Final answer:
The most stable energy level for an electron is the lowest possible energy level, often found in the n = 1 orbit for hydrogen atoms, and outer energy levels that are full according to the octet rule.
Step-by-step explanation:
The most stable energy level for an electron is the one where it has the lowest possible energy, which corresponds to the closest orbit to the nucleus according to the fundamental laws of physics. In a hydrogen atom, this is the n = 1 orbit. On a broader scale, atoms are most stable when their outermost energy level is full, which is exemplified by the noble gases that possess complete electron shells and adhere to the octet rule. In multi-electron atoms, electrons fill up the energy levels in an order determined by the Aufbau principle, starting from the lowest energy sublevel, such as 1s, and moving to higher ones, such as 2s and 2p.