Add Br2/HV to (S)-1,2-Dibromobutane: Optically Inactive Product

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When adding Br2/HV to (S)-1,2-dibromobutane, the radical bromine is expected to preferentially bond to the carbon atom that already has a bromine substituent, leading to the formation of 1,2,2-tribromobutane. The reasoning behind this is that the intermediate radical formed during the reaction is most stable at the second carbon. This stability is attributed to the +M (mesomeric) effect from the adjacent bromine atom and the hyperconjugation effects from neighboring carbon atoms. The discussion also notes that the final product is optically inactive, which suggests that the reaction leads to a racemic mixture or a symmetrical compound.
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If we add br2 / hv to (s)-1,2-dibromobutane. Where would the radical bromine go? The book hints that the product is an optically inactive substance.

So I'm guessing that the bromine would go towards the carbon that has the bromine atom on it making 1,2,2-tribromobutane?

Would appreciate any clarification!
 
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Because the intermediate radical of 1,2-dibromobutane will be most stable at 2nd Carbon. Not only it is getting +M effect of Br atom attached to it, it is also experiencing Hyperconjugation from neighbouring C-atoms.
 
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