Four isomeric optically active compounds `overset (NaHCO_3) rarr CO_2 (g) (A, B , C, D) (C_4 H_8 O_3)`
Compound `(A) overset (LAH) rarr ( E)` (Archiral compound)
Compound `(B) overset (KMnO_4) underset (or CrO_3) rarr` Inert to oxidation.
Compound `( C) underset (NaOI//H_3 O^(oplus)) rarr CHI_3 (Yellow ppt.) + Compound (F)`.
Compound `(D)` is :

Options

A. `(I)`
B. `(II)`
C. `(III)`
D. `(IV)`

Explanation

To solve the problem, we need to identify the four isomeric optically active compounds (A, B, C, D) with the molecular formula C₄H₈O₃ and determine the structure of compound D based on the given reactions.

### Step 1: Determine the Degree of Unsaturation (DU)
The formula for calculating the degree of unsaturation (DU) is:
\[ DU = \frac{(2 \times \text{number of carbons}) + 2 - \text{number of hydrogens}}{2} \]
For C₄H₈O₃:
- Number of carbons (C) = 4
- Number of hydrogens (H) = 8

Calculating DU:
\[ DU = \frac{(2 \times 4) + 2 - 8}{2} = \frac{8 + 2 - 8}{2} = \frac{2}{2} = 1 \]
This indicates that there is one degree of unsaturation, suggesting the presence of one carbonyl group (C=O) or a double bond.

### Step 2: Identify Possible Structures for Compounds A, B, C, and D
Given that we have four isomeric optically active compounds, we can propose the following structures:

1. **Compound A**: A possible structure could be a hydroxy acid, such as 2-hydroxybutanoic acid (CH₃-CH(OH)-CH₂-COOH).
2. **Compound B**: This compound is inert to oxidation, suggesting it could be a tertiary alcohol or an ether. A possible structure could be 2-methyl-2-butanol (CH₃-C(OH)(CH₃)-CH₂-CH₃).
3. **Compound C**: This compound reacts with NaOI/H₃O⁺ to yield CH₃I and another compound. A suitable structure could be 3-hydroxybutanoic acid (CH₃-CH(OH)-CH₂-COOH).
4. **Compound D**: This compound is formed from compound C and should be a product of the reaction with NaOI/H₃O⁺.

### Step 3: Reaction of Compound C
When compound C (3-hydroxybutanoic acid) reacts with NaOI in the presence of H₃O⁺, it undergoes the iodoform reaction, producing CH₃I (iodoform) and another compound (which is likely to be a carboxylic acid).

### Step 4: Identify Compound D
From the reaction, we can deduce that compound D is likely to be a carboxylic acid derived from the oxidation of compound C. Given the structure of compound C, compound D could be 3-oxobutanoic acid (CH₃-CO-CH₂-COOH).

### Conclusion
Thus, the structure of compound D is 3-oxobutanoic acid (or acetoacetic acid).