`underset((X))(K_(6)[(CN)_(5)" "Co-O-O-Co(CN)_(5)])overset("oxidizes")rarrunderset((Y))(K_(5)[(CN)_(5)Co-O-O-Co(CN)_(5)])`
In both the complexes Co have `t_(20)""^(6)e_(g)^(@)` configuration.
The bond energy of `(O-O)` in X ans Y is `:`

Options

A. bond energy of `(O-O)` in `Y lt` bond energy of `(O-O)` in X.
B. bond energy of `(O-O)` in `X lt` bond energy of `(O-O)` in Y.
C. bond energy of `(O-O)` in `X=` bond energy of `(O-O)` in Y.
D. bond energy of `(O-O)` in X and bond energ of `(O-O)` in Y can't be comparable.

Explanation

To solve the problem, we need to determine the bond energy of the O-O bond in two complexes, X and Y, based on their bond orders. Here’s a step-by-step solution:

### Step 1: Identify the complexes and their configurations
We have two complexes:
- Complex X: \( K_6[(CN)_5Co-O-O-Co(CN)_5] \)
- Complex Y: \( K_5[(CN)_5Co-O-O-Co(CN)_5] \)

Both complexes have cobalt in the \( t_{2g}^6 e_g^0 \) configuration.

### Step 2: Determine the oxidation state of cobalt in each complex
In complex X, cobalt is in a +3 oxidation state, while in complex Y, cobalt is in a +2 oxidation state. This is important because the oxidation state affects the bond order of the O-O bond.

### Step 3: Calculate the bond order for the O-O bond in complex X
In complex X, the O-O bond can be represented as \( O_2^{2-} \). The bond order can be calculated using the formula:

\[ \text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals}) - (\text{Number of electrons in anti-bonding orbitals})}{2} \]

For \( O_2^{2-} \):
- Number of electrons in bonding orbitals = 10
- Number of electrons in anti-bonding orbitals = 8

So, the bond order for complex X is:

\[ \text{Bond Order} = \frac{10 - 8}{2} = 1 \]

### Step 4: Calculate the bond order for the O-O bond in complex Y
In complex Y, the O-O bond can be represented as \( O_2 \) (a single bond). The bond order can be calculated similarly:

For \( O_2 \):
- Number of electrons in bonding orbitals = 10
- Number of electrons in anti-bonding orbitals = 7

So, the bond order for complex Y is:

\[ \text{Bond Order} = \frac{10 - 7}{2} = 1.5 \]

### Step 5: Compare the bond orders
From the calculations:
- Bond order in complex X = 1
- Bond order in complex Y = 1.5

### Step 6: Relate bond order to bond energy
Since bond energy is directly proportional to bond order, we can conclude:
- The bond energy of the O-O bond in complex X is lower than that in complex Y.

### Conclusion
Thus, the bond energy of the O-O bond in complex X is less than that in complex Y.