When ethylbenzene is treated with nbs and irradiated with uv light, two stereoisomeric compounds are obtained in equal amounts. draw the products and explain why they are obtained in equal amounts:

1-Phenyl ethyl radical is formed as an intermediate in the reaction and since Phenyl ethyl radical has  a trigonal planar geometry so it is a planar molecule having two faces.  So Br radical radical can recombine  with the  two faces with equal probability  leading to a racemic mixture in 50:50ratio of products.Hence two products are formed which are known as enatiomers.

Explanation:

When we irradiate the ethylbenzene with UV light , it leads to homolytic cleavage and 1- Phenyl ethyl free radical is generated.

Phenyl ethyl free radical is generated because it is very stable as it is on a  secondary carbon center as well as on a benzylic position so it can be stabilized by the resonance as well as inductive effect at the secondary carbon center.

NBS(N-bromosuccinimide) is a source of bromine radical and provides bromine free radical.

Once the  1- Phenyl ethyl free radical is generated then bromine free radical can recombine with benzyl free radical leading to product formation.

Since  1- Phenyl ethyl free radical  has a trigonal planar geometry so it is a planar molecule which has two faces  and hence the radical recombination with bromine free radical can occur with either of the two faces available.

Kindly refer the attachments for structure as well as the mechanism of the reaction.

So two isomers which are enantiomers are produced  are obtained.