Stereochemistry is the study of the different spatial arrangements of atoms in a given molecule. The stereochemistry of radical halogenations can be understood from three different situations:

Halogenation to form a new chiral center:

For example, radical halogenation of butane forms the products 2-chlorobutane and 1-chlorobutane, where the former has a chiral center. However, 2-chlorobutane is obtained as a racemic mixture due to the trigonal planar structure of the formed radical intermediate.

Halogenation at an existing chiral center:

If the radical halogenation occurs at an existing chiral carbon, a 1:1 ratio of enantiomers is formed. This is also because of the trigonal planar structure of the radical intermediate, where the chirality of the starting material has been lost.

Halogenation to generate a second chiral center:

If the radical halogenation of an enantiomer occurs at a position other than the chiral carbon, diastereomers are formed. In this case, also the trigonal planar radical intermediate is formed without affecting the existing chiral center. This chiral center differentiates the two faces of the radical intermediate, so the halogen attacks unequally at two faces leading to the formation of unequal amounts of diastereomers.