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 \([Ma_2bcde]^{n+}\) indicates that there are two identical ligands (A), and four different ligands (b, c, d, e) coordinated to the metal ion (M).

### Step 2: Draw the Cis Isomers
In cis isomers, the two identical ligands (A) are positioned adjacent to each other. We can visualize the arrangement as follows:

1. **Cis Isomer 1**: A A b c d e
2. **Cis Isomer 2**: A A b c e d
3. **Cis Isomer 3**: A A b d c e
4. **Cis Isomer 4**: A A c b d e
5. **Cis Isomer 5**: A A c d b e
6. **Cis Isomer 6**: A A d b c e

Thus, we can see that there are **6 possible cis isomers**.

### Step 3: Draw the Trans Isomers
In trans isomers, the two identical ligands (A) are positioned opposite each other. The arrangements can be visualized as follows:

1. **Trans Isomer 1**: A b c d e A
2. **Trans Isomer 2**: A b c e d A
3. **Trans Isomer 3**: A b d c e A

Thus, we can see that there are **3 possible trans isomers**.

### Step 4: Calculate the Ratio
Now that we have the number of cis and trans isomers, we can calculate the ratio:

\[ \text{Ratio of cis to trans isomers} = \frac{\text{Number of cis isomers}}{\text{Number of trans isomers}} = \frac{6}{3} = 2 \]

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

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