In the context of quantum tunneling, when an atom "escapes" from a solid through tunneling, it typically refers to the atom moving from one region to another by passing through a potential barrier that it classically cannot overcome. The energy of the initial state and the final state can vary depending on the specific system and conditions.
In most cases, when an atom tunnels out of a solid, it will tunnel to a state that is equal or lower in energy than the initial state. This is because the tunneling process involves the atom overcoming a potential energy barrier. If the final state had a higher energy than the initial state, the atom would need to gain energy during the tunneling process, which is less probable.
However, it is important to note that quantum tunneling can be a complex phenomenon, and there can be exceptions or special cases where the final state has a higher energy. These cases might involve intricate energy landscapes or non-trivial interactions. Nevertheless, in typical scenarios, the atom would tunnel to a state of equal or lower energy than the initial state.