In formation of polyethylene(free radical method), the free radicals when attached to another ethene molecule release a hydrogen(I think).But addition polymerization does not release and by product, so what happens to that hydrogen atoms?
Consider the reaction stoichiometry.
You begin with ethylene (that is, CH2CH2). The polyethylene chain is a chain of single-bonded carbons. Hence, it is a -[...]-CH2-CH2-CH2-CH2-[...]- chain).
As you can se, no hydrogens are removed by the monomer. So, no hydrogens are released during polymerization.
What is happening in that reaction is an electron transfer, not an atomic transfer: the double bond of ethylene, full of electrons, reacts with the radical and forms a more stable structure with a radical carbon (a radical carbon has three bonds, in this case with C, H and H, and an unpaired electron). The carbon radical reacts with another ethylene monomer: the "old" radical carbon now forms four bonds (C, H, H, plus the new C from the ethylene monomer), the new ethylene monomer loses its double bond, and forms a carbon radical (again, the radical carbon has three bonds and an unpaired electron).
This is the logic of that tipe of polymerization: no hydrogen is involved.