Organic chemistry - alkanes step up reaction

Well I was studying organic chemistry, and I came across this reaction for increasing the length of the carbon chain. Upon asking my teacher about the following reaction, she said she was unsure about it. Is this a valid reaction? And if it is, can you please provide the name of the reagent and the actual mechanism?


![enter image description here](https://i.stack.imgur.com/odbw2.png)




I think the reagent you're talking about is ketene (R=H in the figure below). It is a linear molecule (the central carbon is $\ce{sp}$ hybridized) and very reactive. 


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


When mixed with an alkane and heated it dimerizes to form diketene rather than react with the alkane.


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


However, when irradiated with light, ketene will produce the reactive carbene "methlylene" ($\ce{CH2:}$). When this photolysis is performed in the presence of an alkane, the methylene will insert itself into the various $\ce{C-H}$ bonds like you've drawn. However the reaction is not synthetically useful for a number of reasons. For example, the $\ce{C-H}$ insertion reaction is very indiscriminate and a variety of products will be formed if different $\ce{C-H}$ bonds exist in the molecule. 


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I would describe the reaction as a C-H insertion reaction of the carbene generated in situ from ketene. The reaction starts with an initial release of carbon monoxide to generate the highly electrophilic 6 electrons carbene species, which is then involved in a C-H insertion process. The C-H insertion can proceed through two mechanism: via singlet state or triplet state of the carbene. The carbene is a very electrophilic sp2 hybridized species with 6 electrons: a lone pair and two pairs in bond orbitals (with H atoms). Singlet carbenes have the lone pair of electrons in a nonbonding sp2 orbital and have an empty p orbital, while triplet carbenes have two unpaired electrons, one in a sp2 and the other in a p orbital. C-H insertion mediated by singlet carbenes is believed to proceed through a concerted mechanism, with the side-on approach of the carbene which provide constructive orbitals overlapping. Triplet carbene insertions should follow a two-step radical pathway, but it is generally accepted that the reaction proceed through singlet state carbenes (supported by retention of stereochemistry observed when if the C-H bond is at a stereogenic center).


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