Is it possible to create a ketone using ozonolysis, when you have an alkene with no alkyl groups?

Can Butan-2-one ($\ce{CH3-CH2-CO-CH3}$) be created from Butene ($\ce{C4H8}$) using ozonolysis? 




I don't think that's possible. 


The general reactions scheme for ozonolysis is as follows: [![enter image description here](https://i.stack.imgur.com/axmTI.jpg)](https://i.stack.imgur.com/axmTI.jpg)


Consider the case of butene: 


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


Herein $R\_1$ and $R\_3$ can be identified as methyl groups, and similarly $R\_2$ and $R\_4$ are plain old hydrogens. Following the reaction scheme, one would naturally expect **Ethanal** as a product (if you use $\ce{Zn}$, ethanoic acid may be obtained if you use something else).


I'll drop by later and write out a mechanism perhaps.


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