The atomic orbitals of hydrogen atoms, specifically H1 (hydrogen with one electron) and H2 (hydrogen molecule with two electrons), can be at the same energy level due to a phenomenon called orbital degeneracy.
In the case of H1, the single electron occupies the lowest energy orbital, known as the 1s orbital. This orbital is spherically symmetric and centered around the hydrogen nucleus.
When two hydrogen atoms combine to form H2, their atomic orbitals overlap and interact, resulting in the formation of molecular orbitals. The two 1s atomic orbitals of the hydrogen atoms combine to form two molecular orbitals: a lower-energy bonding orbital (σ bonding orbital) and a higher-energy antibonding orbital (σ* antibonding orbital).
The key concept here is that for the H2 molecule to be stable, the electrons must occupy the lower-energy bonding molecular orbital. Both electrons will have opposite spins to follow the Pauli exclusion principle. Since each molecular orbital can accommodate two electrons with opposite spins, the H2 molecule has its two electrons in the bonding orbital.
Now, the reason why the atomic orbitals of H1 and H2 are considered to be at the same energy is that the energy levels of the atomic and molecular orbitals are approximately equal in energy due to the similar electronic environments. The energy difference between them is relatively small, making them essentially degenerate. However, it's important to note that the molecular orbital energy levels may experience slight shifts compared to the isolated atomic orbitals due to molecular interactions.
So, in summary, the atomic orbitals of H1 and H2 can be considered at the same energy because they are approximately degenerate, and the electrons in the H2 molecule occupy the lower-energy molecular bonding orbital.