What is the difference between homolytic and heterolytic cleavage?
In heterolytic cleavage, a covalent bond breaks in such a way that one fragment gets both of the shared electrons.
In homolytic cleavage, a covalent bond breaks in such a way that each fragment gets one of the shared electrons.
The word heterolytic comes from the Greek heteros, "different", and lysis, "loosening".
If both atoms are originally uncharged, the process generates a cation and an anion.
Heterolytic cleavage is most likely to occur in polar bonds. The electrons move toward the more electronegative atom.
An example is the heterolytic cleavage of the C-Br bond in t-butyl bromide.
Since Br is more electronegative than C, the electrons move to the Br. We get a t-butyl cation and a bromide anion.
The word homolytic comes from the Greek homoios, "equal".
For example, the homolytic cleavage of a Br-Br bond is
Homolytic cleavage produces free radicals — atoms with unpaired valence electrons.
Here is a video on homolytic and heterolytic cleavage.