Final answer:
EcoRI would produce the most stable sticky ends due to longer overhangs and more potential hydrogen bonds compared to the other enzymes listed.
Step-by-step explanation:
Among the restriction enzymes listed (BamHI, EcoRI, Haell, and PstI), the stability of the sticky ends formed after cutting DNA depends on two main factors: the length of the overhangs and the GC content of the sticky ends. GC pairs are more stable than AT pairs due to the presence of three hydrogen bonds in GC pairs compared to two in AT pairs. BamHI produces a 5' GATCC overhang, EcoRI results in a 5' AATT overhang, Haell generates blunt ends, and PstI creates a 3' CTGCA overhang.
Considering these factors, EcoRI would generate sticky ends that are the most stable, because it produces a four-nucleotide overhang which allows more base pairs to form hydrogen bonds between complementary sticky ends, compared to PstI which produces a shorter three-nucleotide overhang. BamHI has an intermediate overhang length but also a lower GC content, giving EcoRI an advantage in terms of stability upon annealing. Hall is ruled out as it produces blunt ends that do not have overhangs capable of base pairing.