Final answer:
The total number of orbitals in a shell is given by n². Each principal shell consists of n subshells with varying numbers of orbitals determined by the secondary quantum number.
Step-by-step explanation:
The total number of orbitals in a shell with principal quantum number (n) is n². This is because each principal shell has n subshells, and each subshell has 2l + 1 orbitals, where l is the secondary (angular momentum) quantum number ranging from 0 to n-1.
For example, the first shell (n=1) has 12 which is 1 orbital, the second shell (n=2) has 22 which is 4 orbitals, and the third shell (n=3) has 32 which is 9 orbitals, and so on. Notably, the number of orbitals dictates where electrons are most likely to be found and is associated with the energy levels of an atom.