EAN of a metal carbonyl `M(CO)_(x)` is 36. If atomic number of metal M is 26, what is the value of x?

Options

A. 5
B. 4
C. 6
D. none of these

Answer

To solve the problem, we need to determine the value of \( x \) in the metal carbonyl \( M(CO)_{x} \) given that the Effective Atomic Number (EAN) is 36 and the atomic number of the metal \( M \) is 26.

### Step-by-Step Solution:

1. **Understand the Formula for EAN**:
The Effective Atomic Number (EAN) can be calculated using the formula:
\[ \text{EAN} = Z - n + 2 \times C \]
where:
- \( Z \) = Atomic number of the metal
- \( n \) = Oxidation state of the metal
- \( C \) = Coordination number (number of ligands)

2. **Identify Given Values**:
From the problem:
- EAN = 36
- Atomic number \( Z \) = 26 (for metal \( M \))
- For carbonyl ligands (CO), the oxidation state \( n \) of the metal is 0.

3. **Substituting Known Values into the EAN Formula**:
Substitute the known values into the EAN formula:
\[ 36 = 26 - 0 + 2 \times C \]
This simplifies to:
\[ 36 = 26 + 2C \]

4. **Rearranging the Equation**:
Rearranging the equation to solve for \( C \):
\[ 36 - 26 = 2C \]
\[ 10 = 2C \]

5. **Solving for Coordination Number \( C \)**:
Divide both sides by 2:
\[ C = \frac{10}{2} = 5 \]

6. **Conclusion**:
Therefore, the value of \( x \) (the number of carbonyl ligands) is 5.

### Final Answer:
The value of \( x \) is 5.