Question

"when oxygen molecules split into single atoms that have unpaired electrons, they become unstable free radicals that seek other atoms or molecules to bond to."

Answer 1

when oxygen molecule  (O2) is decomposed into single atom then each single atom cannot exists and they tend to react with another atom to form a molecule.

most likely these atoms which were created by decomposition of (O2) tend to react react with hydrogen(H2) molecule to form water (H2O)

there reactions are given below

O2 decomposes into O+O

then it reacts with hydrogen and gives

H2+O=H2O