What is meant by the highest occupied energy level in an atom?
It is the highest-energy atomic orbital in an atom that is filled with electrons. It is otherwise known as a valence orbital, or a frontier orbital (i.e. an orbital at the "frontier" of chemical reactions, performing the interesting legwork to move the reaction forward).
Ordering orbitals by energy is straightforward; energy is quantized, so the higher the principal quantum number
(Of course, that is a simplification that neglects the influence of the shape of the orbital on its energy, but for our purposes it is a good general rule.)
Suppose all the orbitals below are fully occupied. Can you identify the highest-occupied atomic orbitals here? (There are 3.)
Note that the