Halogenation of alkanes is a radical process, that tends to be indiscriminate (i.e. dihalogenated products are possible in that radical mechanisms can be quite unselective):
#"H"_3"CCH"_2"CH"_3 +"Br"_2 stackrel(hnu)rarr "H"_3"CCHBrCH"_3 +"HBr"#
The mechanism of halogenation is in your text, and the starting point is the homolysis of the bromine molecule by UV light:
#Br_2 +hnurarr2dotBr#
The #dotBr# radical, a 7 electron species, is very reactive inasmuch as when it reacts it generates another radical species to continue the chain of reaction:
#R-CH_3+dotBr rarrR-dotCH_2 +HBr#
#R-dotCH_2 +Br_2 rarr RCH_2Br + dotBr#
And the #dotBr# radical can continue the chain of reaction.......The reaction can terminate by the coupling of 2 radicals:
#R-dotCH_2 +dotCH_2R rarr RH_2C-CH_2R#
The presence of such #C-C# coupled products is good evidence for the intermediacy of these radicals. Most of the time, however, radical halogenation of alkanes will lead to a mess (whereas radical halogenation of benzyl groups is a bit more discriminating in that the stabilization of a benzyl radical allows selective formation of #PhCH_2Br#).
