The effective atomic number of cobalt in the complex `[Co(NH_3)_6]^(3+)` is

Options

A. (a) `36`
B. (b) `33`
C. (c) `24`
D. (d) `30`

Explanation

To find the effective atomic number (EAN) of cobalt in the complex \([Co(NH_3)_6]^{3+}\), we can follow these steps:

### Step 1: Understand the EAN Formula
The formula for calculating the effective atomic number (EAN) is:
\[ \text{EAN} = Z - n + 2 \times L \]
where:
- \(Z\) = atomic number of the metal
- \(n\) = oxidation state of the metal
- \(L\) = number of ligands

### Step 2: Determine the Atomic Number of Cobalt
The atomic number of cobalt (Co) is:
\[ Z = 27 \]

### Step 3: Determine the Oxidation State of Cobalt
In the complex \([Co(NH_3)_6]^{3+}\), the overall charge is \(+3\). Since ammonia (NH₃) is a neutral ligand, the oxidation state of cobalt can be calculated as follows:

Let the oxidation state of cobalt be \(x\):
\[ x + 6(0) = +3 \]
This simplifies to:
\[ x = +3 \]

### Step 4: Count the Number of Ligands
In the complex, there are 6 ammonia ligands:
\[ L = 6 \]

### Step 5: Substitute Values into the EAN Formula
Now, we can substitute the values into the EAN formula:
\[ \text{EAN} = 27 - 3 + 2 \times 6 \]
Calculating this step-by-step:
1. Calculate \(2 \times L\):
\[ 2 \times 6 = 12 \]
2. Substitute into the equation:
\[ \text{EAN} = 27 - 3 + 12 \]
3. Perform the arithmetic:
\[ \text{EAN} = 27 - 3 = 24 \]
\[ \text{EAN} = 24 + 12 = 36 \]

### Final Answer
The effective atomic number (EAN) of cobalt in the complex \([Co(NH_3)_6]^{3+}\) is:
\[ \text{EAN} = 36 \]

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