`PhCH_(2)-overset(CH_(3))overset(|)(CH)-CH_(2)-overset(O)overset(||)C-NH_(2)overset(Br_(2),NaOH)toX, X` is

Options

A. `CH_(3)-overset(CH_(3))overset(|)(CH)-CH_(2)-NH-Ph`
B. `Ph-Ch_(2)-overset(CH_(3))overset(|)(CH)-underset(OH)underset(|)(CH)-NH_(2)`
C. `Ph-CH_(2)-overset(CH_(3))overset(|)(CH)-CH_(2)-NH_(2)`
D. `PH-overset(CH_(3))overset(|)(CH)-overset(CH_(3))overset(|)(CH)-underset(O)underset(||)C-NH_(2)`

Answer

To solve the problem, we need to analyze the reaction of the compound given with bromine (Br₂) and sodium hydroxide (NaOH), which is a classic example of the Hofmann degradation reaction. Here’s the step-by-step solution:

### Step 1: Identify the Compound
The compound given is PhCH₂(CH)CH₂(C=O)NH₂, which can be simplified as an amide (specifically a primary amide) where the carbonyl group (C=O) is attached to the nitrogen (NH₂).

### Step 2: Understand the Reaction Conditions
The reaction involves bromine (Br₂) and sodium hydroxide (NaOH). This combination is indicative of the Hofmann degradation reaction, which is used to convert primary amides into primary amines with the loss of one carbon atom as carbon dioxide (CO₂).

### Step 3: Mechanism of the Hofmann Reaction
1. **Formation of N-bromoamide**: The base (NaOH) will deprotonate the amide nitrogen, forming a negatively charged nitrogen. This nitrogen can then attack bromine (Br₂), leading to the formation of an N-bromoamide.

2. **Formation of Isocyanate**: The N-bromoamide will undergo further reaction where the bromine leaves, and a rearrangement occurs, resulting in the formation of an isocyanate intermediate.

3. **Hydrolysis of Isocyanate**: The isocyanate will react with water (from the NaOH) to form a carbamic acid, which will then decompose to release carbon dioxide (CO₂) and yield the primary amine.

### Step 4: Identify the Product
After the reaction, the original compound will lose one carbon atom in the form of CO₂, and the remaining structure will be a primary amine. Thus, the product (X) will be PhCH₂(CH)CH₂NH₂.

### Final Answer
The product X is PhCH₂(CH)CH₂NH₂ (a primary amine).