The total number of optically active isomers for `CH_(2)OH(CHOH)_(3)CHO` are

Options

A. 16
B. 8
C. 4
D. 2

Explanation

To determine the total number of optically active isomers for the compound CH₂OH(CHOH)₃CHO, we need to follow these steps:

### Step 1: Identify the Structure
The compound can be represented as:
- CH₂OH (a hydroxymethyl group)
- (CHOH)₃ (three hydroxymethyl groups attached to a carbon chain)
- CHO (an aldehyde group)

### Step 2: Identify Chiral Centers
A chiral center is a carbon atom that is bonded to four different groups. In the given compound, we need to analyze each carbon atom to determine if it is chiral.

1. **First Carbon (C1)**: CH₂OH - This carbon has two hydrogen atoms, so it is **not chiral**.
2. **Second Carbon (C2)**: CHOH - This carbon is bonded to:
- OH (hydroxyl group)
- H (hydrogen)
- CH₂OH (hydroxymethyl group)
- CHO (aldehyde group)
This carbon is **chiral**.
3. **Third Carbon (C3)**: CHOH - Similar to C2, this carbon is bonded to:
- OH (hydroxyl group)
- H (hydrogen)
- CH₂OH (hydroxymethyl group)
- Another CHOH (from the next carbon)
This carbon is also **chiral**.
4. **Fourth Carbon (C4)**: CHO - This carbon is part of the aldehyde group and is bonded to:
- O (from the carbonyl)
- H (hydrogen)
- CHOH (from the previous carbon)
- CH₂OH (from the first carbon)
This carbon is **not chiral**.

### Step 3: Count the Chiral Centers
From the analysis, we find that there are **two chiral centers** (C2 and C3).

### Step 4: Calculate the Number of Optically Active Isomers
The formula to calculate the number of optically active isomers based on the number of chiral centers (n) is given by:
\[ \text{Number of isomers} = 2^n \]
Where n is the number of chiral centers.

In our case, we have:
\[ n = 2 \]
Thus, the number of optically active isomers is:
\[ 2^2 = 4 \]

### Conclusion
The total number of optically active isomers for CH₂OH(CHOH)₃CHO is **4**.

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