Total Number of Cyclic Isomers for C4H6 Hydrocarbon

To find the total number of cyclic isomers for a hydrocarbon with the molecular formula $\text{C}_4\text{H}_6$, we first calculate its Degree of Unsaturation ($\text{DU}$) or Index of Hydrogen Deficiency ($\text{IHD}$):

$\text{DU} = C + 1 - \frac{H}{2} = 4 + 1 - \frac{6}{2} = 5 - 3 = 2$

Since we are looking for cyclic isomers, each isomer must contain at least one ring ($\text{DU} \ge 1$). The remaining unsaturation ($\text{DU} = 1$) can be present as either:

1. A double bond (monocyclic alkene / exocyclic double bond)
2. A second ring (bicyclic alkane)

---

1. Four-membered ring isomers (Monocyclic with a double bond):

• Cyclobutene

2. Three-membered ring isomers (Monocyclic with an endocyclic double bond):

• 1-Methylcyclopropene
• 3-Methylcyclopropene

3. Three-membered ring isomers (Monocyclic with an exocyclic double bond):

• Methylenecyclopropane

4. Bicyclic isomers (Two fused rings):

• Bicyclo[1.1.0]butane

---

Summary of Isomers:

1. Cyclobutene
2. 1-Methylcyclopropene
3. 3-Methylcyclopropene
4. Methylenecyclopropane
5. Bicyclo[1.1.0]butane

None of these structures exhibit stereoisomerism (optical or geometrical isomerism).

Therefore, the total number of cyclic isomers for $\text{C}_4\text{H}_6$ is 5.