What is the total number of orbitals associated with the principal quantum number n = 2 ?

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 ml=0) , there are three 3p orbital (n = 3 , l=1 and `m_(l)=-1,0+1)` , there are five 3d orbitals (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`.