Assertion The `d_(C-O)` in bridging carbonyl geroup is longer than that of terminal carbonyl group
Reason With increase in extent of synergic bonding the `C-O` bond length increases .

Options

A. If both `(A)` and ` (R )` are correct and `(R )` is the correct explanation of `(A ) ` .
B. If both `(A)` and ` (R )` are correct and `(R )` is the correct explanation of `(A ) ` .
C. If`(A)` is correct, but `( R )` is incorrect .
D. Both `(A)` and `(R ) ` are incorrect .

Explanation

To solve the question regarding the assertion and reason about the bond lengths in bridging and terminal carbonyl groups, we can break it down into a step-by-step analysis.

### Step-by-Step Solution:

**Step 1: Understand the Assertion**
- The assertion states that the `C-O` bond length in a bridging carbonyl group is longer than that in a terminal carbonyl group.
- **Hint:** Recall the definitions of bridging and terminal carbonyl groups. Bridging carbonyls connect two metal centers, while terminal carbonyls are bonded to only one metal center.

**Step 2: Analyze the Reason**
- The reason provided states that with an increase in the extent of synergic bonding, the `C-O` bond length increases.
- **Hint:** Consider what synergic bonding entails. It involves both sigma and pi bonding interactions between the metal and the carbonyl group.

**Step 3: Explore Bonding in Carbonyl Groups**
- In carbonyl complexes, the carbonyl group can participate in two types of bonding: sigma (σ) and pi (π) bonds.
- In terminal carbonyls, the carbonyl group typically forms a stronger bond with the metal due to the presence of only one metal center.
- **Hint:** Think about how the number of metal centers involved might affect the bond strength and length.

**Step 4: Compare Bond Lengths**
- In bridging carbonyls, the `C-O` bond is influenced by two metal centers, which can lead to a decrease in bond strength due to increased electron delocalization and shared bonding.
- This results in a longer `C-O` bond in bridging carbonyls compared to terminal carbonyls.
- **Hint:** Remember the relationship between bond strength and bond length: stronger bonds are typically shorter.

**Step 5: Conclusion on Assertion and Reason**
- Both the assertion and reason are correct. The assertion correctly states that the `C-O` bond length in bridging carbonyls is longer than in terminal carbonyls, and the reason correctly explains this phenomenon through the concept of synergic bonding.
- **Hint:** Consider how the explanation connects the two statements logically.

### Final Conclusion:
- Therefore, the correct answer is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.