}}{\text{Number of Trans Isomers}} = \frac{144}{72} = 2:1 \]

### Final Answer
The ratio of cis to trans isomers of the complex \([Ma_2bcde]^{n+}\) is **2:1**.

---