Which of the following would you expect to be more favorable energetically? Explain. a. an \(\mathrm{H}_{2}\) molecule in which enough energy is added to excite one electron from the bonding to the antibonding \(\mathrm{MO}\) b. two separate \(\mathrm{H}\) atoms

In the first scenario, we have an \(\mathrm{H}_{2}\) molecule with enough energy added to excite one electron from the bonding molecular orbital to the antibonding molecular orbital. The bonding MO is formed by the constructive overlap of atomic orbitals, leading to an overall lower energy state and stabilization of the molecule. The antibonding MO is formed by destructive overlap of atomic orbitals, which leads to an overall higher energy state and destabilization of the molecule. When the electron is excited to the antibonding MO, it effectively cancels out the stabilization provided by the bonding MO and increases the overall energy of the molecule. This can make the molecule less stable and more reactive.

In the second scenario, we have two separate \(\mathrm{H}\) atoms. These atoms do not interact with each other, so there is no bonding or antibonding MO involved. Each hydrogen atom has one electron in its 1s atomic orbital, which is the ground state for hydrogen. In this state, the hydrogen atoms have relatively low energy and are stable.

Now that we have examined both scenarios, we can compare their energetic favorability. In the first scenario, the \(\mathrm{H}_{2}\) molecule with an excited electron has an increased energy level and decreased stability due to the presence of the electron in the antibonding MO. In the second scenario, the two separate \(\mathrm{H}\) atoms have lower energy levels and are stable in their ground state.

Based on the analysis above, we can conclude that the more energetically favorable scenario is: b. two separate \(\mathrm{H}\) atoms This is because they have lower energy levels and are stable in their ground state, whereas the \(\mathrm{H}_{2}\) molecule with the excited electron has a higher energy level and decreased stability due to the presence of the electron in the antibonding MO.