Final answer:
1,3-dibromocyclopentane has three stereoisomers: one meso form and a pair of enantiomers.
Step-by-step explanation:
The question asks how many stereoisomers of 1,3-dibromocyclopentane exist. In such cyclic compounds, stereoisomers arise due to different spatial arrangements of the substituents, leading to isomers which are not superimposable on their mirror image. For 1,3-dibromocyclopentane, we are concerned with its cis and trans configurations. The cis isomer, where both bromine atoms are on the same side of the cyclopentane ring, is a meso structure because it has an internal plane of symmetry. The trans isomer, with the bromine atoms on opposite sides of the ring, does not have a plane of symmetry, so it exists as a pair of enantiomers. Therefore, a total of three stereoisomers exist: the meso form and the pair of enantiomers.