Only one of the following amines will lose its nitrogen atom as trimethyl amine by repeated Hofmann elimination reactions :

Options

A.
B.
C.
D.

Explanation

To solve the problem of which amine will lose its nitrogen atom as trimethylamine by repeated Hofmann elimination reactions, we need to analyze the given options based on the stability of the nitrogen atom in the amine structure. The Hofmann elimination involves the formation of a nitrogen cation, which is more likely to occur in a planar structure. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding Hofmann Elimination
Hofmann elimination is a reaction where a quaternary ammonium salt loses an amine to form an alkene and a nitrogen gas. For this process to occur, the nitrogen must be able to adopt a planar structure (sp² hybridization) to stabilize the positive charge that forms during the reaction.

**Hint:** Remember that for a nitrogen atom to participate in Hofmann elimination, it needs to be in a planar configuration.

### Step 2: Analyzing the Options
We need to evaluate each option to determine which amine can achieve this planar structure.

- **Option A:** Contains a nitrogen in a cyclic structure that does not allow for a planar arrangement conducive to Hofmann elimination.

**Hint:** Check if the nitrogen can adopt a planar structure in this option.

- **Option B:** Similar to option A, this nitrogen also cannot achieve a planar configuration due to steric hindrance from the surrounding groups.

**Hint:** Look for steric hindrance that might prevent planarity.

- **Option C:** This option has a nitrogen atom with one methyl group and other groups that may hinder the formation of a stable cation.

**Hint:** Consider the arrangement of groups around the nitrogen atom.

- **Option D:** This option features a nitrogen atom at a bridging position, which is less stable when a positive charge is formed. The instability encourages the nitrogen to leave the structure during Hofmann elimination.

**Hint:** Identify if the nitrogen's position could lead to instability and promote its elimination.

### Step 3: Conclusion
After analyzing all options, we find that **Option D** is the correct answer. The nitrogen atom in this option is in a bridging position, which makes it less stable when a positive charge is formed. This instability will lead to the nitrogen being expelled as trimethylamine during repeated Hofmann elimination reactions.

**Final Answer:** The amine that will lose its nitrogen atom as trimethylamine by repeated Hofmann elimination reactions is **Option D**.