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).
