`[Ni(CO)_(x)]` and `[Fe(CO)_(y)]` what will be the value of x and y respectively are :

Options

A. 4 and 4
B. 4 and 5
C. 5 and 4
D. 5 and 5

Explanation

To solve the question regarding the values of \( x \) and \( y \) in the coordination compounds \([Ni(CO)_{x}]\) and \([Fe(CO)_{y}]\), we will use the concept of effective atomic number (EAN) as described in Sidwick's rule. The EAN for a stable complex is equal to the atomic number of the nearest noble gas, which is 36 for nickel and iron in the fourth period.

### Step-by-Step Solution:

1. **Identify the Atomic Numbers**:
- The atomic number of Nickel (Ni) is 28.
- The atomic number of Iron (Fe) is 26.

2. **Determine the Oxidation States**:
- In both complexes, CO is a neutral ligand, which means it does not contribute any charge. Therefore, the oxidation states of both Ni and Fe in their respective complexes are 0.

3. **Apply the EAN Formula**:
The formula for calculating the effective atomic number (EAN) is:
\[ \text{EAN} = Z - \text{oxidation state} + 2 \times \text{coordination number} \]
where \( Z \) is the atomic number, the oxidation state is the charge on the metal, and the coordination number is the number of ligands attached to the metal.

4. **Calculate EAN for Nickel**:
For \([Ni(CO)_{x}]\):
- \( Z = 28 \)
- Oxidation state = 0
- Coordination number = \( x \)

Plugging into the formula:
\[ \text{EAN} = 28 - 0 + 2x = 28 + 2x \]
Set EAN equal to 36:
\[ 28 + 2x = 36 \]
Solving for \( x \):
\[ 2x = 36 - 28 \\ 2x = 8 \\ x = 4 \]

5. **Calculate EAN for Iron**:
For \([Fe(CO)_{y}]\):
- \( Z = 26 \)
- Oxidation state = 0
- Coordination number = \( y \)

Plugging into the formula:
\[ \text{EAN} = 26 - 0 + 2y = 26 + 2y \]
Set EAN equal to 36:
\[ 26 + 2y = 36 \]
Solving for \( y \):
\[ 2y = 36 - 26 \\ 2y = 10 \\ y = 5 \]

6. **Final Values**:
- The value of \( x \) is 4.
- The value of \( y \) is 5.

### Conclusion:
Thus, the values of \( x \) and \( y \) in the coordination compounds \([Ni(CO)_{x}]\) and \([Fe(CO)_{y}]\) are:
\[ x = 4, \quad y = 5 \]