The total theoretical number of individual degenerate atomic orbitals possible within the principal

Question

The total theoretical number of individual degenerate atomic orbitals possible within the principal energy level $n=4$ of an atom is

Professor PC Thomas Classes · Answer

(c) : The total number of orbitals present within a principal energy level designated by the quantum number '$n$' is rigorously given by the formula $n^2$. For the fourth principal shell ($n=4$), the total number of orbitals is $4^2 = 16$. These encompass one $4s$ orbital, three $4p$ orbitals, five $4d$ orbitals, and seven $4f$ orbitals ($1 + 3 + 5 + 7 = 16$).