what is the total number of orbitals associated with the principal quartum number n= 3?

Explanation

For n = 3, l = 0, 1, 2, i.e., there are three subshells designated as 3s, 3p and 3d
For 3s subshell, l = 0, `:.` m = 0 (i.e., one orbital), For 3p subshell, l = 1, `:.m = -1, 0 + 1` (i.e., 3 orbitals )
For 3d subshell l = 2, `m = -2, -1, 0 + 1, + 2` (i.e., 5 orbitals)
`:.` Total no. of orbitals present in the shell with n = 3 will be 1 + 3 + 5 = 9
Alternatively, no of orbitals presents in nth shell `= n^(2):.` No. of orbitals in the 3rd shell (n = 3) `= 3^(2) = 9`