Final answer:
To find the total number of orbitals at a given energy level, you multiply the principal quantum number squared, n^2. For example, the second energy level (n=2) would have 2^2 = 4 orbitals in total. This includes s and p suborbitals.
Step-by-step explanation:
To find the total number of orbitals using an energy level, one can use the principal quantum number, n. Each principal energy level above n=1 consists of different types of suborbitals: the s, p, d, and f.
For instance, the first energy level has only an s orbital, so there is a total of 1*2 = 1 orbital. At the second energy level (n=2), there are s and p orbitals. The s subshell always has 1 orbital, and the p subshell has 3 orbitals, making a total of 4 orbitals for n=2. Generally, the number of orbitals in an energy level is given by n2. So, for the third energy level (n=3), which includes s, p, and d orbitals, there would be a total of 32 = 9 orbitals.
It's important to note that within each type of subshell, orbitals may have the same energy, which is referred to as degeneracy. For example, all three p orbitals in a given energy level have the same energy and are thus degenerate.