Final answer:
The statement in question is true; orbitals within a higher principal energy level are indeed higher in energy than those in the next lower energy level due to increased distance from the nucleus and the shielding effect.
Step-by-step explanation:
The statement that "The orbitals of a principal energy level are lower in energy than the orbitals in the next higher principal energy level" is true. In atomic structure, energy levels are denoted by the principal quantum number, n. Each principal energy level contains orbitals, and these orbitals are regions in space where there is a high probability of finding electrons. According to the Aufbau principle, electrons fill the lowest available energy orbitals first. Therefore, as the principal quantum number increases, implying a move to a higher principal energy level, the orbitals within that level also have higher energy compared to those in the lower principal energy level.
For example, the 1s orbital is the lowest in energy, followed by 2s, and so on. Due to the increasing distance from the nucleus and the effect of shielding, electrons in the higher principal energy levels experience a weaker attraction to the nucleus, resulting in these orbitals having higher energy. While there may be some overlap between energy sublevels of different principal energy levels, the overall trend is that orbitals in a higher principal energy level are higher in energy than those in the next lower energy level.
The phenomenon of electron arrangement and energy level overlapping is further illustrated when, for instance, the 4s sublevel is filled before the 3d, even though they are part of different principal energy levels. The general rule remains, however, that each consecutive principal energy level is higher in energy than the one before it.