`overset(Theta)overset(..)CH_(2)-underset(O)underset(||)C-CH_(3) and CH_(2)=underset( :underset(..)O:_(Theta))underset(|)C-CH_(3)` are :

Options

A. Resonating structures
B. Tautomers
C. Geometrical isomers
D. Optical isomers

Answer

To determine the relationship between the two given structures, we need to analyze them step by step.

### Step 1: Identify the Structures
The two structures given are:
1. \( \overset{\Theta}{\overset{..}{CH_2}} \underset{O}{\underset{||}{C}} - CH_3 \)
2. \( CH_2 = \underset{: \underset{..}{O}}{\underset{|}{C}} - CH_3 \)

### Step 2: Analyze the First Structure
In the first structure, we have a carbon atom (C) that is double-bonded to an oxygen atom (O) and single-bonded to a \( CH_3 \) group. The \( CH_2 \) group has a negative charge. This indicates that there is a potential for electron delocalization.

### Step 3: Analyze the Second Structure
In the second structure, we see a double bond between the \( CH_2 \) group and the carbon atom that is also bonded to the oxygen atom. The oxygen atom has a lone pair of electrons, which can interact with the double bond.

### Step 4: Determine the Type of Relationship
To classify the relationship between these two structures, we need to consider the definitions of resonating structures, tautomers, geometrical isomers, and optical isomers:

- **Resonating Structures**: These are structures that differ only in the arrangement of electrons, not in the arrangement of atoms. They typically involve delocalization of electrons.
- **Tautomers**: These are isomers that can interconvert by the movement of a hydrogen atom and a double bond.
- **Geometrical Isomers**: These are isomers that differ in the spatial arrangement of groups around a double bond.
- **Optical Isomers**: These are isomers that have chiral centers and can rotate plane-polarized light.

### Step 5: Conclusion
In this case, the two structures show delocalization of electrons between the carbon and oxygen atoms. There is no shifting of atoms, and thus they do not qualify as tautomers. They also do not exhibit geometrical or optical isomerism because there are no chiral centers or different spatial arrangements around a double bond.

Therefore, the correct classification for the two structures is **resonating structures**.

### Final Answer
The two structures are **resonating structures**.

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