What is the total number of orbitals associated with the principal quantum number n=3 ?

Explanation

For n = 3, the possible values of l are 0,1 and 2. Thus, there is one 3s orbital (n = 3, l = 0 and `m_l` = 0), there are three p orbitals (n = 3, l = 1 and ml = -1, 0, 1) there are five 3d orbitals (n = 3, l = 2, ml = -2, -1, 0, 1, 2).
Therefore, the total number of orbitals is 1+3+5 = 9.