Show the homolysis reaction of benzoyl peroxide,$(C_6H_5CO)_2O_2$.

The homolysis of benzoyl peroxide $(C_6H_5CO)_2O_2$ involves the cleavage of the $O-O$ bond to form two benzoyloxy radicals,which subsequently undergo decarboxylation to form phenyl radicals and carbon dioxide:
$(C_6H_5CO)_2O_2$ $\xrightarrow{\text{Homolysis}} 2 C_6H_5COO\bullet$ $\rightarrow 2 C_6H_5\bullet + 2 CO_2$