Final answer:
An electron in the bonding molecular orbital has lower energy due to increased electron-nucleus attraction and overlapping orbitals that stabilize the system and reduce potential energy.
Step-by-step explanation:
An electron in the bonding molecular orbital in the H₂ molecule has a lower energy than an electron in the 1s atomic orbital of either of the separated hydrogen atoms because as the hydrogen atoms approach each other, their 1s orbitals begin to overlap, leading to increased electron-nucleus attraction.
This overlap allows the electrons to be simultaneously attracted to both nuclei, thereby stabilizing the system and decreasing the potential energy. Consequently, the energy in the bonding molecular orbital is lower than in the individual atomic orbitals.