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

Explanation

for n=3 , the possible values of l are 0,1 and 2. thus there is one 3 s orbital ( n =3 ,l =0 and `m_(1) =0) : ` there are three 3p obitals `(n =3 l=1 and m_(1) =-1 , 0 , + 1 )` : there are five 3d obitrals ` ( n = 3 , l = 2` and `m_(1) =-2 ,-1 ,0 +1+, +2 )`
therefore the total number of orbitals is 1+3=5=9
the same value can also be obtained by using the relation: number of orbitals `= n_(2) , i.e 3^(2) =9`.