The total number of atomic orbitals in a principal energy level ($n$) is given by the formula $n^2$.

For the fourth energy level ($n=4$):

1. Formula: $n^2 = 4^2 = 16$.
2. Detailed Breakdown: The fourth shell consists of four subshells: $s, p, d,$ and $f$. $4s$: 1 orbital $4p$: 3 orbitals $4d$: 5 orbitals (Referenced in Unit 4, d-block elements) $4f$: 7 orbitals (Referenced in Unit 4, f-block elements)

• Total: $1 + 3 + 5 + 7 = 16$ orbitals.

Note: The maximum number of electrons would be $2n^2 = 32$.