Answer :

Homolytic FissionConsider the fission of a single covalent bond in the substance X-YX-Y  X. + Y.The dots in the equation represent unpaired electrons that came from the covalent bond. The electrons have been re-distributed equally and this is known as homolytic fission.The following are real examples of homolytic fission.Br-Br  Br. + Br.Two identical bromine atoms are produced from a bromine molecule. As the atoms each have an unpaired electron, they are very reactive units.This can also happen to bonds in certain organic molecules where R represents part of the organic molecule.R-Y  R. + Y.R. is also a reactive unit as it has an unpaired electron, but it cannot be described as an atom. It is known as a free radical.Homolytic fission is more likely to happen in when the electrons are shared equally between the atoms involved in the fission. 
Heterolytic Fission
This can happen in one of two ways, depending on the electronegativity values of the two atoms concerned:X-Y  X+ + Y-X-Y  X- + Y+A real example of heterolytic fission is shown below to hydrogen chloride. The chlorine atom takes both bonding electrons and becomes a negative ion which can also be shown as :Cl-H-Cl  H+ + Cl-The compound bromomethane (and others) can split heterolytically as shown:CH3-Br  CH3+ + Br-The carbocation (or carbonium ion) is a reactive and therefore, short-lived unit. This is derived from the term 'cation', used in inorganic chemistry, for a positive ion or an ion that is attracted to the cathode or negative electrode.Heterolytic fission is more likely to happen in when the electrons are shared unequally between the atoms involved in the fission.Depending on the nature and electronegativity of the atom attached in place of bromine, the bond can break heterolytically to form a negative ion instead of a carbocation. Such negative ions are known as carbanions. This is derived from the term 'anion', used in inorganic chemistry, for a negative ion or an ion that is attracted to the anode or positive electrode.
Homolytic fission is a type of fission in which the The electrons have been re-distributed equally.Whereas Heterolytic fission is more likely to happen in when the electrons are shared unequally between the atoms involved in the fission.
Homolytic fission-- R-Y⇒ ·R+Y·..........[dot(·) represent unpaired electron]
and Br-Br⇒·Br+Br·
Heterolytic fission--X-Y⇒X⁻ + Y⁺
and H-Cl⇒ H⁺ + Cl⁻

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