What is the total number of orbitals present in the shell with the principal quantum number, n = 3

Explanation

For n = 3, the possible values of I are 0, 1 and 2. Thus there is one 3s orbital (n = 3, 1= 0 and `m_(l)` = 0), "there are three 3p orbitals (n = 3,1 = 1.and `m_(l)= -1, 0, +1` ), there are five 3d orbitals (n = 3,1 = 2 and `m_(l)= -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`.