Final answer:
Within the 3rd principal energy level, there are three energy sublevels: 3s, 3p, and 3d. These correspond to different types of orbitals and the total number of orbitals sums up to nine.
Step-by-step explanation:
The student asked about the number of energy sublevels within the 3rd principal energy level. In the world of Chemistry, the 3rd principal energy level (also known as the n=3 shell) contains three different types of sublevels: the 3s, 3p, and 3d sublevels. We can determine this based on quantum mechanics, which tells us that for a principal quantum number n, the possible sublevels are determined by the azimuthal or angular momentum quantum number l, which can range from 0 to n-1. For n=3, l can be 0 (s sublevel), 1 (p sublevel), or 2 (d sublevel). Hence, there are three energy sublevels within the 3rd principal energy level.
Additionally, the total number of orbitals within the third principal energy level can be calculated using the equation for the maximum number of electrons that can be in a subshell, which is 2(2l + 1). Plugging in the values of l for the 3rd principal energy level, we find 1 s orbital, 3 p orbitals, and 5 d orbitals for a total of 9 orbitals.