`CH_3-overset(O)overset(||)Cunderset(a)(-)Ounderset(b)(-)CH_3` ,
The correct relation between the bond lengths a and b is:

Options

A. `a=b`
B. `bgta`
C. `blta`
D. Impossible to predict

Explanation

To determine the correct relationship between the bond lengths \( a \) and \( b \) in the compound \( CH_3-C(=O)-O-CH_3 \), we will analyze the structure and the effects of resonance on the bonds.

### Step-by-Step Solution:

1. **Identify the Structure**:
The given compound is \( CH_3-C(=O)-O-CH_3 \). Here, we have a carbonyl group (C=O) connected to an oxygen atom, which is further connected to another methyl group (CH3).

2. **Label the Bonds**:
- Let bond \( a \) be the bond between carbon (C) and oxygen (O) in the carbonyl group (C=O).
- Let bond \( b \) be the bond between carbon (C) and oxygen (O) in the ether part (C-O).

3. **Understand Resonance**:
The structure can exhibit resonance. The lone pairs on the oxygen can participate in resonance by forming a double bond with the carbon, leading to different resonance structures. This means that the C-O bond can exhibit double bond character due to resonance.

4. **Analyze Bond Character**:
- In the carbonyl bond (C=O), the bond is a double bond, which is typically shorter and stronger than a single bond.
- In the ether bond (C-O), it is a single bond, which is longer and weaker compared to a double bond.

5. **Compare Bond Lengths**:
- Since bond \( a \) (C=O) has double bond character, it will be shorter than bond \( b \) (C-O), which is a single bond.
- Therefore, the bond length of \( a \) is less than the bond length of \( b \).

6. **Conclusion**:
The correct relationship between the bond lengths is:
\[ b > a \]