How many structurally isomeric cyclic isomers of molecular formula `C_(3)H_(7)N` are possible:

Explanation

To determine how many structurally isomeric cyclic isomers of the molecular formula \( C_3H_7N \) are possible, we can follow these steps:

### Step 1: Calculate the Double Bond Equivalent (DBE)
The formula for calculating the double bond equivalent (DBE) is:
\[ DBE = \frac{(C - H + X + N)}{2} + 1 \]
Where:
- \( C \) = number of carbon atoms
- \( H \) = number of hydrogen atoms
- \( X \) = number of halogen atoms (none in this case)
- \( N \) = number of nitrogen atoms

For \( C_3H_7N \):
- \( C = 3 \)
- \( H = 7 \)
- \( N = 1 \)

Plugging in the values:
\[ DBE = \frac{(3 - 7 + 0 + 1)}{2} + 1 = \frac{-3}{2} + 1 = -1 + 1 = 0 \]

This indicates that there are no double bonds or rings present in the structure.

### Step 2: Identify Possible Cyclic Structures
Since we are looking for cyclic isomers, we can consider the following structures:

1. **Cyclopropylamine**: A three-membered ring with an amine group.
- Structure:
\[ \text{Cyclic structure: } \text{C}_3\text{H}_6\text{N} \]
- This structure has the amine group attached to one of the carbon atoms in the cyclopropane.

2. **Isopropylamine**: A branched structure where the nitrogen is attached to a carbon chain.
- Structure:
\[ \text{Cyclic structure: } \text{C}_3\text{H}_7\text{N} \]
- This structure has a nitrogen atom bonded to a carbon chain.

3. **N-Methylcyclopropylamine**: A three-membered ring with a methyl group attached to the nitrogen.
- Structure:
\[ \text{Cyclic structure: } \text{C}_3\text{H}_7\text{N} \]

4. **Cyclobutylamine**: A four-membered ring with an amine group.
- Structure:
\[ \text{Cyclic structure: } \text{C}_4\text{H}_9\text{N} \]
- This structure has the nitrogen atom in a four-membered ring.

### Step 3: Count the Isomers
After considering the possible cyclic structures, we find that there are four distinct cyclic isomers for the molecular formula \( C_3H_7N \).

### Conclusion
Thus, the total number of structurally isomeric cyclic isomers of \( C_3H_7N \) is **four**.

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