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Normally, a carbon atom is $\ce{sp^3}$ hybridized, whereas in a transition state five bonds are present, then what's the hybridisation of carbon?

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In transition state of SN2 mechanism, the carbon atom is $\ce{sp^2}$ hybridised due to its planar structure. At this point, carbon almost acquires 'pentavalency' with three full bonds and two 'partial' bonds, and a planar complex is formed, which is $\ce{sp^2}$ hybridised.

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