Number of cyclic isomers of C4H6 [duplicate]








**This question already has answers here**:
 
 




[Hydrocarbons with only 4 carbon atoms](/questions/19475/hydrocarbons-with-only-4-carbon-atoms)

 (2 answers)
 

Closed 6 years ago.



I faced a question 



> 
> How many cyclic isomers are possible for $\ce{C4H6}$?
> 
> 
> 


I and my friend found the following four.
![enter image description here](https://i.stack.imgur.com/A42Q6.jpg)


But the answer key says there are 5. So what's the other one?




You can answer such questions using D.U. (Degree of unsaturation)


The formula is $\mathrm{C + 1 - }\frac{H + X - N}{2}$



```
C = Carbon.
H = Hydrogen.
X = Halogen.
N = Nitrogen.

```

**If you get D.U. to be one, then in the structure there could be:**


* 1 double bond.
* 1 ring.


Let's take an example of $\ce{C4H8}$ which has D.U. equal to one.


* It can have three structures of **1 double bond**:


![enter image description here](https://i.stack.imgur.com/v8mN5m.jpg)


* It can have two structures of **1 ring**:


![enter image description here](https://i.stack.imgur.com/KMkpJm.jpg)


**Now for D.U. equal to two, the possibilities are:**


* 2 double bond.
* 2 ring.
* 1 double bond and 1 ring.
* 1 triple bond.


Let's take your example of $\ce{C4H6}$ which has D.U. equal to two:


* It can have two structures of **2 double bond**:


![enter image description here](https://i.stack.imgur.com/uQvf5m.jpg)


* It can have one structure of **2 ring**:


![enter image description here](https://i.stack.imgur.com/P4unzm.jpg)


* It can have four structures of **1 double bond + 1 ring**:


![enter image description here](https://i.stack.imgur.com/nWrTtm.jpg)


* It can have two structures of **1 triple bond**:


![enter image description here](https://i.stack.imgur.com/wNMxMm.jpg)


So, the answer is 5 cyclic isomers as you can see above.


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