Question

How many orbitals are described by each of the below combinations of quantum numbers? 

n= 3, l =0 

_______ orbitals 

n=4, l = 2, ml = 2 

_______ orbitals

Answer 1

Answer :

For principal quantum number n , no. of atomic orbitals possible are n^{​​​​​​2} .

e.g. for n= 3 , 9 atomic orbitals are possible  

3s contain 1 orbital

3p contain 3 orbitals

3d contain 5 orbitals . So, in n=3 , total 9 orbitals

(1) : no. of orbitals in n=3 , l = 0

Only 1 atomic orbital possible (3s) . Since l= 0 for s orbital

(2) : no. of orbitals in n= 4 , l = 2 , m= 2

n= 4 can have 16 orbitals

l=2 for d subshell

n= 4 , l= 2 can have 5 orbitals (4d)

n= 4 , l=2 , m=2 have only 1 orbital (4d_x²-y²)