When an optically active amine 'A' having molecular formula `C_(4)H_(11)N` is subjected to Hoffmann's exhaustive methylation followed by hydrolysis, an alkene 'B' is produced which upon ozonolysis and subsequent hydrolysis yields formaldehyde and propanal. The amine 'A' is

Options

A. `CH_(3)-underset(NH_(2))underset("| ")"CH"CH_(2)CH_(3)`
B. `CH_(3)NH-underset(CH_(3))underset("| ")"CH"-CH_(3)`
C. `CH_(3)-underset(CH_(3))underset("| ")"NC"H_(2)CH_(3)`
D. `CH_(3)CH_(2)CH_(2)CH_(2)NH_(2)`

Answer

To solve the problem, let's break it down step by step:

### Step 1: Identify the structure of the optically active amine 'A'
Given the molecular formula \(C_4H_{11}N\), we need to find an optically active amine. An optically active amine must have a chiral center. A suitable candidate is 2-aminobutane, which has the structure:

```
CH3
|
CH3-CH-CH2-NH2
|
CH3
```

### Step 2: Perform Hofmann's exhaustive methylation
Hofmann's exhaustive methylation involves treating the amine with excess methyl iodide (\(CH_3I\)) and a strong base (like \(Ag_2O\)). This results in the formation of a quaternary ammonium salt. In our case, 2-aminobutane will be converted into a quaternary ammonium salt, which can be represented as:

```
CH3
|
CH3-CH-CH2-N(CH3)3+
|
CH3
```

### Step 3: Hydrolysis of the quaternary ammonium salt
Upon hydrolysis, the quaternary ammonium salt will lose a methyl group, leading to the formation of an alkene. The hydrolysis will yield the alkene 'B', which is 2-butene:

```
CH3
|
CH3-CH=CH2
```

### Step 4: Ozonolysis of alkene 'B'
The ozonolysis of 2-butene will cleave the double bond, producing two carbonyl compounds. The ozonolysis reaction can be represented as follows:

```
CH3-CH=CH2 + O3 → CH3CHO + HCHO
```

### Step 5: Hydrolysis of ozonolysis products
After ozonolysis, the products are formaldehyde (HCHO) and propanal (CH3CHO). This confirms that the ozonolysis of alkene 'B' produces the required aldehydes.

### Conclusion
Thus, the optically active amine 'A' is 2-aminobutane.

### Final Answer:
The amine 'A' is **2-aminobutane**.

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