The molecular formula C₄H₆ indicates a hydrocarbon with 4 carbon atoms and 6 hydrogen atoms. For cyclic isomers, we need to consider structures where the carbon atoms form a ring. The degree of unsaturation helps determine the number of rings or multiple bonds. The formula for degree of unsaturation is:

$U=\frac{2C+2-H-X+N}{2}$, where C is carbon atoms, H is hydrogen atoms, X is halogen atoms, and N is nitrogen atoms. For C₄H₆, C=4, H=6, X=0, N=0, so:

$U=\frac{2\times 4+2-6-0+0}{2}=\frac{8+2-6}{2}=\frac{4}{2}=2$. This means there are 2 degrees of unsaturation, which could be due to a triple bond, two double bonds, one double bond and one ring, or two rings.

For cyclic isomers, we consider structures with at least one ring. The possible cyclic isomers for C₄H₆ are:

Step 1: Cyclic isomers with one ring

- Cyclobutene: A 4-membered ring with one double bond. This has the formula C₄H₆ and is a valid isomer.

- Methylenecyclopropane: A 3-membered ring with a methylene group (=CH₂) attached. This is also C₄H₆ and is a distinct isomer.

Step 2: Cyclic isomers with two rings

- Bicyclo[1.1.0]butane: A structure with two fused rings, which satisfies C₄H₆. This is another isomer.

Additionally, consider stereoisomers for cyclobutene. Cyclobutene can exhibit cis-trans isomerism, but due to the small ring size, the double bond is planar, and no stereoisomers are possible for this formula. Similarly, the other structures do not have chiral centers or geometric isomerism that would produce additional cyclic isomers under this count.

Thus, the total cyclic isomers are: cyclobutene, methylenecyclopropane, and bicyclo[1.1.0]butane. So, there are 3 cyclic isomers.

Final Answer: 3

Related Topics

Degree of Unsaturation: This is a calculation used to determine the number of rings or multiple bonds in a molecule based on its molecular formula. It helps in predicting possible structures for organic compounds.

Cycloalkenes and Bicyclic Compounds: Cycloalkenes are cyclic hydrocarbons with double bonds, while bicyclic compounds contain two fused rings. Understanding their stability and isomerism is key in organic chemistry.

Formulae

Degree of Unsaturation: $U=\frac{2C+2-H-X+N}{2}$, where C is number of carbon atoms, H is hydrogen atoms, X is halogen atoms, N is nitrogen atoms.