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

[dolpho]

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!

 

[AGNuke]

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.